Thermodynamics

Equating the coefficients of dT and dP in Eqs. 12–31 and 12–33, we obtainUsing the fourth Maxwell relation (Eq. 12–19), we havea 0h0P b v T a 0vT 0T b PSubstituting this into Eq. 12–31, we obtain the desired relation for dh:(12–34)(12–35)The change in enthalpy of a simple compressible system associated with achange of state from (T 1 , P 1 ) to (T 2 , P 2 ) is determined by integration:h 2 h 1 T 2a 0s0T b c pP Ta 0h0P b v T a 0sT 0P b Tdh c p d T c v T a 0v0T b d dPPT 1c p dT P 2(12–36)In reality, one needs only to determine either u 2 u 1 from Eq. 12–30 orh 2 h 1 from Eq. 12–36, depending on which is more suitable to the data athand. The other can easily be determined by using the definition of enthalpyh u Pv:h 2 h 1 u 2 u 1 1P 2 v 2 P 1 v 1 2P 1c v T a 0v0T b d dPP(12–37)Chapter 12 | 663Entropy ChangesBelow we develop two general relations for the entropy change of a simplecompressible system.The first relation is obtained by replacing the first partial derivative in thetotal differential ds (Eq. 12–26) by Eq. 12–28 and the second partial derivativeby the third Maxwell relation (Eq. 12–18), yieldingand(12–38)(12–39)The second relation is obtained by replacing the first partial derivative in thetotal differential of ds (Eq. 12–32) by Eq. 12–34, and the second partialderivative by the fourth Maxwell relation (Eq. 12–19), yieldingandds c vTs 2 s 1 T 2T 1ds c PTc vT dT v 20vdT a0T b dPPc p0PdT a0T b dvv(12–40)T 2s 2 s 1 (12–41)T dT T 1 P 2a 0v0T b dPP P1Either relation can be used to determine the entropy change. The properchoice depends on the available data.v 1a 0P0T b dvv