Thermodynamics

674 | ThermodynamicsandThen the enthalpy and entropy changes of oxygen during this process aredetermined by substituting the values above into Eqs. 12–58 and 12–63,andT R2 T 2 300 KT cr 154.8 K 1.94P R2 P ∂ Z2 10 MPah2 0.48, Z s2 0.20P cr 5.08 MPa 1.97h 2 h 1 1h 2 h 1 2 ideal R u T cr 1Z h2 Z h12 2332 kJ>kmol 18.314 kJ>kmol # K23154.8 K 10.48 0.5324 2396 kJ/kmols2 s 1 1 s 2 s 12 ideal R u 1Z s2 Z s12 3.28 kJ>kmol # K 18.314 kJ>kmol # K210.20 0.252 3.70 kJ/kmol # KDiscussion Note that the ideal-gas assumption would underestimate theenthalpy change of the oxygen by 2.7 percent and the entropy change by11.4 percent.SUMMARYSome thermodynamic properties can be measured directly, butmany others cannot. Therefore, it is necessary to developsome relations between these two groups so that the propertiesthat cannot be measured directly can be evaluated. The derivationsare based on the fact that properties are point functions,and the state of a simple, compressible system is completelyspecified by any two independent, intensive properties.The equations that relate the partial derivatives of propertiesP, v, T, and s of a simple compressible substance to eachother are called the Maxwell relations. They are obtainedfrom the four Gibbs equations, expressed asdu T ds P dvdh T ds v dPda s dT P dvdg s dT v dPThe Maxwell relations area 0T0v b a 0Ps 0s b va 0T0P b a 0vs 0s b Pa 0s0v b a 0PT 0T b va 0s0P b a 0vT 0T b PThe Clapeyron equation enables us to determine the enthalpychange associated with a phase change from a knowledge ofP, v, and T data alone. It is expressed asa dPdT b h fgsat T v fg