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

Answer 1

It is most likely  that option (c) pA < pB and TA > TB

1. Given for the gas in state A is Cp − Cv is 1.00 R
2. It mean gas in state A is ideal
3. Given for the gas in state B is Cp − Cv is 1.08 R
4. It mean gas in state B is not ideal
5. For a gas to behave as ideal gas the temperature should be high and pressure is low
6. The gas in state behave like a ideal so the temperature TA must be higher and pressure pA must be lower
7. So the option c is correct  pA < pB and TA > TB

Answer 2

Explanation:

• It is most like that TA > TB and pA < pB in state A, Cp − Cv  = R for the gas. This shows that as an ideal gas in that state, it is acting, whereas in state B, Cp − Cv = 1.08 R, that is, the gas has the behaviour which in that state, is that of a real gas.
• An ideal gas should be a real gas at STP must be at a low pressure and very high temperature.
• Consequently, TA > TB and PA < PB, where the pressures are denoted by PA and PB and the temperature of the systems A and B are denoted by TA and TB.

Therefore the correct option is (c) pA = pB and TA < TB