Two samples A and B of a gas initially at the same pressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically). The final pressure of A is
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For sample $A \to$ in isothermal process By Boyle's law
$p_1 V_1 = p_2 V_2$ $\Rightarrow p_2 = p \left(\frac{V_1}{V_2}\right)$ $p_2 = p \left(\frac{V}{V/2}\right) = 2p$
$For sample B \rightarrow in adiabatic process By Poisson's law pV_{1}^{\gamma} = p_{2}V_{2}^{\gamma} \\ \therefore p_{2} = p(2)^{\gamma} \\ \therefore \gamma > 1 \\ \therefore 2\gamma > 2 \\ \therefore 2\gamma p > 2p \\ \text{or } (p_{2})_{B} > (p_{2})_{A} \\ \text{Final pressure of A is less than pressure of B.}$
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