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732 the results obtained in this way usually are

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Unformatted text preview: eat values evaluated at the average temperature (Fig. 7–32). The results obtained in this way usually are sufficiently accurate if the temperature range is not greater than a few hundred degrees. The entropy-change relations for ideal gases under the constant-specificheat assumption are easily obtained by replacing Cυ(T) and Cp(T) in Eqs. 7–31 and 7–32 by Cυ, av and Cp, av, respectively, and performing the integrations. We obtain s2 s1 Cυ, av ln T2 T1 R ln υ2 υ1 (kJ/kg · K) (7–33) and s2 s1 Cp, av ln T2 T1 R ln P2 P1 (kJ/kg · K) (7–34) Entropy changes can also be expressed on a unit-mole basis by multiplying these relations by molar mass: – s2 – s1 T2 – C υ, av ln T1 Ru ln υ2 υ1 (kJ/kmol · K) (7–35) – s2 – s1 T2 – C p, av ln T1 Ru ln P2 P1 (kJ/kmol · K) (7–36) and Cp Actual Cp Average Cp Cp, av T1 Tav T2 T FIGURE 7–32 Under the constant-specific-heat assumption, the specific heat is assumed to be constant at some average value. cen54261_ch07.qxd 11/18/03 9:57 AM Page 298 298 FUNDAMENTALS OF THERMAL-FLUID SCIENCES Variable Specific Heats (Exact Analysis) When the temperature change during a process is large and the specific heats of the ideal gas vary nonlinearly within the temperature range, the assumption of constant spe...
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