Question

An ideal gas has molar heat capacity $C_v$ at constant volume. Then molar heat capacity of this gas as a function of its volume V, if it undergoes process $T=T_0{e}^{\alpha V}$ is

• A. $C_v+\frac{RV}{\alpha }$
• B. $C_v+\frac{R}{\alpha V}$
• C. $C_v+\frac{R\alpha }{V^2}$
• D. $C_v+\frac{R{V}^2}{\alpha }$

Answer 1

The correct option is B $C_v+\frac{R}{\alpha V}$

Specific heat $C=\frac{\Delta Q}{n\Delta T}=\frac{n{C}_v\Delta T}{n\Delta T}+\frac{P\Delta V}{n\Delta T}$

$T=T_0{e}^{\alpha V}\Rightarrow \Delta T=T_0\alpha e^{\alpha V}\Delta V=\alpha T\Delta V$

$PV=nRT$

$C=C_v+\frac{nRT\Delta V}{Vn\alpha T\Delta V}=C_v+\frac{R}{\alpha V}$