Question

The temperature of an ideal gas undergoing adiabatic expansion varies with volume as $T \propto V^{- \frac{3}{4}},$ then the value of $\frac{C_{P}}{C_{V}}$ for the gas is

• A. $\frac{3}{5}$
• B. $\frac{5}{3}$
• C. $\frac{7}{3}$
• D. $\frac{7}{4}$

Answer 1

Answer: (D)

Given,
$T \propto V^{- 3/4}\Rightarrow TV^{3/4}=Constant$
Comparing it with the relation for the adiabatic process we get
$TV^{\gamma - 1}=TV^{3/4}\Rightarrow \gamma -1=\frac{3}{4}\Rightarrow \gamma =\frac{7}{4}$