Question

An ideal gas is expanding such that $\frac{V}{T^2}=constant$. The Molar Specific heat capacity 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 B $\frac{7R}{2}$

Given, $\frac{V}{T^2}=constant$
From idea gas equation, $\frac{PV}{T}=constant$
Hence for given ideal gas, $P^{2}V=constant\Rightarrow P{V}^{1/2}=constant$
For polytropic process $P{V}^x=constant$,
heat capacity $C=\frac{R}{1-x}+\frac{R}{\gamma -1}$
Here $x=\frac{1}{2},\gamma =\frac{5}{3}\Rightarrow C=2R+\frac{3R}{2}=\frac{7R}{2}$