Question

The specific heat at constant pressure of a real gas obeying $PV^2 = RT$ equation is:

• A. $C_V + R$
• B. $\frac{R}{3} + C_V$
• C. $R$
• D. $C_V + \frac{R}{2V}$

Answer 1

Answer: (D)

$C_V + \frac{R}{2V}$

Answer 2

The first law of thermodynamics gives: $dQ = du + dW$

At constant pressure, this becomes: C dT = C_v dT + P dV \tag{1}

Given $PV^2 = RT$, differentiating both sides with respect to $T$ at constant $P$: $P(2V dV) = R dT$ $P dV = \frac{R}{2V} dT$

Substitute $P dV$ into equation (1): $C dT = C_v dT + \frac{R}{2V} dT$ $C = C_v + \frac{R}{2V}$

Thus, the specific heat at constant pressure is: $C = C_v + \frac{R}{2V}.$