Question

A gas expand adiabatically at constant pressure such that
$T\propto V^{-3/4}$. The value of $\gamma \left(\frac{C_p}{C_v}\right)$ of the gas will be:

• A. $1.5$
• B. $1.75$
• C. $1.33$
• D. $1.6$

Answer 1

The correct option is B $1.75$

Given: $T\propto V^{-3/4}$
$\Rightarrow T=k{V}^{-3/4}(\because k=\text{propertionality constant})$
$\Rightarrow k=T{V}^{3/4}....\left(1\right)$

We also know, for adiabatic process
$k=T{V}^{\gamma -1}....\left(2\right)$
where $k=$ constant

Equating both the equations we get,
$T{V}^{3/4}=T{V}^{\gamma -1}$
$\Rightarrow \gamma -1=\frac{3}{4}$
$\Rightarrow \gamma =\frac{7}{4}=1.75$