{"id":17229,"date":"2018-03-11T19:07:29","date_gmt":"2018-03-11T19:07:29","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=17229"},"modified":"2022-11-10T12:13:55","modified_gmt":"2022-11-10T12:13:55","slug":"third-law-of-thermodynamics-3rd-law","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/third-law-of-thermodynamics-3rd-law\/","title":{"rendered":"Third Law of Thermodynamics – 3rd Law"},"content":{"rendered":"
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According to the third law of thermodynamics:<\/strong><\/p>\n

The entropy of a system approaches a constant value as the temperature approaches absolute zero.<\/em><\/p>\n

Based on empirical evidence, this law states that the entropy of a pure crystalline substance is zero<\/strong> at the absolute zero of temperature<\/strong>, 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.<\/p>\n<\/div><\/div>\n

The German chemist Walther Nernst<\/strong> developed the third law of thermodynamics during the years 1906\u201312. For this research, Walther Nernst won the 1920 Nobel Prize in chemistry. Therefore the third law of thermodynamics is often referred to as Nernst\u2019s theorem<\/strong> or Nernst\u2019s postulate<\/strong>. As can be seen, the third law of thermodynamics states that the entropy of a system in thermodynamic equilibrium approaches zero<\/strong> as the temperature approaches zero.<\/strong> Or conversely, the absolute temperature <\/strong>of any pure crystalline substance<\/strong> in thermodynamic equilibrium approaches zero<\/strong> when the entropy approaches zero.<\/strong><\/p>\n

Nernst Heat Theorem<\/strong> (a consequence of the Third Law) is:<\/p>\n

It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations.<\/em><\/p>\n

Mathematically:<\/p>\n

\"nernst<\/a><\/p>\n

German physicist Max Planck later used the Nernst heat theorem<\/strong> to define the third law of thermodynamics in terms of entropy and absolute zero.<\/p>\n

Some materials (e.g.,, any amorphous solid) do not have a well-defined order at absolute zero. In these materials (e.g.,, glass), some finite entropy also remains at absolute zero because the system\u2019s microscopic structure (atom by atom) can be arranged in different ways (W \u2260 1). This constant entropy is known as the residual entropy, which is the difference between a non-equilibrium state and the crystal state of a substance close to absolute zero.<\/p>\n

Note that the exact definition of entropy is:<\/p>\n

Entropy = (Boltzmann\u2019s constant k) x logarithm of the number of possible states<\/strong><\/p>\n

S = k<\/em>B<\/sub><\/em> logW<\/em><\/span><\/strong><\/p>\n

This equation, which relates the microscopic details, or microstates, of the system (via W<\/em>) to its macroscopic state (via the entropy S<\/em><\/strong>), is the key idea of statistical mechanics.<\/p>\n

Absolute Zero<\/h2>\n

Absolute zero<\/strong> is the coldest theoretical temperature, 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.<\/p>\n

Mathematically:<\/p>\n

lim ST\u21920<\/sub> = 0 \u00a0<\/span><\/em><\/strong><\/p>\n

where<\/em><\/p>\n

S = entropy (J\/K)<\/em><\/p>\n

T = absolute temperature (K)<\/em><\/p>\n

Classically<\/strong>, this would be a state of motionlessness<\/strong>, but quantum<\/strong> uncertainty dictates that the particles still possess finite zero-point energy<\/strong>. Absolute zero<\/strong> is denoted as 0 K on the Kelvin scale, \u2212273.15 \u00b0C<\/strong> on the Celsius scale, and \u2212459.67 \u00b0F<\/strong> on the Fahrenheit scale.<\/p>\n

Relation to Heat Engines<\/h2>\n

According to Carnot\u2019s principle,<\/strong> which specifies limits on the maximum efficiency any heat engine can have is the Carnot efficiency. This principle also states that the efficiency of a Carnot cycle depends solely on the difference between the hot and cold temperature reservoirs.<\/p>\n

\"Carnot<\/a><\/p>\n

where:<\/p>\n