{"id":16185,"date":"2017-12-11T17:10:37","date_gmt":"2017-12-11T17:10:37","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=16185"},"modified":"2022-11-04T08:54:21","modified_gmt":"2022-11-04T08:54:21","slug":"thermodynamic-properties","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/","title":{"rendered":"Thermodynamic Properties"},"content":{"rendered":"<p><span data-preserver-spaces=\"true\">Within thermodynamics, physical property is any measurable property and whose value describes a state of a physical system. Our goal here will be to introduce\u00a0<\/span><strong><span data-preserver-spaces=\"true\">thermodynamic properties that are used in engineering thermodynamics<\/span><\/strong><span data-preserver-spaces=\"true\">. These properties will be further applied to energy systems and finally to\u00a0<\/span><strong><span data-preserver-spaces=\"true\">thermal<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0or\u00a0<\/span><strong><span data-preserver-spaces=\"true\">nuclear power plants<\/span><\/strong><span data-preserver-spaces=\"true\">.<\/span><\/p>\n<figure id=\"attachment_16538\" aria-describedby=\"caption-attachment-16538\" style=\"width: 324px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Extensive-vs.-Intensive-properties-min.png\"><img loading=\"lazy\" class=\"size-full wp-image-16538\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Extensive-vs.-Intensive-properties-min.png\" alt=\"Extensive vs. intensive thermodynamic properties\" width=\"334\" height=\"421\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Extensive-vs.-Intensive-properties-min.png 334w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Extensive-vs.-Intensive-properties-min-238x300.png 238w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/a><figcaption id=\"caption-attachment-16538\" class=\"wp-caption-text\">Extensive and intensive properties of the medium in the pressurizer.<\/figcaption><\/figure>\n<p>In general, <strong>thermodynamic properties<\/strong> can be divided into two general classes:<\/p>\n<ul>\n<li><strong><a title=\"Extensive and Intensive Properties\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/extensive-and-intensive-properties\/\">Extensive properties<\/a>:<\/strong> An <strong>extensive property<\/strong> depends on the <strong>amount of mass<\/strong> present or upon the <strong>size or extent of a system<\/strong>. For example, the following properties are extensive:\n<ul>\n<li><a title=\"What is Enthalpy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/\">Enthalpy<\/a><\/li>\n<li><a title=\"What is Entropy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/\">Entropy<\/a><\/li>\n<li><a title=\"Gibbs Free Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/gibbs-free-energy\/\">Gibbs Free Energy<\/a><\/li>\n<li><a title=\"Heat Capacity \u2013 Specific Heat Capacity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\">Heat Capacity<\/a><\/li>\n<li><a title=\"Internal Energy \u2013 Thermal Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\">Internal Energy<\/a><\/li>\n<li><a title=\"What is Mass and Weight\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-mass-and-weight\/\">Mass<\/a><\/li>\n<li><a title=\"What is Volume \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-volume-physics\/\">Volume<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li><strong><a title=\"Extensive and Intensive Properties\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/extensive-and-intensive-properties\/\">Intensive property<\/a>:<\/strong> An<strong> intensive property<\/strong> is <strong>independent of the amount<\/strong> of mass and may vary from place to place within the system at any moment.\u00a0For example, the following properties are extensive:\n<ul>\n<li>Compressibility<\/li>\n<li><a title=\"What is Density \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-density-physics\/\">Density<\/a><\/li>\n<li><a title=\"Specific Enthalpy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/specific-enthalpy\/\">Specific Enthalpy<\/a><\/li>\n<li><a title=\"Specific Entropy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/specific-entropy\/\">Specific Entropy<\/a><\/li>\n<li><a title=\"Heat Capacity \u2013 Specific Heat Capacity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\">Specific Heat Capacity<\/a><\/li>\n<li><a title=\"What is Pressure \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\">Pressure<\/a><\/li>\n<li><a title=\"What is Temperature \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/\">Temperature<\/a><\/li>\n<li>Thermal Conductivity<\/li>\n<li>Thermal Expansion<\/li>\n<li><a title=\"Vapor Quality \u2013 Dryness Fraction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/vapor-quality-dryness-fraction\/\">Vapor Quality<\/a><\/li>\n<li><a title=\"What is Specific Volume\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-specific-volume\/\">Specific Volume<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Specific Properties<\/h2>\n<p><strong><span data-preserver-spaces=\"true\">Specific properties<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0of a material\u00a0<\/span><strong><span data-preserver-spaces=\"true\">are<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0<\/span><strong><span data-preserver-spaces=\"true\">derived<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0from other intensive and extensive properties of that material. For example, the\u00a0<\/span><strong><span data-preserver-spaces=\"true\">density<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0of water is an intensive property. It can be derived from measurements of the mass of a water volume (an extensive property) divided by the volume (another extensive property). Also,\u00a0<\/span><strong><span data-preserver-spaces=\"true\">heat capacity<\/span><\/strong><span data-preserver-spaces=\"true\">, an extensive property of a system, can be derived from <\/span><strong><span data-preserver-spaces=\"true\">heat capacity<\/span><\/strong><span data-preserver-spaces=\"true\">,\u00a0<\/span><strong><em><span data-preserver-spaces=\"true\">Cp<\/span><\/em><\/strong><span data-preserver-spaces=\"true\">, and the\u00a0<\/span><strong><span data-preserver-spaces=\"true\">system\u2019s mass<\/span><\/strong><span data-preserver-spaces=\"true\">. Dividing these extensive properties gives the\u00a0<\/span><strong><span data-preserver-spaces=\"true\">specific heat capacity<\/span><\/strong><span data-preserver-spaces=\"true\">,\u00a0<\/span><strong><em><span data-preserver-spaces=\"true\">cp<\/span><\/em><\/strong><span data-preserver-spaces=\"true\">, which is an\u00a0<\/span><strong><span data-preserver-spaces=\"true\">intensive property<\/span><\/strong><span data-preserver-spaces=\"true\">.<\/span><\/p>\n<p><span data-preserver-spaces=\"true\">Specific properties are often used in reference tables to record material data in a manner independent of size or mass. They are\u00a0<\/span><strong><span data-preserver-spaces=\"true\">very useful for comparing<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0one attribute while canceling out the effect of variations in another attribute.<\/span><\/p>\n<figure id=\"attachment_16029\" aria-describedby=\"caption-attachment-16029\" style=\"width: 698px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Table-of-specific-properties-thermodynamics.png\"><img loading=\"lazy\" class=\"size-full wp-image-16029\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Table-of-specific-properties-thermodynamics.png\" alt=\"Specific properties - thermodynamics\" width=\"708\" height=\"306\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Table-of-specific-properties-thermodynamics.png 708w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Table-of-specific-properties-thermodynamics-300x130.png 300w\" sizes=\"(max-width: 708px) 100vw, 708px\" \/><\/a><figcaption id=\"caption-attachment-16029\" class=\"wp-caption-text\">Table of some specific properties<\/figcaption><\/figure>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Mass vs. Weight<\/h2>\n<p><span data-preserver-spaces=\"true\">One of the most familiar forces is the\u00a0<\/span><strong><span data-preserver-spaces=\"true\">body\u2019s weight<\/span><\/strong><span data-preserver-spaces=\"true\">, the\u00a0<\/span><strong><span data-preserver-spaces=\"true\">gravitational force<\/span><\/strong><span data-preserver-spaces=\"true\"> that the Earth exerts on the body. In general, gravitation is a natural phenomenon by which all things with\u00a0<\/span><strong><span data-preserver-spaces=\"true\">mass<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0are brought toward one another. The terms\u00a0<\/span><strong><span data-preserver-spaces=\"true\">mass and weight<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0are often confused, but it is important to<\/span><strong><span data-preserver-spaces=\"true\">\u00a0distinguish between them<\/span><\/strong><span data-preserver-spaces=\"true\">. It is essential to understand clearly the distinctions between these two physical quantities.<\/span><\/p>\n<p><span data-preserver-spaces=\"true\"><div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What is Mass<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">The<\/span><strong><span data-preserver-spaces=\"true\">\u00a0mass<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0of an object is a fundamental property of the object. It is a numerical measure of its\u00a0<\/span><strong><span data-preserver-spaces=\"true\">inertia\u00a0<\/span><\/strong><span data-preserver-spaces=\"true\">and an object\u2019s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in <\/span><strong><span data-preserver-spaces=\"true\">Newton\u2019s second law <\/span><\/strong><span data-preserver-spaces=\"true\">(F=ma).<\/span><\/p>\n<p><span data-preserver-spaces=\"true\">The\u00a0<\/span><strong><span data-preserver-spaces=\"true\">mass<\/span><\/strong><span data-preserver-spaces=\"true\"> of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on Earth, an object has a<\/span><strong><span data-preserver-spaces=\"true\">\u00a0certain mass<\/span><\/strong><span data-preserver-spaces=\"true\">\u00a0and a\u00a0<\/span><strong><span data-preserver-spaces=\"true\">certain weight<\/span><\/strong><span data-preserver-spaces=\"true\">. When the same object is placed in outer space, away from the Earth\u2019s gravitational field, its mass remains the same, but it is now in a \u201cweightless\u201d condition. This means in this condition. It will weigh zero because of gravitational acceleration and, thus, the force will equal to zero.<\/span><\/p>\n<p><strong><span data-preserver-spaces=\"true\">Mass and weight are related<\/span><\/strong><span data-preserver-spaces=\"true\">: Bodies having a large mass also have a large weight. A large stone is hard to throw because of its large mass and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone with an acceleration of magnitude g (g = 9.81 m\/s2 is the acceleration due to Earth\u2019s gravitational field). Newton\u2019s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:<\/span><\/p>\n<p><em>F = ma = 1 [kg] x 9.81 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 N<\/em><\/p>\n<p>The force that makes the body accelerate downward is its weight. Anybody near the surface of the Earth with a mass of 1 kg must weigh 9.8 N to give it the acceleration we observe when it is in free fall.<\/p>\n<p><strong>Example: The weight of a stone on the Earth, on Mars, and the Moon <\/strong><\/p>\n<p><strong>Weight of a stone on the Earth<\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-16255\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min-191x300.png\" alt=\"gravitational-field-earth-mars-moon\" width=\"191\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min-191x300.png 191w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min.png 348w\" sizes=\"(max-width: 191px) 100vw, 191px\" \/><\/a>The acceleration due to Earth&#8217;s gravitational field is <em>g<\/em><em><sub>Earth<\/sub><\/em> = 9.81 m\/s<sup>2<\/sup>.The weight of a stone with mass <em>1 kg<\/em> on the Earth can be calculated as:<\/p>\n<p><em>F<\/em><em><sub>Earth<\/sub><\/em><em> = 1 [kg] x 9.81 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 N<\/em><\/p>\n<p><strong>Weight of a stone on the Mars<\/strong><\/p>\n<p>The acceleration of gravity on Mars is approximately <em>38%<\/em> of the acceleration of gravity on the Earth. The acceleration due to Moon\u2019s gravitational field is <em>g<\/em><em><sub>Mars<\/sub><\/em> = 3.71 m\/s<sup>2<\/sup>.