Question

A gas expand adiabatically at constant pressure such that
$T\propto V^{\frac{-3}{2}}$. The value of $\gamma (\frac{C_p}{C_v}$) of the gas will be:

• A. 1.33
• B. 2.5
• C. 1.5
• D. 1.4

Answer 1

The correct option is B 2.5

Given: $T\propto V^{\frac{-3}{2}}$
$T=k{V}^{\frac{-3}{2}}$ or
$k=T{V}^{\frac{3}{2}}$....(1)

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

equating both the equations we get,

$T{V}^{\frac{3}{2}}=T{V}^{\gamma -1}$
$\gamma -1=\frac{3}{2}$
$\gamma =\frac{5}{2}$