Question

The molar heat capacity of a diatomic ideal gas undergoing the process $P{V}^{1/4}=\text{constant}$ is

• A. $\frac{17}{6}R$
• B. $\frac{2}{5}R$
• C. $\frac{23}{6}R$
• D. 0.0

Answer 1

The correct option is C $\frac{23}{6}R$

$P{V}^{1/4}=\text{constant}$
$\Rightarrow \frac{RT}{V}\times V^{1/4}=\text{constant}$

$T{V}^{-3/4}=\text{constant}$
$dT.V^{-3/4}-\frac{3}{4}dV.V^{-7/4}.T=0$
or $\frac{dV}{dT}=\frac{4V}{3T}$
$C=\frac{dQ}{dT}=\frac{dU}{dT}+P\frac{dV}{dT}=C_{\text{v}}+P\frac{4V}{3T}$

$C=\frac{5}{2}R+\frac{4}{3}R=\frac{23}{6}R$