<\/p>\n<p>Therefore the weight of the same stone with mass <em>1 kg<\/em> on the Mars is:<\/p>\n<p><em>F<\/em><em><sub>Moon<\/sub><\/em><em> = 1 [kg] x 3.71 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 3.71 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 3.71 N<\/em><\/p>\n<p><strong>Weight of a stone on the Moon<\/strong><\/p>\n<p>The acceleration of gravity on the Moon is approximately <em>1\/6<\/em> of the acceleration of gravity on the Earth. The acceleration due to Moon\u2019s gravitational field is <em>g<\/em><em><sub>Moon<\/sub><\/em> = 1.62 m\/s<sup>2<\/sup>.<\/p>\n<p>Therefore the weight of the same stone with mass <em>1 kg<\/em> on the Moon is:<\/p>\n<p><em>F<\/em><em><sub>Moon<\/sub><\/em><em> = 1 [kg] x 1.62 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 1.62 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 1.62 N<\/em><\/p>\n<p><strong>The Standard Kilogram<\/strong><\/p>\n<p>The usual symbol for mass is m, and its SI unit is the <strong>kilogram<\/strong>. The SI standard of mass is a cylinder of platinum and iridium kept at the International Bureau of Weights and Measures near Paris and assigned, by international agreement, a mass of 1 kilogram.<\/p>\n<figure id=\"attachment_16253\" aria-describedby=\"caption-attachment-16253\" style=\"width: 590px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/standard-kilogram-min.png\"><img loading=\"lazy\" class=\"size-full wp-image-16253\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/standard-kilogram-min.png\" alt=\"Standard Kilogram\" width=\"600\" height=\"437\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/standard-kilogram-min.png 600w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/standard-kilogram-min-300x219.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/standard-kilogram-min-220x161.png 220w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/a><figcaption id=\"caption-attachment-16253\" class=\"wp-caption-text\">A computer-generated image of the International Prototype kilogram (IPK), which is made from an alloy of 90% platinum and 10% iridium (by weight) and machined into a right-circular cylinder (height = diameter) of 39.17 mm. Source: wikipedia.org; License: CC BY-SA<\/figcaption><\/figure>\n<p><strong>Toggle: Relativistic Mass<\/strong><\/p>\n<p>While the mass is normally considered an unchanging property of an object at speeds approaching the <strong>speed of light,<\/strong> one must consider the increase in the <strong>relativistic mass<\/strong>. The relativistic definition of <strong>momentum<\/strong> is sometimes interpreted as an increase in the mass of an object. In this interpretation, a particle can have a relativistic mass, <strong>m<sub>rel<\/sub><\/strong>. The increase in effective mass with speed is given by the expression:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/relativistic-mass.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16257\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/relativistic-mass.png\" alt=\"relativistic-mass-min\" width=\"288\" height=\"294\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/relativistic-mass.png 288w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/relativistic-mass-66x66.png 66w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><\/a><\/p>\n<p>In this \u201cmass-increase\u201d formula, m is referred to as the rest mass of the object. It follows from this formula that an object with a nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object\u2019s <strong>momentum increase<\/strong> without bound. On the other hand, when the relative velocity is zero, the Lorentz factor is simply equal to 1, and the relativistic mass is reduced to the rest mass. With this interpretation, the <strong>mass<\/strong> of an object <strong>appears to increase<\/strong> as its speed increases. It must be added, many physicists believe an object has only one mass (its rest mass) and that it is only the momentum that increases with speed.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What is Mass Defect<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">See also: <a title=\"Mass Defect\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/nuclear-energy\/mass-defect\/\">Mass Defect<\/a><\/p>\n<p>In the special theory of relativity, certain types of matter may be created or destroyed. Still, the mass and energy associated with such matter remain unchanged in quantity in all of these processes. It was found the rest mass of an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a>,\u00a0and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the\u00a0<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/binding-energy\/nuclear-binding-energy\/\">nuclear binding energy\u00a0<\/a>which holds the nucleus together. According to the Einstein relationship (<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/nuclear-energy\/emc2-meaning\/\">E=mc<sup>2<\/sup><\/a>), this binding energy is proportional to this mass difference, known as the mass defect.<\/div><\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What is Weight<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">The terms are often confused with one another, but it is important to distinguish between them. In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. In general, gravitation is a natural phenomenon by which all things with mass are brought toward one another.<\/p>\n<p>The<strong> mass<\/strong> of an object is a fundamental property of the object. It is a numerical measure of its <strong>inertia <\/strong>and the measure of an object\u2019s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in <strong>Newton\u2019s second law <\/strong>(F=ma).<\/p>\n<p>The <strong>mass<\/strong> of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on Earth, an object has a<strong> certain mass<\/strong> and a <strong>certain weight<\/strong>. When the same object is placed in outer space, away from the Earth\u2019s gravitational field, its mass remains the same, but it is now in a \u201cweightless\u201d condition. This means in this condition, and it will weigh zero because of gravitational acceleration and, thus, the force will equal zero.<\/p>\n<p><strong>Mass and weight are related<\/strong>:<\/p>\n<p>Bodies having large masses also have a large weight. A large stone is hard to throw because of its large mass and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone with an acceleration of magnitude g (g = 9.81 m\/s<sup>2<\/sup> is the acceleration due to Earth\u2019s gravitational field). Newton\u2019s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:<\/p>\n<p><em>F = ma = 1 [kg] x 9.81 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 N<\/em><\/p>\n<p>The force that makes the body accelerate downward is its weight. Anybody near the surface of the Earth with a mass of 1 kg must weigh 9.8 N to give it the acceleration we observe when it is in free fall.<\/p>\n<p><strong>Example: The weight of a stone on the Earth, on Mars, and the Moon <\/strong><\/p>\n<p><strong>Weight of a stone on the Earth<\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-16255\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min-191x300.png\" alt=\"gravitational-field-earth-mars-moon\" width=\"191\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min-191x300.png 191w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/gravitational-field-Earth-Mars-Moon-min.png 348w\" sizes=\"(max-width: 191px) 100vw, 191px\" \/><\/a>The acceleration due to Earth&#8217;s gravitational field is <em>g<\/em><em><sub>Earth<\/sub><\/em> = 9.81 m\/s<sup>2<\/sup>.The weight of a stone with mass <em>1 kg<\/em> on the Earth can be calculated as:<\/p>\n<p><em>F<\/em><em><sub>Earth<\/sub><\/em><em> = 1 [kg] x 9.81 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 9.8 N<\/em><\/p>\n<p><strong>Weight of a stone on the Mars<\/strong><\/p>\n<p>The acceleration of gravity on Mars is approximately <em>38%<\/em> of the acceleration of gravity on the Earth. The acceleration due to Moon\u2019s gravitational field is <em>g<\/em><em><sub>Mars<\/sub><\/em> = 3.71 m\/s<sup>2<\/sup>.<\/p>\n<p>Therefore the weight of the same stone with mass <em>1 kg<\/em> on the Mars is:<\/p>\n<p><em>F<\/em><em><sub>Moon<\/sub><\/em><em> = 1 [kg] x 3.71 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 3.71 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 3.71 N<\/em><\/p>\n<p><strong>Weight of a stone on the Moon<\/strong><\/p>\n<p>The acceleration of gravity on the Moon is approximately <em>1\/6<\/em> of the acceleration of gravity on the Earth. The acceleration due to Moon\u2019s gravitational field is <em>g<\/em><em><sub>Moon<\/sub><\/em> = 1.62 m\/s<sup>2<\/sup>.<\/p>\n<p>Therefore the weight of the same stone with mass <em>1 kg<\/em> on the Moon is:<\/p>\n<p><em>F<\/em><em><sub>Moon<\/sub><\/em><em> = 1 [kg] x 1.62 [m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 1.62 [kg m\/s<\/em><em><sup>2<\/sup><\/em><em>] = 1.62 N<\/em><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Artificial Gravity<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In the 20th century, <strong>Einstein&#8217;s principle of equivalence<\/strong> put all observers, moving or accelerating, on the same footing. Einstein summarised this notion in a postulate:<\/p>\n<p><strong>Principle of Equivalence:<\/strong><\/p>\n<p><em>An observer cannot determine, in any way whatsoever, whether the laboratory he occupies is in a uniform gravitational field or is in a reference frame that is accelerating relative to an inertial frame.<\/em><\/p>\n<p>This led to an ambiguity as to what exactly is meant by the <strong>force of gravity<\/strong> and <strong>weight<\/strong>. A scale in an accelerating elevator cannot be distinguished from a scale in a gravitational field. \u00a0Gravitational force and weight thereby became essentially frame-dependent quantities. According to the general theory of relativity, gravitational and inertial mass are not different properties of matter but two aspects of matter\u2019s fundamental and single property.<\/p>\n<figure id=\"attachment_16260\" aria-describedby=\"caption-attachment-16260\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Artificial-Gravity.gif\"><img loading=\"lazy\" class=\"size-full wp-image-16260\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Artificial-Gravity.gif\" alt=\"Artificial Gravity\" width=\"300\" height=\"300\" \/><\/a><figcaption id=\"caption-attachment-16260\" class=\"wp-caption-text\">An animation of a 50-meter diameter rotating space station. Source: wikipedia.org (P.Fraundorf) License: CC BY-SA 4.0<\/figcaption><\/figure>\n<p>In situations in which gravitation is absent, but the chosen coordinate system is not inertial. Still, it is accelerated with the observer, then g-forces and corresponding proper accelerations felt by observers in these coordinate systems are caused by the mechanical forces which resist their weight in such systems. The most realistic method of producing artificial gravity, for example, aboard a space station, can be imitated in a rotating spaceship. Objects inside would be pushed toward the hull, and they will have some weight. This weight is produced by fictitious forces or \u201c<strong>inertial forces,<\/strong>\u201d which appear in all such accelerated coordinate systems. Unlike real gravity, which pulls towards the planet\u2019s center, the centripetal force pushes towards the axis of rotation.<\/div><\/div><\/div>\n<h2>What is Volume<\/h2>\n<p><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/what-is-volume-min.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-16483\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/what-is-volume-min-300x300.png\" alt=\"what is volume - physics\" width=\"300\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/what-is-volume-min-300x300.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/what-is-volume-min-150x150.png 150w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/what-is-volume-min-66x66.png 66w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/what-is-volume-min.png 1000w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>Volume<\/strong> is a basic <strong>physical quantity<\/strong>. <strong>Volume<\/strong> is a derived quantity, and it expresses the <strong>three-dimensional\u00a0extent<\/strong> of an <strong>object<\/strong>. Volume is often quantified numerically using the SI-derived unit, the <strong>cubic meter<\/strong>. For example, the volume inside a <strong>sphere<\/strong> (that is, the volume of a ball) is derived from being<strong> V = 4\/3\u03c0r<sup>3<\/sup><\/strong>, where r is the sphere\u2019s radius. As another example, the volume of a cube is equal to side times side. Since each side of a square is the same, it can simply be the length of one side <strong>cubed<\/strong>.