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Thermodynamics: Entropy Change of Solids, Liquids, and an Ideal Gas

For an accurate prediction of entropy change the thermal dynamic tables should be used. However, in certain cases reasonable assumptions can be made to calculate the entropy change.

To predict entropy without use of the thermal dynamics tables to general equations could be used. Refer to equations 1 and 2. Both equations can only consider an isothermal process. If the process is not isothermal a more complex equation will need to be derived to relate the change in temperature to δQ.

change in entropy using internal energy change (1)

change in entropy using change in enthalpy (2)

Notice in both equations 1 and 2 the specific heat for volume can be used to estimate the specific energy, while the specific heat for pressure can be used to estimate the change in enthalpy. This can only be used for ideal gases, and is more accurate for small temperature changes or linear specific heat relation to temperatures so that an average can be used. If this relationship is not linear, large changes in temperature will affect the accuracy of the calculation.

Average cp compared to actual Cp temperature change

If a solid or liquid is of interest then it is safe to assume that a solid and a liquid are approximately incompressible. Due to this assumption the change in specific volume can be considered negligible, and the change in specific energy can then be used to approximate the entropy change of a solid or a liquid. Refer to equation 3.

Change in entropy for a solid (3)

Finally, for an gas going under an isothermal process equations 1 and 2 can be modified to include the ideal gas law. Refer to equations 4 and 5.

ideal gas change in entropy, volume (4)

ideal gas change in entropy, pressure (5)

For an ideal gas that is going under an isentropic process the temperature, specific volume, and pressure can be related using the following equations. These equations assume constant specific heat which means they will lose accuracy as the temperature difference increases.

temperature specific volume relation ideal gas (6)

temperature pressure relation ideal gas (7)

pressure specific volume rleation ideal gas (8)

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