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. The final pressure of the gas is
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(b)$\because \;P{V^\gamma } = k$(constant) ==> ${P_1}V_1^\gamma = {P_2}V_2^\gamma $
$⇒$ ${P_2} = {P_1}{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^\gamma } = {10^5} \times {(2)^{1.3}}$ $(\because \;{V_2} = \frac{{{V_1}}}{2})$
$⇒$ ${P_2} = {P_1}{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^\gamma } = {10^5} \times {(2)^{1.3}}$ $(\because \;{V_2} = \frac{{{V_1}}}{2})$
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