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Unformatted text preview: own in (P0 Fig. 12–16. Although this approach increases the number of integrations, it also simplifies them since one property remains constant now during each part of the process. The pressure P0 can be chosen to be very low or zero, so that constant process. the gas can be treated as an ideal gas during the P0 Using a superscript asterisk (*) to denote an idealgas state, we can express the enthalpy change of a real gas during process 12 as
h2
P2 P 0 =0 P 2 h1 1 h2 h* 2 2 1 h* 2 h* 2 1
P2 1 h* 1 h1 2 (12–53) where, from Eq. 12–36,
h2 h* 2 h* 1 h* 2 h* 1
T1 * P1 0
P* 2 T2 cv 0 Ta 0v bd 0T P T
T2 dP
T2 P0 cv Ta 0v bd 0T P T dP (12–54)
T2 cp dT cv T1 cp0 1 T 2 dT
P1 (12–55) h1 0
P1 Ta 0v bd 0T P T dP
T1 P0 cv Ta 0v bd 0T P T dP (12–56)
T1 The difference between h and h* is called the enthalpy departure, and it represents the variation of the enthalpy of a gas with pressure at a fixed temperature. The calculation of enthalpy departure requires a knowledge of the PvT behavior of the gas. In the absence of such data, we can use the relation Pv ZRT, where Z is the compressibility factor. Substituting cen84959_ch12.qxd 4/5/05 3:58 PM Page 671 Chapter 12
v ZRT/P and simplifying Eq. 12–56, we can write the enthalpy departure at any temperature T and pressure P as
1 h* h2T
P  671 RT 2
0 a 0 Z dP b 0T P P The above equation can be generalized by expressing it in terms of the reduced Pcr PR. After some manipulations, the coordinates, using T TcrTR and P enthalpy departure can be expressed in a nondimensionalized form as
Zh 1 h* R uTcr h2T
PR 2 TR 0 a 0Z b d 1 ln PR 2 0 TR PR (12–57) where Zh is called the enthalpy departure factor. The integral in the above equation can be performed graphically or numerically by employing data from the compressibility charts for various values of PR and TR. The values of Zh are presented in graphical form as a function of PR and TR in Fig. A–29. This graph is called the generalized enthalpy departure chart, and it is used to determine the deviation of the enthalpy of a gas at a given P and T from the enthalpy of an ideal gas at the same T. By replacing h* by hideal for clarity, Eq. 12–53 for the enthalpy change of a gas during a process 12 can be rewritten as
h2 h1 1 h2 1 h2 h1 2 ideal h1 2 ideal RuTcr 1 Zh2 RTcr 1 Zh2 Zh1 2 Zh1 2
(12–58) or
h2 h1 (12–59) where the values–of Zh–are determined from the generalized enthalpy deparh1)ideal is determined from the idealgas tables. Notice ture chart and (h2 that the last terms on the righthand side are zero for an ideal gas. Internal Energy Changes of Real Gases
The internal energy change of a real gas is determined by relating it to the – – u ZR T: – – enthalpy change through the definition h u Pv u
u2 u1 1 h2 h1 2 R u 1 Z 2 T2 Z 1T1 2
(12–60) Entropy Changes of Real Gases
The entropy change of a real gas is determined by following an approach similar to that used above for the enthalpy change. There is some difference in derivation, however, owing to the dependence of the idealgas entropy on pressure as well as the temperature....
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This note was uploaded on 03/09/2009 for the course ME 430 taught by Professor Y during the Spring '09 term at CUNY City.
 Spring '09
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