Entropy Changes of an Ideal Gas

For one mole or a unit mass of fluid undergoing a mechanically reversible process in a closed system, the first law, Eq. (2.8), becomes  

For an ideal gas, dH = CpdT and V = RT/P. Witli these substitutions and then division 

Although derived for a mechanically reversible process, tliis equation relates properties only, and is independent of the process causing the change of state. It is therefore a general equation for the calculation of entropy changes of an ideal gas. 

Smce dtis integral must often be evaluated, we mclude m App. D representative computer programs for its evaluation. For computational purposes tlie ri it side of Eq. (5,15) is defined as the fimction, ICPS(TO,T A,B,C,D), Equation (5.15) then becomes  

The computer programs also calculate a meait heat capacity defined a.s  

Consider one mole of an ideal gas that goes from state 1 (7j, Vj, Pj) to state 2 J2, V2, /y Since our hypothetical path is reversible, dW = PdV, and Eq.3.10.1 yields  

Notice that while the enthalpy and internal energy changes of an ideal gas are functions of temperature only (Section 2.6.3), the entropy change depends on both, temperature and pressure (or volume), changes. 

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This equation for the entropy change of an ideal gas finds application in the next chapter. 

This form of the eqnation for entropy changes of an ideal gas may be useful when iterative calculations are reqnired. 

Entropy change of an ideal gas with 7 and P as independent variables if CJ, is a constant... 

Entropy change of an ideal gas is derived from the thermod5mamic relations (Equation 3.42a or 3.42b) and expressed as... 

Before we abandon the device of Example 3.6, let us take a second look at it. How can we make the total entropy change positive We have seen, in Section 3.12.4, that the entropy change of an ideal gas between two states depends not only on its tenq>erature change, but also on that of its pressure. What will happen, thus, if the pressure of the entering air is - say - S atm, and everything else remains the same Assume, for simplicity, ideal gas behavior with Cp temperature independent and equal to 28 J/mol K. 

Develop a hypothetical reversible path to calculate the entropy change between any two states. Develop the expression for the entropy change of an ideal gas, a liquid, or a solid when the heat capacity is known. 

Since entropy is defined in terms of heat absorbed during a recersibZe process, we can calculate the entropy between any two states by constructing a path that follows a reversible process from state 1 to state 2. In this way, we found that the entropy change of an ideal gas is given by ... 

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