<\/p>\n<p>If a square has one side of 3 meters, the volume would be 3 meters times 3 meters times 3 meters, or 27 cubic meters.<\/p>\n<p>See also: <a title=\"Volume of Coolant in Reactor Coolant System\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/volume-reactor-coolant-system\/\">Volume of Coolant in Reactor Coolant System<\/a><\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Volume of an Atom and Nucleus<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_11250\" aria-describedby=\"caption-attachment-11250\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/12\/Structure-of-Matter.jpg\"><img loading=\"lazy\" class=\"size-medium wp-image-11250\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/12\/Structure-of-Matter-300x132.jpg\" alt=\"Structure of Matter.\" width=\"300\" height=\"132\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/12\/Structure-of-Matter-300x132.jpg 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/12\/Structure-of-Matter.jpg 1006w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-11250\" class=\"wp-caption-text\">Structure of Matter.<\/figcaption><\/figure>\n<p><strong>The atom<\/strong> consists of a small but massive <strong>nucleus<\/strong> surrounded by a cloud of rapidly moving <strong>electrons<\/strong>. The nucleus is composed of <strong>protons and <\/strong><a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\"><strong>neutrons<\/strong><\/a>. Typical nuclear radii are of the order 10<sup>\u221214<\/sup> m. Nuclear radii can be calculated according to the following formula assuming spherical shape:<\/p>\n<p>r = r<sub>0<\/sub> . A<sup>1\/3<\/sup><\/p>\n<p>where r<sub>0<\/sub> = 1.2 x 10<sup>-15 <\/sup>m = 1.2 fm<\/p>\n<p>If we use this approximation, we, therefore, expect the volume of the nucleus to be of the order of 4\/3\u03c0r<sup>3<\/sup> or 7,23 \u00d710<sup>\u221245 <\/sup>m<sup>3<\/sup> for hydrogen nuclei or 1721\u00d710<sup>\u221245<\/sup> m<sup>3<\/sup> for <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a> nuclei. These are nuclei volumes, and atomic nuclei (protons and neutrons) contain about <strong>99.95%<\/strong> of the atom\u2019s mass.<\/p>\n<p>See also: <a title=\"Volume of an Atom and Nucleus\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/atomic-nuclear-structure\/volume-atom-nucleus\/\">Is an atom an empty space?<\/a><\/div><\/div><\/div>\n<h2>What is Density<\/h2>\n<figure id=\"attachment_16264\" aria-describedby=\"caption-attachment-16264\" style=\"width: 231px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-Gas-Liquid-Solid-min.png\"><img loading=\"lazy\" class=\"wp-image-16264 size-medium\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-Gas-Liquid-Solid-min-241x300.png\" alt=\"Density - Gas - Liquid - Solid\" width=\"241\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-Gas-Liquid-Solid-min-241x300.png 241w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-Gas-Liquid-Solid-min.png 372w\" sizes=\"(max-width: 241px) 100vw, 241px\" \/><\/a><figcaption id=\"caption-attachment-16264\" class=\"wp-caption-text\">Typical densities of various substances at atmospheric pressure.<\/figcaption><\/figure>\n<p><strong>Density<\/strong> is defined as the <strong>mass per unit volume<\/strong>. It is an <a title=\"Extensive and Intensive Properties\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/extensive-and-intensive-properties\/\"><strong>intensive property<\/strong><\/a>, which is mathematically defined as mass divided by volume:<\/p>\n<p><strong>\u03c1 = m\/V<\/strong><\/p>\n<p>In other words, the density (\u03c1) of a substance is the total mass (m) of that substance divided by the total volume (V) occupied by that substance. The standard SI unit is <strong>kilograms per cubic meter<\/strong> (<strong>kg\/m<sup>3<\/sup><\/strong>). The Standard English unit is <strong>pounds mass per cubic foot<\/strong> (<strong>lbm\/ft<sup>3<\/sup><\/strong>). The density (\u03c1) of a substance is the reciprocal of its<strong> specific volume<\/strong> (\u03bd).<\/p>\n<p><strong>\u03c1 = m\/V = 1\/\u03c1<\/strong><\/p>\n<p><strong>Specific volume<\/strong> is an<strong> intensive variable<\/strong>, whereas volume is an extensive variable. The SI system\u2019s standard unit for specific volumes is cubic meters per kilogram (m<sup>3<\/sup>\/kg). The standard unit in the English system is cubic feet per pound-mass (ft<sup>3<\/sup>\/lbm).<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Changes of Density<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, <strong>density<\/strong> can be <strong>changed<\/strong> by changing either the <strong>pressure<\/strong> or the <strong>temperature<\/strong>. Increasing the <strong>pressure always increases<\/strong> the <strong>density<\/strong> of a material. The effect of pressure on the densities of <strong>liquids<\/strong> and <strong>solids<\/strong> is very, very small. On the other hand, the density of gases is strongly affected by pressure. This is expressed by <strong>compressibility<\/strong>. <strong>Compressibility<\/strong> measures the relative volume change of a fluid or solid as a response to a pressure change.<\/p>\n<p>The <strong>effect of temperature<\/strong> on the densities of liquids and solids is also very important. Most substances <strong>expand when heated<\/strong> and <strong>contract when cooled<\/strong>. However, the amount of expansion or contraction varies, depending on the material. This phenomenon is known as <strong>thermal expansion<\/strong>. The change in volume of a material that undergoes a temperature change is given by the following relation:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/thermal-expansion.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16267\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/thermal-expansion.png\" alt=\"thermal-expansion\" width=\"130\" height=\"62\" \/><\/a><\/p>\n<p>where \u2206T is the temperature change, V is the original volume, \u2206V is the volume change, and <strong>\u03b1<sub>V<\/sub><\/strong> is the<strong> coefficient of volume expansion<\/strong>.<\/p>\n<p>It must be noted and there are exceptions to this rule. For example, <strong>water<\/strong> differs from most liquids in that it becomes <strong>less dense as it freezes<\/strong>. It has a maximum density of 3.98 \u00b0C (1000 kg\/m<sup>3<\/sup>), whereas the density of ice is 917 kg\/m<sup>3<\/sup>. It differs by about 9% and therefore<strong> ice floats<\/strong> on liquid water<\/div><\/div><\/div>\n<p>See also: <a title=\"Moderator Temperature Coefficient \u2013 MTC\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/moderator-temperature-coefficient-mtc\/\">How density influences reactor reactivity<\/a>.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Densest Materials on the Earth<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Since <strong>nucleons<\/strong> (<strong>protons<\/strong> and <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\"><strong>neutrons<\/strong><\/a>) make up most of the mass of ordinary atoms, the density of normal matter tends to be limited by how closely we can pack these nucleons and depends on the internal atomic structure of a substance. The <strong>densest material<\/strong> found on Earth is the <strong>metal osmium. <\/strong>Still, its\u00a0density pales by comparison to the densities of exotic astronomical objects such as white<strong> dwarf stars<\/strong> and <strong>neutron stars<\/strong>.<\/p>\n<p><strong>List of densest materials:<\/strong><\/p>\n<ol>\n<li>Osmium &#8211; 22.6 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Iridium &#8211; 22.4 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Platinum &#8211; 21.5 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Rhenium &#8211; 21.0 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Plutonium &#8211; 19.8 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Gold &#8211; 19.3 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Tungsten &#8211; 19.3 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Uranium &#8211; 18.8 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Tantalum &#8211; 16.6 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Mercury &#8211; 13.6 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Rhodium &#8211; 12.4 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Thorium &#8211; 11.7 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Lead &#8211; 11.3 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Silver &#8211; 10.5 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<\/ol>\n<p>It must be noted, plutonium is a manufactured isotope and is created from <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/\">uranium<\/a> in <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/what-is-nuclear-reactor\/\">nuclear reactors<\/a>. But scientists have found trace amounts of naturally-occurring plutonium.<\/p>\n<p>If we include manufactured elements, the densest so far is<strong> Hassium<\/strong>. <strong>Hassium<\/strong> is a chemical element with the symbol <strong>Hs<\/strong> and atomic number 108. \u00a0It is a synthetic element (first synthesized at Hasse in Germany) and radioactive. The most stable known isotope, <strong><sup>269<\/sup>Hs<\/strong>, has a half-life of approximately 9.7 seconds. It has an estimated density of<strong> 40.7 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/strong>. \u00a0The density of Hassium results from its <strong>high atomic weight<\/strong> and the significant decrease in <strong>ionic radii<\/strong> of the elements in the lanthanide series, known as <strong>lanthanide and actinide contraction<\/strong>.<\/p>\n<p>The density of Hassium is followed by <strong>Meitnerium<\/strong> (element 109, named after the physicist Lise Meitner), which has an estimated density of<strong> 37.4 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/strong>.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Density of Water - Specific Volume<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-of-Water-Specific-Volume-of-Water.png\"><img loading=\"lazy\" class=\"alignright wp-image-16268\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-of-Water-Specific-Volume-of-Water.png\" alt=\"Density of Water - Specific Volume\" width=\"601\" height=\"466\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-of-Water-Specific-Volume-of-Water.png 928w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Density-of-Water-Specific-Volume-of-Water-300x233.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/a>Pure water has its highest density <strong><em>1000 kg\/m<\/em><em><sup>3<\/sup><\/em><\/strong> at temperature <strong><em>3.98<\/em><em><sup>o<\/sup><\/em><\/strong><em><strong>C<\/strong> (39.2<\/em><em><sup>o<\/sup><\/em><em>F). <\/em>Water differs from most liquids in that it becomes <strong>less dense as it freezes<\/strong>. It has a maximum density of 3.98 \u00b0C (1000 kg\/m<sup>3<\/sup>), whereas the density of ice is 917 kg\/m<sup>3<\/sup>. It differs by about 9%, and therefore<strong> ice floats<\/strong> on liquid water. It must be noted, the change in density is not linear with temperature because the volumetric thermal expansion coefficient for water is not constant over the temperature range. The density of water (1 gram per cubic centimeter) was originally used to define the gram. The density (\u2374) of a substance is the reciprocal of its specific volume ().<\/p>\n<p>\u03c1 = m\/V = 1\/<\/p>\n<p>The specific volume () of a substance is the total volume (V) of that substance divided by the total mass (m) of that substance (volume per unit mass). It has units of cubic meters per kilogram (m<sup>3<\/sup>\/kg).<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Density of Heavy Water<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Pure<strong> heavy water<\/strong> (D<sub>2<\/sub>O) has a density about <strong>11% greater than water<\/strong>\u00a0but is otherwise physically and chemically similar.