{"id":17279,"date":"2018-03-23T19:23:27","date_gmt":"2018-03-23T19:23:27","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=17279"},"modified":"2022-11-10T12:45:21","modified_gmt":"2022-11-10T12:45:21","slug":"isentropic-process","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-processes\/isentropic-process\/","title":{"rendered":"Isentropic Process"},"content":{"rendered":"
An isentropic process<\/strong> is a thermodynamic process<\/strong><\/a>\u00a0in which the entropy<\/strong> <\/a>of the fluid or gas remains constant. It means the isentropic process<\/strong> is a special case of an adiabatic process<\/strong> in which there is no transfer of heat or matter. It is a reversible adiabatic process<\/strong>. An isentropic process<\/strong> can also be called a constant entropy process.<\/div><\/div>\n

In engineering, such an idealized process is very useful for comparison with real processes.<\/p>\n

Since there are changes in internal energy<\/a> (dU) and changes in system volume (\u2206V), engineers often use the enthalpy<\/strong><\/a> of the system, which is defined as:<\/p>\n

H = U + pV<\/em><\/strong><\/p>\n

\"Isentropic<\/a>
Table of main characteristics<\/figcaption><\/figure>\n

In many thermodynamic analyses, it is convenient to use enthalpy<\/strong> instead of internal energy, especially in the case of the first law of thermodynamics<\/strong>.<\/p>\n

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Isentropic Process and the First Law<\/h2>\n

The first law of thermodynamics in terms of enthalpy<\/a><\/strong>:<\/p>\n

dH = dQ + Vdp<\/span><\/strong><\/p>\n

or<\/span><\/strong><\/p>\n

dH = TdS + Vdp<\/span><\/strong><\/p>\n

 <\/p>\n

See also: First Law of Thermodynamics<\/a><\/p>\n

See also: Ideal Gas Law<\/a><\/p>\n

See also: What is Enthalpy<\/a><\/p>\n

In this equation, the term Vdp<\/strong> is a flow process work. <\/strong>This work, \u00a0Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e., change in pressure. As can be seen, this form of the law simplifies the description of energy transfer<\/strong>. At constant entropy<\/strong>, i.e., in isentropic process, the enthalpy change<\/strong> equals the flow process work<\/strong> done on or by the system:<\/p>\n

Isentropic process (dQ = 0):<\/strong><\/p>\n

dH = Vdp \u00a0\u00a0\u00a0\u00a0\u2192 \u00a0\u00a0\u00a0\u00a0W = H<\/strong>2<\/sub><\/strong> \u2013 H<\/strong>1<\/sub><\/strong> \u00a0\u00a0\u00a0\u00a0\u2192 \u00a0\u00a0\u00a0\u00a0H<\/strong>2<\/sub><\/strong> \u2013 H<\/strong>1<\/sub><\/strong> = C<\/em><\/strong>p<\/sub><\/em><\/strong> (T<\/em><\/strong>2<\/sub><\/em><\/strong> – T<\/em><\/strong>1<\/sub><\/em><\/strong>) \u00a0\u00a0\u00a0<\/em><\/strong>(for ideal gas<\/a>)<\/em><\/p>\n

Isentropic Expansion – Isentropic Compression<\/h2>\n

See also: What is an Ideal Gas<\/a><\/p>\n

In an ideal gas<\/a>, molecules have no volume and do not interact. According to the ideal gas law<\/a>, pressure<\/a> varies linearly with temperature<\/a> and quantity and inversely with volume<\/a>.<\/p>\n

pV = nRT<\/em><\/span><\/strong><\/p>\n

where:<\/p>\n