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Question

The value of Cp − Cv is 1.00 R for a gas sample in state A and 1.08 R in state B. Let pA and pB denote the pressures and TA and TB denote the temperatures of the states A and B, respectively. It is most likely that
(a) pA < pB and TA > TB
(b) pA > pB and TA < TB
(c) pA = pB and TA < TB
(d) pA > pB and TA = TB

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Solution

(a) pA < pB and TA > TB

Cp − Cv = R for the gas in state A, which means it is acting as an ideal gas in that state, whereas CpCv = 1.08R in state B, i.e. the behaviour of the gas is that of a real gas in that state. To be an ideal gas, a real gas at STP should be at a very high temperature and low pressure. Therefore, PA < PB and TA > TB where PA and PB denotes the pressure and TA and TB denotes the temperature of system A and B reepectively.

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