A gas ( γ = 1 . 5 ) is suddenly compressed to ( 1 / 4 ) t h its initial volume. Then find the ratio of…

When the compression process is performed suddenly or instantly then there is not enough time for heat transfer, therefore the sudden compression process is a adiabatic compression process.

Ideal gas equation for adiabatic process, $P{V}^{\gamma }=\text{Constant}$

$$\begin{gathered} \therefore P_i{V}_i^{\gamma }=P_f{V}_f^{\gamma } \\ \Rightarrow \frac{P_f}{P_i}=\frac{V_i^{\gamma }}{V_f^{\gamma }}={\left[\frac{V_i}{V_f}\right]}^{\gamma }={\left[\frac{V_i}{{\displaystyle \frac{V_i}{4}}}\right]}^{1.5} \\ \Rightarrow \frac{P_f}{P_i}=\frac{8}{1} \end{gathered}$$