<\/p>\n<p>This difference is caused by the fact and the <strong>deuterium<\/strong> nucleus is<strong> twice as heavy as the hydrogen<\/strong> nucleus. Since about 89% of the molecular weight of water comes from the single oxygen atom rather than the two hydrogen atoms, the weight of a heavy water molecule is not substantially different from that of a normal water molecule. The molar mass of water is M(H<sub>2<\/sub>O) = 18.02, and the molar mass of heavy water is M(D<sub>2<\/sub>O) = 20.03 (each deuterium nucleus contains one neutron in contrast to the hydrogen nucleus). Therefore heavy water (D<sub>2<\/sub>O) has a density about 11% greater (20.03\/18.03 = 1.112).<\/p>\n<p>Pure <strong>heavy water<\/strong> (D<sub>2<\/sub>O) has its<strong> highest density of <em>1106 kg\/m<\/em><em><sup>3<\/sup><\/em><\/strong> at a temperature of <strong><em>11.6<\/em><em><sup>o<\/sup><\/em><\/strong><em><strong>C<\/strong> (52.9<\/em><em><sup>o<\/sup><\/em><em>F). <\/em>Also, heavy water differs from most liquids in that it becomes <strong>less dense as it freezes<\/strong>. It has a maximum density of <strong><em>11.6<\/em><em><sup>o<\/sup><\/em><\/strong><em><strong>C<\/strong><\/em> (1106 kg\/m<sup>3<\/sup>), whereas its solid form ice density is 1017 kg\/m<sup>3<\/sup>. It must be noted, the change in density is not linear with temperature because the volumetric thermal expansion coefficient for water is not constant over the temperature range.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Density of Steam<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/steam-properties-enthaply-density-volume-specific-heat-temperature.png\"><img loading=\"lazy\" class=\"alignright size-large wp-image-16049\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/steam-properties-enthaply-density-volume-specific-heat-temperature-1024x618.png\" alt=\"steam properties - steam tables\" width=\"669\" height=\"404\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/steam-properties-enthaply-density-volume-specific-heat-temperature-1024x618.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/steam-properties-enthaply-density-volume-specific-heat-temperature-300x181.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/steam-properties-enthaply-density-volume-specific-heat-temperature.png 1405w\" sizes=\"(max-width: 669px) 100vw, 669px\" \/><\/a>Water and steam are a common medium because their properties are very <strong>well known<\/strong>. Their properties are tabulated in so-called <strong>\u201c<\/strong><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\"><strong>Steam Tables<\/strong><\/a><strong>\u201d<\/strong>. In these tables, the basic and key properties, such as pressure, temperature, enthalpy, <strong>density,<\/strong> and specific heat, are tabulated along the vapor-liquid saturation curve as a function of both temperature and pressure.<\/p>\n<p>The density (\u2374) of any substance is the reciprocal of its specific volume ().<\/p>\n<p>\u03c1 = m\/V = 1\/<\/p>\n<p>The specific volume () of a substance is the total volume (V) of that substance divided by the total mass (m) of that substance (volume per unit mass). It has units of cubic meters per kilogram (m<sup>3<\/sup>\/kg).<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Density of Steel<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">The density of steel varies based on the alloying constituents but usually ranges between 7.5 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup> and 8 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup>.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Density of Zirconium<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, zirconium has very low <a title=\"Neutron Absorption Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/neutron-absorption-cross-section\/\">absorption cross-section<\/a> of thermal neutrons, high hardness, ductility and corrosion resistance. One of the main uses of zirconium alloys is nuclear technology, as cladding of fuel rods in nuclear reactors, due to its very low <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/neutron-absorption-cross-section\/\">absorption cross-section<\/a> (unlike the stainless steel). The density of typical zirconium alloy is about 6.6 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup>.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Density of Uranium<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a title=\"Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/\"><strong>Uranium<\/strong><\/a> is a naturally-occurring chemical element with atomic number 92, which means there are 92 protons and 92 electrons in the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/atomic-nuclear-structure\/\">atomic structure<\/a>. <a title=\"Natural Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/natural-uranium\/\"><strong>Natural uranium<\/strong><\/a> consists primarily of isotope <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a> (99.28%). Therefore the atomic mass of the uranium element is close to the atomic mass of the <sup>238<\/sup>U isotope (238.03u). \u00a0Natural uranium also consists of two other isotopes: <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a> (0.71%) and <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-234\/\"><sup>234<\/sup>U<\/a> (0.0054%). Uranium has the highest atomic weight of the primordially occurring elements. Uranium metal has a very high density of <strong>19.1 g\/cm<sup>3<\/sup><\/strong>, denser than lead (11.3 g\/cm<sup>3<\/sup>), but slightly less dense than tungsten and gold (19.3 g\/cm<sup>3<\/sup>).<\/p>\n<p>Uranium metal is one of the densest materials found on earth:<\/p>\n<ol>\n<li>Osmium &#8211; 22.6 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Iridium &#8211; 22.4 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Platinum &#8211; 21.5 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Rhenium &#8211; 21.0 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Plutonium &#8211; 19.8 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Gold &#8211; 19.3 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Tungsten &#8211; 19.3 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Uranium &#8211; 18.8 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Tantalum &#8211; 16.6 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Mercury &#8211; 13.6 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Rhodium &#8211; 12.4 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Thorium &#8211; 11.7 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Lead &#8211; 11.3 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<li>Silver &#8211; 10.5 x 10<sup>3<\/sup> kg\/m<sup>3<\/sup><\/li>\n<\/ol>\n<p>But most of <a title=\"LWR \u2013 Light Water Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/lwr-light-water-reactor\/\">LWRs<\/a> use <strong>uranium fuel<\/strong>, which is in the form of <strong>uranium dioxide<\/strong>. Uranium dioxide is a black semiconducting solid with very low thermal conductivity. On the other hand, uranium dioxide has a very high melting point and has well-known behavior.<\/p>\n<p>Uranium dioxide has a significantly lower density than uranium in metal form. Uranium dioxide has a density of <strong>10.97 g\/cm<sup>3<\/sup><\/strong>, but this value may vary with fuel burnup because, at low burnup, densification of pellets can occur, and at higher burnup, swelling occurs.<\/div><\/div><\/div>\n<h3>The density of Nuclear Matter<\/h3>\n<p><strong>Nuclear density<\/strong> is the density of the nucleus of an atom. It is the ratio of mass per unit volume inside the nucleus. Since the atomic nucleus carries most of the atom\u2019s mass and the atomic nucleus is very small compared to the entire atom, the nuclear density is very high.<\/p>\n<p>The nuclear density for a typical nucleus can be approximately calculated from the size of the nucleus and its mass. <strong>Typical <a title=\"Nuclear Radius \u2013 Radius of Nucleus\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/nuclear-radius-radius-of-nucleus\/\">nuclear radii<\/a><\/strong> are of the order <strong>10<\/strong><strong><sup>\u221214<\/sup><\/strong><strong> m<\/strong>. Nuclear radii can be calculated according to the following formula assuming spherical shape:<\/p>\n<p>r = r<sub>0<\/sub> . A<sup>1\/3<\/sup><\/p>\n<p>where r<sub>0<\/sub> = 1.2 x 10<sup>-15 <\/sup>m = 1.2 fm<\/p>\n<p>For example, <a title=\"Natural Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/natural-uranium\/\"><strong>natural uranium<\/strong><\/a> consists primarily of isotope <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a> (99.28%). Therefore the atomic mass of the uranium element is close to the atomic mass of the <sup>238<\/sup>U isotope (238.03u). The radius of this nucleus will be:<\/p>\n<p>r = r<sub>0<\/sub> . A<sup>1\/3<\/sup> = 7.44 fm.<\/p>\n<p>Assuming it is spherical, its volume will be:<\/p>\n<p>V = 4\u03c0r<sup>3<\/sup>\/3 = 1.73 x 10<sup>-42<\/sup> m<sup>3<\/sup>.<\/p>\n<p>The usual definition of nuclear density gives for its density:<\/p>\n<p>\u03c1<sub>nucleus<\/sub> = m \/ V = 238 x 1.66 x 10<sup>-27<\/sup> \/ (1.73 x 10<sup>-42<\/sup>) = <strong>2.3 x 10<sup>17<\/sup> kg\/m<sup>3<\/sup><\/strong>.<\/p>\n<p>Thus, the density of nuclear material is more than 2.10<sup>14<\/sup> times greater than that of water. It is an immense density. The descriptive term <em>nuclear density<\/em> is also applied to situations where similarly high densities occur, such as within neutron stars. Such immense densities are also found in neutron stars.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Density of Neutron Star<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">The densest material found on Earth is the metal osmium, but its density pales by comparison to the densities of exotic astronomical objects such as white dwarf stars and neutron stars.<\/p>\n<p>A <strong>neutron star<\/strong> is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist, and they rotate<strong>\u00a0extremely rapidly<\/strong>. A neutron star is a giant atomic nucleus about 11 km in diameter made especially of neutrons. It is believed that under the immense pressures of collapsing massive stars going supernova, the electrons and protons can combine to form neutrons via electron capture, releasing a huge amount of <a title=\"Neutrino\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutrino\/\">neutrinos<\/a>.<\/p>\n<p>They are so dense that one teaspoon of its material would have a mass over 5.5\u00d710<sup>12<\/sup> kg. It is assumed they have densities of 3.7 \u00d7 10<sup>17<\/sup> to 6 \u00d7 10<sup>17<\/sup> kg\/m<sup>3<\/sup>, which is comparable to the approximate density of an atomic nucleus of 2.3 \u00d7 10<sup>17<\/sup> kg\/m<sup>3<\/sup>.<\/div><\/div><\/div>\n<h2>What is Pressure<\/h2>\n<p><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-16368\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement-235x300.png\" alt=\"manometer-pressure-measurement\" width=\"235\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement-235x300.png 235w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement.png 290w\" sizes=\"(max-width: 235px) 100vw, 235px\" \/><\/a>Pressure<\/strong> is a measure of the <strong>force exerted<\/strong> per unit area on the boundaries of a substance. The standard unit for <strong>pressure<\/strong> in the SI system is the <strong>Newton per square meter or pascal (Pa)<\/strong>. Mathematically:<\/p>\n<p><strong>p = F\/A<\/strong><\/p>\n<p>where<\/p>\n<ul>\n<li><strong>p is the pressure<\/strong><\/li>\n<li><strong>F is the normal force<\/strong><\/li>\n<li><strong>A is the area of the boundary<\/strong><\/li>\n<\/ul>\n<p>Pascal is defined as the force of 1N that is exerted on a unit area.<\/p>\n<ul>\n<li><strong>1 Pascal = 1 N\/m<sup>2<\/sup><\/strong><\/li>\n<\/ul>\n<p>However, it is a fairly small unit for most engineering problems, so it is convenient to work with multiples of the pascal: the <strong>kPa<\/strong>, the <strong>bar<\/strong>, and the <strong>MPa<\/strong>.