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

The Correct Option is D

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: \[ C = C_v + \frac{R}{2V}. \]