The specific heat at constant pressure of a real gas obeying equation is:

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Solution

Q.
The specific heat at constant pressure of a real gas obeying $P V^{2} = R T$ equation is: [2024]

1 $\frac{R}{3} + C_{v}$

2 $R$

3 $C_{v} + R$

4 $C_{v} + \frac{R}{2 V}$

Ans.
(4)

$d Q = d U + d W$

$n C d T = n C_{v} d T + d W,$ We need to find $d W$

we have $P V^{2} = R T, P =$ constant

differentiating, $P 2 V d V = R d T \Rightarrow P d V = \frac{R . d T}{2 V}$

Also, $d W = P d V = \frac{R . d T}{2 V}$

For one mole of gas, $C . d T = C_{v} d T + \frac{R . d T}{2 V} \Rightarrow C = C_{v} + \frac{R}{2 V}$

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