<\/p>\n<ul>\n<li><strong>1 MPa \u00a010<sup>6<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 bar \u00a0\u00a0\u00a010<sup>5<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 kPa \u00a0\u00a010<sup>3<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<\/ul>\n<p>In general, pressure or the force exerted per unit area on the boundaries of a substance is caused by the <strong>collisions<\/strong> of the <strong>molecules<\/strong> of the substance with the boundaries of the system. As molecules hit the walls, they exert forces that try to push the walls outward. The forces resulting from all of these collisions cause the <strong>pressure<\/strong> exerted by a system on its surroundings. Pressure as an <a title=\"Extensive and Intensive Properties\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/extensive-and-intensive-properties\/\"><strong>intensive variable<\/strong> <\/a>is constant in a closed system. It is only relevant in liquid or ga搜索引擎优化us systems.<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-16371\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure-300x129.png\" alt=\"What is Pressure\" width=\"300\" height=\"129\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure-300x129.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure.png 538w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<canvas id=\"the_canvas\" width=\"250\" height=\"250\"><\/canvas>\r\n<script>\r\n\r\nvar __VERSION__ = \"0.3.5\"\r\nvar inspector = {};\r\n\r\nvar Physics = {\r\n    \r\n    collide_balls: function(ball1, ball2) {\r\n        \/\/ calculate restitution\r\n        \/\/ TODO: add elasticity attr to circles\r\n        var ball1_elasticity = 1.0;\r\n        var ball2_elasticity = 1.0;\r\n        var restitution = ball1_elasticity * ball2_elasticity;\r\n        \r\n        \/\/ invert masses\r\n        var im1 = 1.0 \/ ball1.m;\r\n        var im2 = 1.0 \/ ball2.m;\r\n        \r\n        \/\/ get minimum translation distance\r\n        var delta = ball1.point().subtract(ball2.point());\r\n        var d = delta.get_length();\r\n        var mtd = delta.multiply(ball1.r + ball2.r - d).multiply(1.0 \/ d);\r\n        \r\n        \/\/ push-pull apart based on mass\r\n        var ball1_pt = ball1.point().add(mtd.multiply(im1 \/ (im1 + im2)));\r\n        var ball2_pt = ball2.point().subtract(mtd.multiply(im2 \/ (im1 + im2)));\r\n        ball1.set_point(ball1_pt.x, ball1_pt.y);\r\n        ball2.set_point(ball2_pt.x, ball2_pt.y);\r\n        \r\n        \/\/ calculate impact speed\r\n        var v = ball1.velocity().subtract(ball2.velocity());\r\n        var vn = v.dot(mtd.normalized());\r\n        \r\n        \/\/ positive vn means balls are already moving away for one another\r\n        if ( vn > 0 ) {\r\n            return;\r\n        }\r\n        \r\n        \/\/ collision impulse\r\n        var i = (-1.0 * (1.0 + restitution) * vn) \/ (im1 + im2);\r\n        var impulse = mtd.normalized().multiply(i);\r\n        \r\n        \/\/ transfer momentum\r\n        var v1 = ball1.velocity().add(impulse.multiply(im1));\r\n        var v2 = ball2.velocity().subtract(impulse.multiply(im2));\r\n        \r\n        \/\/ set new velocities\r\n        ball1.set_velocity(v1.x, v1.y);\r\n        ball2.set_velocity(v2.x, v2.y);\r\n    },\r\n    \r\n    bounce_ball_off_world: function(ball, world) {\r\n        \/\/ translate ball back inside world\r\n        var contact_pt = this.find_contact_point(world, ball);\r\n        ball.set_point(contact_pt.x, contact_pt.y);\r\n    \r\n        \/\/ reflect velocity of ball\r\n        var new_ball_vel = this.reflect_ball(world, ball);\r\n        ball.set_velocity(new_ball_vel.x, new_ball_vel.y);\r\n    },\r\n    \r\n    find_contact_point: function(world, ball) {\r\n        \/\/ see http:\/\/gamedev.stackexchange.com\/a\/29658\r\n        var A = world.point();\r\n        var B = ball.last_point();\r\n        var C = ball.point();\r\n        var R = world.r;\r\n        var r = ball.r;\r\n        \r\n        var AB = B.subtract(A);\r\n        var BC = C.subtract(B);\r\n        var AB_len = AB.get_length();\r\n        var BC_len = BC.get_length();\r\n        \r\n        \/\/ Avoid divide-by-zero erros (this should never really happen)\r\n        if ( ! BC_len ) {\r\n            return C;\r\n        }\r\n\r\n        var b = AB.dot(BC) \/ Math.pow(BC_len, 2) * -1;\r\n        var c = (Math.pow(AB_len, 2) - Math.pow(R - r, 2)) \/ Math.pow(BC_len, 2);\r\n        var d = b * b - c;\r\n        var k = b - Math.sqrt(d);\r\n        \r\n        if ( k < 0 ) {\r\n            k = b + Math.sqrt(d);\r\n        }\r\n        \r\n        var BD = C.subtract(B);\r\n        var BD_len = BC_len * k;\r\n        BD.set_length(BD_len);\r\n        \r\n        var D = B.add(BD);\r\n        return D;\r\n    },\r\n    \r\n    reflect_ball: function(world, ball) {\r\n        \/\/ see http:\/\/stackoverflow.com\/a\/573206\/1093087\r\n        var world_pt = world.point();\r\n        var ball_pt = ball.point();\r\n        var v = ball.velocity();\r\n        var n = ball_pt.subtract(world_pt).normalized();\r\n        \r\n        \/\/ assume perfect elasticity for now\r\n        \/\/ TODO: add elasticity attr to balls\r\n        var ball_elasticity = 1.0;\r\n        var world_elasticity = 1.0;\r\n        var restitution = ball_elasticity * world_elasticity;\r\n        \r\n        \/\/ solve reflection\r\n        var u = n.multiply(v.dot(n));\r\n        var w = v.subtract(u);\r\n        var v_after = w.subtract(u);\r\n        var reflection = v_after.subtract(v).multiply(restitution);\r\n        \r\n        \/\/ return new velocity\r\n        var new_ball_vel = v.add(reflection);\r\n        return new_ball_vel\r\n    },\r\n    \r\n    polar_to_vector: function(distance, angle) {\r\n        var radians = angle * (Math.PI \/ 180);\r\n        return new Vec2d(distance * Math.cos(radians),\r\n            distance * Math.sin(radians));\r\n    },\r\n};\r\n\r\n\r\nvar Graphics = {\r\n\r\n    init: function(canvas) {\r\n        this.ctx = canvas.getContext('2d');\r\n        this.center_x = canvas.width \/ 2;\r\n        this.center_y = canvas.height \/ 2;\r\n    },\r\n\r\n    draw_circle: function(x, y, r, color, line_width, stroke_color) {\r\n        var screen_x = this.world_to_screen_x(x);\r\n        var screen_y = this.world_to_screen_y(y);\r\n\r\n        this.ctx.beginPath();\r\n        this.ctx.arc(screen_x, screen_y, r, 0, Math.PI * 2, false);\r\n        this.ctx.fillStyle = color;\r\n        this.ctx.fill();\r\n\r\n        if (line_width) {\r\n            this.ctx.lineWidth = line_width;\r\n            this.ctx.strokeStyle = stroke_color;\r\n            this.ctx.stroke();\r\n        }\r\n\r\n        this.ctx.closePath();\r\n    },\r\n\r\n    world_to_screen_x: function(x) {\r\n        return this.center_x + x;\r\n    },\r\n\r\n    world_to_screen_y: function(y) {\r\n        return this.center_y - y;\r\n    },\r\n};\r\n\r\n\r\nvar Random = {\r\n    integer: function(min, max) {\r\n        return min + Math.floor(Math.random() * (max - min + 1));\r\n    }\r\n};\r\n\r\n\r\nfunction Vec2d(x, y) {\r\n    this.x = x;\r\n    this.y = y;\r\n    \r\n    this.add = function(v2) {\r\n        return new Vec2d(this.x + v2.x, this.y + v2.y);\r\n    };\r\n    \r\n    this.subtract = function(v2) {\r\n        return new Vec2d(this.x - v2.x, this.y - v2.y);\r\n    };\r\n    \r\n    this.multiply = function(v2) {\r\n        if ( ! v2.length ) {\r\n            \/\/ v2 is a scalar\r\n            return new Vec2d(this.x * v2, this.y * v2);\r\n        }\r\n        else {\r\n            return new Vec2d(this.x * v2.x, this.y * v2.y);\r\n        }\r\n    };\r\n    \r\n    this.get_length = function() {\r\n        return Math.sqrt((this.x * this.x) + (this.y * this.y));\r\n    };\r\n    \r\n    this.set_length = function(new_length) {\r\n        var old_length = this.get_length();\r\n        this.x *= new_length\/old_length;\r\n        this.y *= new_length\/old_length;\r\n        return this;\r\n    };\r\n    \r\n    this.distance = function(v2) {\r\n        return Math.sqrt(Math.pow(this.x - v2.x, 2) + Math.pow(\r\n            this.y - v2.y, 2));\r\n    };\r\n    \r\n    this.dot = function(v2) {\r\n        return (this.x * v2.x) + (this.y * v2.y);\r\n    };\r\n    \r\n    this.normalized = function() {\r\n        var length = this.get_length();\r\n        \r\n        if ( length != 0 ) {\r\n            return new Vec2d(this.x \/ length, this.y \/ length);\r\n        }\r\n        else {\r\n            return new Vec2d(this.x, this.y);\r\n        }\r\n    };\r\n}\r\n\r\n\r\nfunction Circle(x, y, r) {    \r\n    this.init = function(x, y, r) {\r\n        this.set_point(x, y);\r\n        this.r = r;\r\n    };\r\n    \r\n    this.point = function() {\r\n        return new Vec2d(this.x, this.y);\r\n    };\r\n    \r\n    this.set_point = function(x, y) {\r\n        this.x = x;\r\n        this.y = y;\r\n        return this;\r\n    };\r\n    \r\n    this.contains_circle = function(c2) {\r\n        var d = this.point().distance(c2.point());\r\n        return d + c2.r - this.r < 0;\r\n    };\r\n    \r\n    this.overlaps_circle = function(c2) {\r\n        \/\/ overlap if combined length is less than distance (use squares for\r\n        \/\/ quicker calculations)\r\n        var dsq = Math.pow(c2.y - this.y, 2) + Math.pow(c2.x - this.x, 2);\r\n        var lsq = Math.pow(this.r + c2.r, 2);\r\n        return dsq < lsq;\r\n    };\r\n    \r\n    this.init(x, y, r);\r\n}\r\n\r\n\r\nfunction World() {\r\n    \/\/ parasitic inheritance\r\n    \/\/ see http:\/\/www.crockford.com\/javascript\/inheritance.html\r\n    var self = new Circle(0, 0, 100);\r\n    \r\n    self.balls = [];\r\n    \r\n    self.color = 'white';\r\n    self.line = 4;\r\n    self.stroke = 'lightgray';\r\n    \r\n    self.update = function() {\r\n        self.balls.map(function(ball) {\r\n            ball.update();\r\n        });\r\n        self.resolve_collisions();\r\n        self.enforce_boundaries();\r\n        return self;\r\n    };\r\n\r\n    self.draw = function () {\r\n        Graphics.draw_circle(self.x, self.y, self.r, self.color, self.line,\r\n            self.stroke);\r\n        self.balls.map(function(ball) {\r\n            ball.draw();\r\n        });\r\n        return self;\r\n    };\r\n    \r\n    self.enforce_boundaries = function() {\r\n        self.balls.map(function(ball) {\r\n            if (! self.contains_circle(ball)) {\r\n                Physics.bounce_ball_off_world(ball, self);\r\n            }\r\n        });\r\n        return self;\r\n    };\r\n    \r\n    self.resolve_collisions = function() {\r\n        for (var i=0; i<self.balls.length; i++) {\r\n            for (var j=i+1; j<self.balls.length; j++) {\r\n                if ( self.balls[i].collides_with(self.balls[j]) ) {\r\n                    self.balls[i].bounce_off(self.balls[j]);\r\n                }\r\n            }\r\n        }\r\n        return self;\r\n    };\r\n    \r\n    self.add_ball = function(ball) {\r\n        self.balls.push(ball);\r\n        return self;\r\n    };\r\n\r\n    return self;\r\n}\r\n\r\n\r\nfunction Ball(x, y, r, color) {\r\n    var self = new Circle(x, y, r);\r\n    self.color = color;\r\n    \r\n    self.m = 10;\r\n    self.vx = 0;\r\n    self.vy = 0;\r\n    \r\n    \/\/ last point: this is needed to resolve collisions with world's wall\r\n    self.lx = undefined;\r\n    self.ly = undefined;\r\n    \r\n    self.max_speed = r \/ 2.0;\r\n    \r\n    self.update = function() {\r\n        self.move();\r\n    };\r\n\r\n    self.move = function() {\r\n        self.lx = self.x;\r\n        self.ly = self.y;\r\n        self.x += self.vx;\r\n        self.y += self.vy;\r\n        return self;\r\n    };\r\n    \r\n    self.last_point = function() {\r\n        return new Vec2d(self.lx, self.ly);\r\n    };\r\n    \r\n    self.set_velocity = function(vx, vy) {\r\n        self.vx = vx;\r\n        self.vy = vy;\r\n        return self;\r\n    };\r\n    \r\n    self.velocity = function() {\r\n        return new Vec2d(self.vx, self.vy);\r\n    };\r\n    \r\n    self.clamp_speed = function () {\r\n        var v = self.velocity();\r\n        var speed = v.get_length();\r\n        if (speed > self.max_speed) {\r\n            v.set_length(self.max_speed);\r\n            self.set_velocity(v.x, v.y);\r\n        }\r\n        return self;\r\n    };\r\n\r\n    self.draw = function () {\r\n        Graphics.draw_circle(self.x, self.y, self.r, self.color, 0);\r\n        return self;\r\n    };\r\n    \r\n    self.collides_with = function(ball) {\r\n        return self.overlaps_circle(ball);\r\n    };\r\n    \r\n    self.bounce_off = function(ball) {\r\n        Physics.collide_balls(self, ball);\r\n        return self;\r\n    };\r\n    \r\n    self.set_direction = function(degrees) {\r\n        var d = self.velocity().get_length();\r\n        var v = Physics.polar_to_vector(d, degrees);\r\n        