Question

One mole of a mono-atomic ideal gas undergoes a quasi-static process, which is depicted by a straight line joining points $(V_0, T_0)$ and $(2V_0, 3T_0)$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $(V_0, T_0)$ ?

• A. $R$
• B. $\frac{3}{2}R$
• C. $2R$
• D. $0$

Answer 1

The Correct Option is C

Heat capacity of an ideal gas in a thermodynamic process, $\because$ Ideal gas is monoatomic, $ C_{V} =\frac{f R}{2}=\frac{3 R}{2} $ $C_{\text {proces }} =C_{V}+\frac{p}{n} \cdot \frac{d V}{d T} $ $ \therefore =\frac{3}{2} R+\frac{p}{n} \cdot \frac{V_{0}}{2 T} $ $ \therefore C_{\text {proces }}=\frac{3}{2} R+\frac{n R T}{n 2 T} \,[\because pV = nRT]$ $=\frac{3}{2} R+\frac{R}{2}=2 R $