Unformatted text preview: acing s* by sideal for clarity, we can rewrite Eq. 12–61 for the entropy change of a gas during a process 1-2 as s2 s1 1 s2 s 1 2 ideal Ru 1 Zs2 Zs1 2 (12–63) cen84959_ch12.qxd 4/5/05 3:58 PM Page 673 Chapter 12
s2 s1 1 s2 s1 2 ideal R 1 Zs2 Zs1 2
(12–64) | 673 where the values of Zs are determined from the generalized entropy departure chart and the entropy change (s2 s1)ideal is determined from the idealgas relations for entropy change. Notice that the last terms on the right-hand side are zero for an ideal gas.
EXAMPLE 12–11 The h and s of Oxygen at High Pressures Determine the enthalpy change and the entropy change of oxygen per unit mole as it undergoes a change of state from 220 K and 5 MPa to 300 K and 10 MPa (a) by assuming ideal-gas behavior and (b) by accounting for the deviation from ideal-gas behavior. Solution Oxygen undergoes a process between two specified states. The
enthalpy and entropy changes are to be determined by assuming ideal-gas behavior and by accounting for the deviation from ideal-gas behavior. Analysis The critical temperature and pressure of oxygen are Tcr 154.8 K and Pcr 5.08 MPa (Table A–1), respectively. The oxygen remains above its critical temperature; therefore, it is in the gas phase, but its pressure is quite high. Therefore, the oxygen will deviate from ideal-gas behavior and should be treated as a real gas. (a) If the O2 is assumed to behave as an ideal gas, its enthalpy will depend on temperature only, and the enthalpy values at the initial and the final temperatures can be determined from the ideal-gas table of O2 (Table A–19) at the specified temperatures: 1 h2 h 1 2 ideal h 2,ideal 1 8736 h 1,ideal 6404 2 kJ> kmol 2332 kJ/kmol
The entropy depends on both temperature and pressure even for ideal gases. Under the ideal-gas assumption, the entropy change of oxygen is determined from
1s2 s 1 2 ideal s° 2 s° 1 R u ln P2 P1 1 205.213 196.171 2 kJ> kmol # K 1 8.314 kJ> kmol # K 2 ln 10 MPa 5 MPa 3 .28 kJ/kmol # K (b) The deviation from the ideal-gas behavior can be accounted for by determining the enthalpy and entropy departures from the generalized charts at each state: TR1 PR1 T1 Tcr P1 Pcr 220 K 1.42 154.8 K ∂ Z h1 5 MPa 0.98 5.08 MPa 0.53, Z s1 0.25 cen84959_ch12.qxd 4/5/05 3:58 PM Page 674 674 | Thermodynamics
and TR2 PR2 T2 Tcr P2 Pcr 300 K 1.94 154.8 K ∂ Z h2 10 MPa 1.97 5.08 MPa 0.48, Z s2 0.20 Then the enthalpy and entropy changes of oxygen during this process are determined by substituting the values above into Eqs. 12–58 and 12–63, h2 h1 2332 kJ> kmol 2396 kJ/kmol 1 h2 h 1 2 ideal R uTcr 1 Z h2 1 8.314 kJ> kmol Z h1 2 # K 2 3 154.8 K 1 0.48 0.53 2 4 and s2 s1 3.28 kJ> kmol 1 s2 s 1 2 ideal # # R u 1 Z s2 K K 1 8.314 kJ> kmol Z s1 2 # K 2 1 0.20 0.25 2 3.70 kJ/kmol Discussion Note that the ideal-gas assumption would underestimate the enthalpy change of the oxygen by 2.7 percent and the entropy change by 11.4 percent. SUMMARY
Some thermodynamic properties can be measured directly, but many others ca...
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- Thermodynamics, pm Page