self.set_velocity(v.x, v.y);\r\n        return self;        \r\n    };\r\n    \r\n    self.set_random_direction = function() {\r\n        return self.set_direction(Random.integer(0,360));\r\n    };\r\n    \r\n    return self;\r\n}\r\n\r\n\r\nfunction main() {\r\n    console.log('launching version: ' + __VERSION__);\r\n    \r\n    \/\/ load canvas and Graphics handler\r\n    var canvas = document.getElementById(\"the_canvas\");\r\n    Graphics.init(canvas);\r\n    \r\n    \/\/ set animation handler\r\n    var fps = 30;\r\n    var mspf = 1000 \/ fps;    \r\n    window.animate = (function () {\r\n        return window.requestAnimationFrame ||\r\n            window.webkitRequestAnimationFrame ||\r\n            window.mozRequestAnimationFrame ||\r\n            window.oRequestAnimationFrame ||\r\n            window.msRequestAnimationFrame ||\r\n            function (callback, element) {\r\n                window.setTimeout(callback, mspf);\r\n            };\r\n    })();\r\n    \r\n    \/\/ init balls\r\n    var red_ball = new Ball(0, 25, 5, 'blue');\r\n    red_ball.set_velocity(5, 0).set_random_direction();\r\n    var green_ball = new Ball(-17, -17, 5, 'blue');\r\n    green_ball.set_velocity(5, 0).set_random_direction();\r\n    var blue_ball = new Ball(17, -17, 5, 'blue');\r\n    blue_ball.set_velocity(5, 0).set_random_direction();\r\n    var ad_ball = new Ball(17, -17, 5, 'blue');\r\n    ad_ball.set_velocity(5, 0).set_random_direction();\r\n    var add_ball = new Ball(17, -17, 5, 'blue');\r\n    add_ball.set_velocity(5, 0).set_random_direction();\r\n    var addd_ball = new Ball(17, -17, 5, 'blue');\r\n    addd_ball.set_velocity(5, 0).set_random_direction();\r\n    var adddd_ball = new Ball(17, -17, 5, 'blue');\r\n    adddd_ball.set_velocity(5, 0).set_random_direction();\r\n    var addddd_ball = new Ball(17, -17, 5, 'blue');\r\n    addddd_ball.set_velocity(5, 0).set_random_direction();\r\n    var adddddd_ball = new Ball(17, -17, 5, 'blue');\r\n    adddddd_ball.set_velocity(5, 0).set_random_direction();\r\n    var addddddd_ball = new Ball(17, -17, 5, 'blue');\r\n    addddddd_ball.set_velocity(5, 0).set_random_direction();\r\n   \r\n   \r\n    \r\n    \/\/ init world\r\n    var world = new World();\r\n    world.add_ball(red_ball);\r\n    world.add_ball(green_ball);\r\n    world.add_ball(blue_ball);\r\n    world.add_ball(ad_ball);\r\n    world.add_ball(add_ball);\r\n    world.add_ball(addd_ball);\r\n    world.add_ball(adddd_ball);\r\n    world.add_ball(addddd_ball);\r\n    world.add_ball(adddddd_ball);\r\n    world.add_ball(addddddd_ball);\r\n    \r\n    \r\n   \r\n    \r\n    \/\/ attach world to window so that we can inspect\r\n    inspector.world = world;\r\n    \r\n    \/\/ animate\r\n    function anim_loop() {\r\n        world.update();\r\n        world.draw();\r\n        window.animate(anim_loop);\r\n    };\r\n    anim_loop();\r\n}\r\n\r\nmain();\r\n<\/script>\n<h3>Pressure Scales &#8211; Pressure Units<\/h3>\n<h3>Pascal &#8211; Unit of Pressure<\/h3>\n<p>As was discussed, the <strong>SI unit<\/strong> of <strong>pressure<\/strong> and stress is the<strong> pascal<\/strong>.<\/p>\n<ul>\n<li><strong>1 pascal \u00a01 N\/m<sup>2<\/sup> = 1 kg \/ (m.s<sup>2<\/sup>)<\/strong><\/li>\n<\/ul>\n<p>Pascal is defined as one Newton per square meter. However, it is a fairly small unit for most engineering problems, so it is convenient to work with multiples of the pascal: the <strong>kPa<\/strong>, the <strong>bar<\/strong>, and the <strong>MPa<\/strong>.<\/p>\n<ul>\n<li><strong>1 MPa \u00a010<sup>6<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 bar \u00a0\u00a0\u00a010<sup>5<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 kPa \u00a0\u00a010<sup>3<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<\/ul>\n<p>The unit of measurement called <strong>standard atmosphere<\/strong> (<strong>atm<\/strong>) is defined as:<\/p>\n<ul>\n<li><strong>1 atm = 101.33 kPa<\/strong><\/li>\n<\/ul>\n<p>The standard atmosphere approximates the average pressure at sea level at the latitude of 45\u00b0 N. Note that there is a difference between the <strong>standard atmosphere<\/strong> (atm) and the<strong> technical atmosphere<\/strong> (at).<\/p>\n<p>A technical atmosphere is a non-SI unit of pressure equal to one kilogram-force per square centimeter.<\/p>\n<ul>\n<li><strong>1 at = 98.67 kPa<\/strong><\/li>\n<\/ul>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16280\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere.png\" alt=\"Table - Conversion between pressure units - pascal, bar, psi, atmosphere\" width=\"659\" height=\"289\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere.png 659w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere-300x132.png 300w\" sizes=\"(max-width: 659px) 100vw, 659px\" \/><\/a><\/p>\n<p>See also:<a title=\"Pounds per square inch \u2013 psi\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/pounds-per-square-inch-psi\/\"> Pound per square inch \u2013 psi<\/a><\/p>\n<p>See also: <a title=\"Bar \u2013 Unit of Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/bar-unit-of-pressure\/\">Bar \u2013 Unit of Pressure<\/a><\/p>\n<p>See also: <a title=\"Typical Pressures in Engineering \u2013 Examples\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/typical-pressures-in-engineering-examples\/\">Typical Pressures in Engineering<\/a><\/p>\n<h3>Absolute vs. Gauge Pressure<\/h3>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-16281\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure.png\" alt=\"absolute-vs-gauge-pressure\" width=\"388\" height=\"247\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure.png 388w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure-300x191.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/a>Pressure, as discussed above, is called <strong>absolute pressure<\/strong>. Often it will be important to distinguish between <strong>absolute pressure<\/strong> and <strong>gauge pressure<\/strong>. In this article, the term pressure refers to absolute pressure unless explicitly stated otherwise. But in engineering, we often deal with pressures that are <strong>measured<\/strong> by some devices. Although absolute pressures must be used in thermodynamic relations, <strong>pressure-measuring<\/strong> devices often indicate the <strong>difference<\/strong> between the absolute pressure in a system and the absolute pressure of the atmosphere existing outside the measuring device. They measure the <strong>gauge pressure<\/strong>.<\/p>\n<ul>\n<li><strong>Absolute Pressure.<\/strong> When pressure is measured relative to a perfect vacuum, it is called absolute pressure (psia). Pounds per square inch absolute (psia) is used to clarify that the pressure is relative to a vacuum rather than the ambient atmospheric pressure. Since atmospheric pressure at sea level is around 101.3 kPa (14.7 psi), this will be added to any pressure reading made in air at sea level.<\/li>\n<li><strong>Gauge Pressure. <\/strong>When pressure is measured relative to atmospheric pressure (14.7 psi), it is called gauge pressure (psig). The term gauge pressure is applied when the pressure in the system is greater than the local atmospheric pressure, p<sub>atm<\/sub>. The latter pressure scale was developed because almost all pressure gauges register zero when open to the atmosphere. Gauge pressures are positive if they are above atmospheric pressure and negative if they are below atmospheric pressure.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><em>p<\/em><em><sub>gauge<\/sub><\/em><em> = p<\/em><em><sub>absolute<\/sub><\/em><em> &#8211; p<\/em><em><sub>absolute; atm<\/sub><\/em><\/p>\n<ul>\n<li><strong>Atmospheric Pressure. <\/strong>Atmospheric pressure is the pressure in the surrounding air at &#8211; or \u201cclose\u201d to &#8211; the surface of the Earth. The atmospheric pressure varies with temperature and altitude above sea level. The <strong>Standard Atmospheric Pressure <\/strong>approximates to the average pressure at sea-level at the latitude 45\u00b0 N. \u00a0The <strong>Standard Atmospheric Pressure<\/strong> is defined at sea-level at <em>273<\/em><em><sup>o<\/sup><\/em><em>K (0<\/em><em><sup>o<\/sup><\/em><em>C)<\/em> and is:\n<ul>\n<li><strong><em>101325 Pa <\/em><\/strong><\/li>\n<li><strong><em>1.01325 bar<\/em><\/strong><\/li>\n<li><strong><em>14.696 psi<\/em><\/strong><\/li>\n<li><strong><em>760 mmHg<\/em><\/strong><\/li>\n<li><strong><em>760 torr<\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n<li><strong>Negative Gauge Pressure &#8211; Vacuum Pressure. <\/strong>When the local atmospheric pressure is greater than the pressure in the system, the term <strong>vacuum pressure<\/strong> is used. A perfect vacuum would correspond to absolute zero pressure. It is certainly possible to have a negative gauge pressure but not possible to have negative absolute pressure. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of \u221221 kPa (i.e., 21 kPa below atmospheric pressure of 101 kPa).<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><em>p<\/em><em><sub>vacuum<\/sub><\/em><em> = p<\/em><em><sub>absolute; atm<\/sub><\/em><em> &#8211; p<\/em><em><sub>absolute<\/sub><\/em><\/p>\n<p>For example, a car tire pumped up to 2.5 atm (36.75 psig) above local atmospheric pressure (let say 1 atm or 14.7 psia locally), will have an absolute pressure of 2.5 + 1 = 3.5 atm (36.75 + 14.7 = 51.45 psia or 36.75 psig).<\/p>\n<p>On the other hand condensing steam\u00a0<span style=\"font-weight: 400;\">turbines (at <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\">nuclear power plants<\/a>) exhaust <a title=\"Properties of Steam \u2013 What is Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam<\/a> at a pressure well below atmospheric <\/span><span style=\"font-weight: 400;\">(e.g.,, at 0.08 bar or 8 kPa or 1.16 psia)<\/span><span style=\"font-weight: 400;\"> and in a partially condensed state. In relative units, it is a negative gauge pressure of about &#8211; 0.92 bar, &#8211; 92 kPa, or &#8211; 13.54 psig.<\/span><\/p>\n<h3>Typical Pressures in Engineering &#8211; Examples<\/h3>\n<p>The <strong>pascal (Pa)<\/strong> as a unit of pressure measurement is widely used worldwide. It has largely replaced the <strong>pounds per square inch (psi)<\/strong> unit, except in some countries that still use the Imperial measurement system, including the United States. For most engineering problems, pascal (Pa) is a fairly small unit, so it is convenient to work with multiples of the pascal: the kPa, the MPa, or the bar. The following list summarizes a few examples:<\/p>\n<ul>\n<li>Typically most <strong>nuclear power plants<\/strong> operate <strong>multi-stage condensing steam turbines<\/strong>. These turbines exhaust steam at a pressure well below atmospheric (e.g.,, at 0.08 bar or 8 kPa or 1.16 psia) and in a partially condensed state. In relative units, it is a negative gauge pressure of about &#8211; 0.92 bar, &#8211; 92 kPa, or &#8211; 13.54 psig.<\/li>\n<li>The <strong>Standard Atmospheric Pressure<\/strong> approximates to the average pressure at sea-level at the latitude 45\u00b0 N. \u00a0The <strong>Standard Atmospheric Pressure<\/strong> is defined at sea-level at <em>273<\/em><em><sup>o<\/sup><\/em><em>K (0<\/em><em><sup>o<\/sup><\/em><em>C)<\/em> and is:\n<ul>\n<li><strong><em>101325 Pa <\/em><\/strong><\/li>\n<li><strong><em>1.01325 bar<\/em><\/strong><\/li>\n<li><strong><em>14.696 psi<\/em><\/strong><\/li>\n<li><strong><em>760 mmHg<\/em><\/strong><\/li>\n<li><strong><em>760 torr<\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n<li>Car tire overpressure is about 2.5 bar, 0.25 MPa, or 36 psig.<\/li>\n<li>Steam locomotive fire tube boiler: 150\u2013250 psig<\/li>\n<li>A high-pressure stage of condensing steam turbine at nuclear power plant operates at steady state with inlet conditions of \u00a06 MPa (60 bar, or 870 psig) t = 275.6\u00b0C, x = 1<\/li>\n<li>A <strong>boiling water reactor<\/strong> is cooled and moderated by water like a PWR, but at a<strong> lower pressure<\/strong> (e.g.,, 7MPa, 70 bar, or 1015 psig), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines.<\/li>\n<li><strong>Pressurized water reactors<\/strong> are cooled and moderated by high-pressure liquid water (e.g.,, 16MPa, 160 bar, or 2320 psig). At this pressure, water boils at approximately 350\u00b0C (662\u00b0F), which provides a subcooling margin of about 25\u00b0C.