P21_012 - 12. The connection between molar heat capacity...

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12. The connection between molar heat capacity and the degrees of freedom of a diatomic gas is given by setting f = 5 in Eq. 20-51. Thus, C V = 5 2 R , C p = 7 2 R , and γ = 7 5 . In addition to various equations from Chapter 20, we also make use of Eq. 21-4 of this chapter. We note that we are asked to use the ideal gas constant as R and not plug in its numerical value. We also recall that isothermal means constant- temperature, so T 2 = T 1 for the 1 2 process. The statement (at the end of the problem) regarding “permo le”maybetakentomeanthat n may be set identically equal to 1 wherever it appears. (a) The gas law in ratio form (see Sample Problem 20-1) as well as the adiabatic relations Eq. 20-54 and Eq. 20-56 are used to obtain p 2 = p 1 µ V 1 V 2 = p 1 3 , p 3 = p 1 µ V 1 V 3 γ = p 1 3 1 . 4 , T 3 = T 1 µ V 1 V 3 γ 1 = T 1 3 0 . 4 . (b) The energy and entropy contributions from all the processes are process 1 2
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