Question

A gas $(\gamma =1.3)$ is enclosed in an insulated vessel fitted with insulating piston at a pressure of ${10}^{5}N/m^2$. On suddenly pressing the piston the volume is reduced to half the initial volume. Thee final pressure of the gas is

• A. $2^{0.7}\times {10}^5$
• B. $2^{1.3}\times {10}^5$
• C. $2^{1.4}\times {10}^5$
• D. None of these

Answer 1

The correct option is B $2^{1.3}\times {10}^5$

Given: $\gamma =1.3,P_1={10}^{5}N/m^2,V_1=2V_2$

As it is a adiabatic process, so using the relation

$\therefore P{V}^{\gamma }=k\left(constant\right)$

$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$

$P_2=2^{1.3}\times {10}^{5}N/m^2$