<\/li>\n<li>The <strong>supercritical water reactor (SCWR)<\/strong> is operated at <strong>supercritical pressure<\/strong>. The term supercritical in this context refers to the thermodynamic <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/critical-point-of-water\/\"><strong>critical point of water<\/strong><\/a> (T<sub>CR<\/sub> = 374 \u00b0C; \u00a0p<sub>CR<\/sub> = 22.1 MPa)<\/li>\n<li><strong>Common rail direct fuel injection: <\/strong>It features a high-pressure (over 1 000 bar or 100 MPa or 14500 psi) fuel rail on diesel engines.<\/li>\n<\/ul>\n<h2>What is Temperature<\/h2>\n<p>In <strong>physics<\/strong> and <strong>everyday life,<\/strong> a <strong>temperature<\/strong> is an objective comparative measurement of <strong>hot or cold<\/strong> based on our sense of touch. \u00a0A body that usually feels hot has a higher temperature than a similar body that feels cold. But this definition is not a simple matter. For example, a metal rod feels colder than a plastic rod at room temperature simply because metals are generally better at conducting heat away from the skin, as are plastics. Simply <strong>hotness<\/strong> may be represented <strong>abstractly,<\/strong> and therefore it is necessary to have an objective way of measuring temperature. It is one of the basic thermodynamic properties.<\/p>\n<h3>Thermal Equilibrium<\/h3>\n<figure id=\"attachment_16008\" aria-describedby=\"caption-attachment-16008\" style=\"width: 193px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16008\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics-203x300.png\" alt=\"Zeroth law of thermodynamics\" width=\"203\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics-203x300.png 203w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics.png 432w\" sizes=\"(max-width: 203px) 100vw, 203px\" \/><\/a><figcaption id=\"caption-attachment-16008\" class=\"wp-caption-text\">Zeroth law of thermodynamics: If two systems are both in thermal equilibrium with a third, then they are in thermal equilibrium with each other.<\/figcaption><\/figure>\n<p>A particularly important concept is <strong>thermodynamic equilibrium<\/strong>. In general, when two objects are brought into<strong> thermal contact<\/strong>, <strong>heat will flow<\/strong> between them <strong>until<\/strong> they come into <strong>equilibrium<\/strong> with each other. \u00a0When a <strong>temperature difference<\/strong> does exist, heat flows spontaneously <strong>from the warmer system to the colder system<\/strong>. Heat transfer occurs by <strong>conduction<\/strong> or by <strong>thermal radiation<\/strong>. When the <strong>flow of heat stops<\/strong>, they are said to be at the<strong> same temperature<\/strong>. They are then said to be in <strong>thermal equilibrium<\/strong>.<\/p>\n<p>For example, you leave a <strong>thermometer<\/strong> in a cup of coffee. As the two objects interact, the thermometer becomes hotter, and the coffee cools off a little until they come into <strong>thermal equilibrium<\/strong>. Two objects are defined to be in thermal equilibrium if, when placed in thermal contact, <strong>no net energy flows<\/strong> from one to the other, and their <strong>temperatures don\u2019t change<\/strong>. We may postulate:<\/p>\n<p><strong><em>When the two objects are in thermal equilibrium, their temperatures are equal. <\/em><\/strong><\/p>\n<p>This is a subject of a law that is called the \u201czeroth law of thermodynamics\u201d.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Zeroth Law of Thermodynamics<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_16008\" aria-describedby=\"caption-attachment-16008\" style=\"width: 193px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16008\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics-203x300.png\" alt=\"Zeroth law of thermodynamics\" width=\"203\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics-203x300.png 203w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/Thermal-equilibrium-Zeroth-Law-Thermodynamics.png 432w\" sizes=\"(max-width: 203px) 100vw, 203px\" \/><\/a><figcaption id=\"caption-attachment-16008\" class=\"wp-caption-text\">Zeroth law of thermodynamics: If two systems are both in thermal equilibrium with a third, then they are in thermal equilibrium with each other.<\/figcaption><\/figure>\n<p>We can discover an important property of <strong>thermal equilibrium<\/strong> by considering <strong>three systems<\/strong>. A, B, and C <strong>are initially\u00a0not in thermal equilibrium<\/strong>. We separate systems A and B with an adiabatic wall (ideal insulating material), but we let system C interact with systems A and B. We wait until <strong>thermal equilibrium<\/strong> is reached; then, A and B are in thermal equilibrium with C. But are they in thermal equilibrium with each other?<\/p>\n<p><strong>According to many experiments<\/strong>, there will be <strong>no net energy flow<\/strong> between <strong>A<\/strong> and <strong>B<\/strong>. This is <strong>experimental evidence<\/strong> of the following statement:<\/p>\n<p><strong><em>If two systems are both in thermal equilibrium with a third, then they are in thermal equilibrium with each other. \u00a0<\/em><\/strong><\/p>\n<p>This statement is known as the <strong>zeroth law of thermodynamics<\/strong>. It has this unusual name because it was not until after the great first and second laws of thermodynamics were worked out that scientists realized that this obvious postulate needed to be stated first.<\/p>\n<p>This law provides a <strong>definition<\/strong> and <strong>method<\/strong> of <strong>defining temperatures<\/strong>, perhaps the <strong>most important <a title=\"Extensive and Intensive Properties\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/extensive-and-intensive-properties\/\">intensive property<\/a><\/strong> of a system when dealing with thermal energy conversion problems. Temperature is a system property that determines whether the system will be in thermal equilibrium with other systems. When two systems are in thermal equilibrium, their temperatures are, by definition, equal, and no net thermal energy will be exchanged between them. Thus the importance of the zeroth law is that it allows a useful definition of temperature.<\/div><\/div><\/div>\n<p><strong>Temperature<\/strong> is a very important characteristic of matter. Many <strong>properties<\/strong> of matter <strong>change with temperature<\/strong>. The length of a metal rod, <a title=\"Steam Tables \u2013 Specific Properties of Water and Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\">steam pressure<\/a> in a boiler, the ability of a wire to conduct an electric current, and the color of a very hot glowing object. All these <strong>depend on temperature<\/strong>.<\/p>\n<p>For example, most materials expand when their temperature is increased. This property is very important in all of science and engineering, even in <a title=\"Nuclear Engineering\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/\">nuclear engineering<\/a>. The<strong> thermodynamic efficiency<\/strong> of power plants changes with inlet steam temperature or even with the outside temperature. At higher temperatures, solids such as steel glow orange or even white, depending on temperature. The white light from an ordinary incandescent lightbulb comes from an extremely hot tungsten wire. It can be seen temperature is one of the fundamental characteristics that describe matter and influences matter behavior.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Kinetic Temperature<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Kinetic theory<\/strong>\u00a0of gases provides a microscopic explanation of temperature. It is based on the fact that during an <a title=\"Elastic Collisions\" href=\"http:\/\/sitepourvtc.com\/laws-of-conservation\/law-of-conservation-of-energy\/elastic-collisions\/\">elastic collision<\/a> between a molecule with high kinetic energy and one with low kinetic energy, part of the energy will transfer to the molecule of lower kinetic energy. <strong>Temperature<\/strong> is therefore related to the <strong>kinetic energies<\/strong> of the molecules of a material. Since this relationship is fairly complex, it will be discussed later.<\/div><\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>How temperature influences the reactivity of the core<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In operating<strong> power reactors,<\/strong>\u00a0the <a title=\"Neutron Generation \u2013 Neutron Population\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/neutron-generation-neutron-population\/\">neutron population<\/a> is always large enough to generate heat. It is the main purpose of power reactors <strong>to generate a large amount of heat<\/strong>. This causes the <b>system\u2019s temperature<\/b> to change and material densities to change (due to the <strong>thermal expansion<\/strong>).<\/p>\n<p>Because <a title=\"Macroscopic Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/macroscopic-cross-section\/\">macroscopic cross-sections<\/a> are proportional to <a title=\"Atomic Number Density\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/atomic-number-density\/\">densities<\/a> and temperatures, the <a title=\"Neutron Flux Spectra\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-spectra\/\"><strong>neutron flux spectrum<\/strong><\/a> also depends on the density of the <a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a>. These\u00a0changes, in turn, will produce some changes in <a title=\"Reactivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity\/\">reactivity<\/a>. These changes in reactivity are usually called <a title=\"Reactivity Coefficients \u2013 Reactivity Feedbacks\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/\"><strong>reactivity feedbacks<\/strong><\/a> and are characterized by <strong>reactivity coefficients<\/strong>. This is a very important area of reactor design because the reactivity feedbacks influence the<strong> stability of the reactor<\/strong>. For example, reactor design must ensure that the temperature feedback will be <strong>negative <\/strong>under all operating conditions.<\/p>\n<p>See also: <a title=\"Moderator Temperature Coefficient \u2013 MTC\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/moderator-temperature-coefficient-mtc\/\">Moderator Temperature Coefficient<\/a><\/p>\n<p>See also: <a title=\"Fuel Temperature Coefficient \u2013 Doppler Coefficient \u2013 DTC\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/fuel-temperature-coefficient-doppler-coefficient\/\">Doppler Coefficient<\/a><\/div><\/div><\/div>\n<h3>Temperature Scales<\/h3>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/comparison-temperature-scales-min.png\"><img loading=\"lazy\" class=\" wp-image-16243 alignright\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/comparison-temperature-scales-min.png\" alt=\"Temperature Conversion - Fahrenheit - Celsius\" width=\"400\" height=\"318\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/comparison-temperature-scales-min.png 718w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/comparison-temperature-scales-min-300x239.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/comparison-temperature-scales-min-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/comparison-temperature-scales-min-147x118.png 147w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/a>When using a thermometer, we need to mark a scale on the tube wall with numbers. We have to define a<strong> temperature scale<\/strong>. A <strong><em>temperature scale<\/em><\/strong> is a way to measure temperature relative to a <strong>starting point<\/strong> (0 or zero) and a <strong>unit of measurement<\/strong>.<\/p>\n<p>These numbers are arbitrary, and historically many different schemes have been used. For example, this was done by defining some physical occurrences at given temperatures\u2014such as the <strong>freezing<\/strong> and<strong><a title=\"Saturation \u2013 Boiling Point\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturation-boiling-point\/\"> boiling points of water<\/a>\u00a0<\/strong>\u2014 and defining them as 0 and 100, respectively.<\/p>\n<p>Some several scales and units exist for measuring temperature. The most common are:<\/p>\n<ul>\n<li>Celsius (denoted \u00b0C),<\/li>\n<li>Fahrenheit (denoted \u00b0F),<\/li>\n<li>Kelvin (denoted K, especially in science).