Question

An ideal gas is expanding such that $\frac{V}{T^3}=constant$. The Molar Specific heat of the gas is

• A. $\frac{11R}{2}$
• B. $\frac{7R}{2}$
• C. $\frac{5R}{2}$
• D. $\frac{9R}{2}$

Answer 1

The correct option is D $\frac{9R}{2}$

Given, $\frac{V}{T^3}=constant$
From idea gas equation, $\frac{PV}{T}=constant$
Hence for given ideal gas, $P^3{V}^2=constant\Rightarrow P{V}^{2/3}=constant$
For polytropic process $P{V}^x=constant$,
heat capacity $C=\frac{R}{1-x}+\frac{R}{\gamma -1}$
Here $x=\frac{2}{3},\gamma =\frac{5}{3}\Rightarrow C=3R+\frac{3R}{2}=\frac{9R}{2}$