Chemistry - Thermodynamics - I Question with Solution | TestHub

$$C_M=C_V+\frac{R}{1-x}=\frac{3}{2}R+\frac{R}{1-x}=\frac{13R}{6}$$

$$\frac{1}{1-x}=\frac{13}{6}-\frac{3}{2}=\frac{13-9}{6}=\frac{4}{6}$$

$$1-x=\frac{3}{2}\Rightarrow x=-\frac{1}{2}$$

For a polytropic process, $P{V}^x=const.$, so $P{V}^{-1/2}=K\Rightarrow P^2=KV$.

Also, $T{V}^{x-1}=const.$, so $T{V}^{-3/2}=K^{\prime }\Rightarrow T^2=K^{\prime }{V}^3$