<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Fahrenheit Scale<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_16242\" aria-describedby=\"caption-attachment-16242\" style=\"width: 245px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Fahrenheit-temperature-scale-min.png\"><img loading=\"lazy\" class=\"size-full wp-image-16242\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Fahrenheit-temperature-scale-min.png\" alt=\"Fahrenheit temperature scale\" width=\"255\" height=\"526\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Fahrenheit-temperature-scale-min.png 255w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Fahrenheit-temperature-scale-min-145x300.png 145w\" sizes=\"(max-width: 255px) 100vw, 255px\" \/><\/a><figcaption id=\"caption-attachment-16242\" class=\"wp-caption-text\">Fahrenheit temperature scale is based on two points: the temperature of a brine solution as 0\u00b0F and the average human body temperature as 100\u00b0F.<\/figcaption><\/figure>\n<p>The <strong>Celsius scale<\/strong> and the <strong>Fahrenheit scale<\/strong> are based on a specification of the number of increments between the <strong>freezing point<\/strong> and <a title=\"Saturation \u2013 Boiling Point\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturation-boiling-point\/\"><strong>boiling point of water<\/strong> <\/a>at standard atmospheric pressure. The Celsius scale has 100 units between these points, and the <strong>Fahrenheit scale has 180 units<\/strong>, where each unit represents 1\u00b0C or 1 \u00b0F, respectively. The zero points on the scales are arbitrary.<\/p>\n<p>Fahrenheit scale is based on two points:<\/p>\n<ul>\n<li>The lower defining point, <strong>0 \u00b0F<\/strong>, was established as <strong>the temperature of a solution of brine<\/strong> made from equal parts of ice and salt.<\/li>\n<li>The upper defining point, <strong>96 \u00b0F<\/strong>, was established as <strong>the average human body temperature<\/strong> (96 \u00b0F, about 2.6 \u00b0F less than the modern value due to a later redefinition of the scale)<\/li>\n<\/ul>\n<p>The difference in height between the two points would then be marked off in <strong>180 divisions,<\/strong> with each division representing 1 \u00b0F. Today, the scale is usually defined by two fixed points: the temperature at which water freezes into ice is 32 \u00b0F, and the boiling point of water is 212 \u00b0F.<\/p>\n<p><strong>Temperature Conversion &#8211; Fahrenheit &#8211; Celsius<\/strong><\/p>\n<p>To convert from a <strong>Fahrenheit temperature<\/strong> to a <strong>Celsius temperature,<\/strong> we have to subtract <strong>32 degrees<\/strong> from the Fahrenheit reading to get to the zero point on the Celsius scale and then adjust for the different size degrees. The ratio of the size of the degrees is <strong>5\/9<\/strong> so that the following equations represent the relationship between the scales:<\/p>\n<p><strong>\u00b0F = 32.0 + (9\/5)\u00b0C<\/strong><\/p>\n<p><strong>\u00b0C = (\u00b0F &#8211; 32.0)(5\/9)<\/strong><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Celsius Scale<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_16241\" aria-describedby=\"caption-attachment-16241\" style=\"width: 311px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Celsius-temperature-scale-min.png\"><img loading=\"lazy\" class=\"size-full wp-image-16241\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Celsius-temperature-scale-min.png\" alt=\"Celsius temperature scale\" width=\"321\" height=\"508\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Celsius-temperature-scale-min.png 321w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Celsius-temperature-scale-min-190x300.png 190w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/a><figcaption id=\"caption-attachment-16241\" class=\"wp-caption-text\">Celsius temperature scale is based on two points: the boiling point of water as 100\u00b0 C and the freezing point of water as 0\u00b0 C.<\/figcaption><\/figure>\n<p>About 20 years after Fahrenheit proposed its temperature scale for\u00a0thermometer, Swedish professor <strong>Anders Celsius<\/strong> defined a better scale for measuring temperature. He proposed using the <a title=\"Saturation \u2013 Boiling Point\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturation-boiling-point\/\"><strong>boiling point of water<\/strong><\/a> as <strong>100\u00b0 C<\/strong> and the<strong> freezing point of water<\/strong> as<strong> 0\u00b0 C<\/strong>. Water was chosen as the reference material because it was always available in most laboratories worldwide.<\/p>\n<p><strong>Celsius <\/strong>is also called the <strong>centigrade temperature scale <\/strong>because of the <strong>100-degree<\/strong> interval between the defined points. The Celsius temperature for a state colder than freezing water is a negative number. The Celsius scale is used, both in everyday life and in science and industry, almost everywhere globally.<\/p>\n<p><strong>Absolute zero<\/strong>, the lowest temperature possible, is defined as being precisely 0\u00a0K and \u2212273.15\u00a0\u00b0C. The temperature of the <a title=\"Triple Point of Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/triple-point-of-water\/\"><strong>triple point of water<\/strong><\/a> is defined as precisely 273.16\u00a0K and 0.01\u00a0\u00b0C.\u00a0This definition fixes the magnitude of both the degree Celsius and the kelvin as precisely 1 part in 273.16 of the difference between absolute zero and the triple point of water.<\/p>\n<p>It must be added, by international agreement the unit \u201cdegree Celsius\u201d and the Celsius scale are currently defined by two different points: <strong>absolute zero<\/strong>\u00a0and the <strong>triple point of water <\/strong>(instead of boiling and freezing points). This definition also precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature.<\/p>\n<p><strong>Temperature Conversion &#8211; Fahrenheit &#8211; Celsius<\/strong><\/p>\n<p>To convert from a<strong> Fahrenheit temperature<\/strong> to a <strong>Celsius temperature,<\/strong> we have to subtract <strong>32 degrees<\/strong> from the Fahrenheit reading to get to the zero point on the Celsius scale and then adjust for the different size degrees. The ratio of the size of the degrees is <strong>5\/9<\/strong> so that the following equations represent the relationship between the scales:<\/p>\n<p><strong>\u00b0F = 32.0 + (9\/5)\u00b0C<\/strong><br \/>\n<strong>\u00b0C = (\u00b0F &#8211; 32.0)(5\/9)<\/strong><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Kelvin Scale<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_16244\" aria-describedby=\"caption-attachment-16244\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Kelvin-temperature-scale-thermodynamic-scale-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16244\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Kelvin-temperature-scale-thermodynamic-scale-min-300x275.png\" alt=\"Kelvin temperature scale\" width=\"300\" height=\"275\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Kelvin-temperature-scale-thermodynamic-scale-min-300x275.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Kelvin-temperature-scale-thermodynamic-scale-min.png 568w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-16244\" class=\"wp-caption-text\">The Kelvin temperature scale was determined based on the Celsius scale but with a starting point at absolute zero.<\/figcaption><\/figure>\n<p><strong>Kelvin temperature scale<\/strong> is the base unit of <strong>thermodynamic temperature<\/strong> measurement in the International System (SI) of measurement. The<strong> Kelvin scale<\/strong> was determined based on the Celsius scale but with a starting point at<strong> absolute zero<\/strong>. Temperatures in the Kelvin scale are 273 degrees less than in the Celsius scale. The kelvin is defined as the fraction \u200a1\u2044273.16 of the thermodynamic temperature of the triple point of water. By international agreement, the <a title=\"Triple Point of Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/triple-point-of-water\/\"><strong>triple point of water<\/strong><\/a> has been assigned a value of<strong> 273.16 K (0.01 \u00b0C; 32.02 \u00b0F)<\/strong> and partial vapor pressure of <strong>611.66 pascals (6.1166 mbar; 0.0060366 atm)<\/strong>. In other words, it is defined such that the triple point of water is exactly 273.16 K.<\/p>\n<p>Note that the unit on the absolute scale is Kelvins, not degrees Kelvin. It was named in honor of Lord Kelvin, who had a great deal to do with temperature measurement and thermodynamics development.<\/p>\n<p>The<strong> absolute temperature scale<\/strong> that corresponds to the Celsius scale is called the Kelvin (K) scale, and the absolute scale that corresponds to the Fahrenheit scale is called the Rankine (R) scale. The zero points on both absolute scales represent the same physical state. The relationships between the absolute and relative temperature scales are shown in the following equations.<\/p>\n<p><strong>Kelvin &#8211; Celsius<\/strong><\/p>\n<p><strong>K = \u00b0C + 273.15<\/strong><\/p>\n<p><strong>\u00b0C = K &#8211; 273.15<\/strong><\/p>\n<p><strong>Rankine &#8211; Fahrenheit<\/strong><\/p>\n<p><strong>R = \u00b0F + 460<\/strong><\/p>\n<p><strong>\u00b0F =\u00a0R &#8211; 460<\/strong><\/p>\n<h2><strong>Absolute Zero<\/strong><\/h2>\n<p>Such a scale has as its <strong>zero point<\/strong>. The coldest theoretical temperature is called <strong>absolute zero<\/strong>, at which the thermal motion of atoms and molecules reaches its minimum. \u00a0This is a state at which the enthalpy and entropy of a cooled ideal gas reach its minimum value, taken as 0. <strong>Classically<\/strong>, this would be a state of <strong>motionlessness<\/strong>, but <strong>quantum<\/strong> uncertainty dictates that the particles still possess <strong>finite zero-point energy<\/strong>. <strong>Absolute zero<\/strong> is denoted as 0 K on the Kelvin scale, <strong>\u2212273.15 \u00b0C<\/strong> on the Celsius scale, and <strong>\u2212459.67 \u00b0F<\/strong> on the Fahrenheit scale.<\/p>\n<h3>Absolute Zero and Third Law of Thermodynamics<\/h3>\n<p>Third law of thermodynamics states:<\/p>\n<p><em>The entropy of a system approaches a constant value as the temperature approaches absolute zero.<\/em><br \/>\nBased on empirical evidence, this law states that the entropy of a pure crystalline substance is zero at the absolute zero of temperature, 0 K and that it is impossible using any process, no matter how idealized, to reduce the temperature of a system to absolute zero in a finite number of steps. This allows us to define a zero point for the thermal energy of a body.<\/div><\/div><\/div>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Reactor Physics and Thermal Hydraulics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC\u00a0Press; 2\u00a0edition, 2012, ISBN:\u00a0978-0415802871<\/li>\n<li>Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN:\u00a0978-3-319-13419-2<\/li>\n<li>Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition,\u00a0John Wiley &amp; Sons, 2006, ISBN:\u00a0978-0-470-03037-0<\/li>\n<li>Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010,\u00a0ISBN 978-1-4020-8670-0.<\/li>\n<li>U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2, and 3. June 1992.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Thermodynamics<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Within thermodynamics, physical property is any measurable property and whose value describes a state of a physical system. Our goal here will be to introduce\u00a0thermodynamic properties that are used in engineering thermodynamics. These properties will be further applied to energy systems and finally to\u00a0thermal\u00a0or\u00a0nuclear power plants. In general, thermodynamic properties can be divided into two &#8230; <a title=\"Thermodynamic Properties\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/\" aria-label=\"More on Thermodynamic Properties\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":16012,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16185"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=16185"}],"version-history":[{"count":6,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16185\/revisions"}],"predecessor-version":[{"id":34413,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16185\/revisions\/34413"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16012"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=16185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}