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 adiabatically). The final pressure of $ A$ is
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(c)$A$ is compressed isothermally, hence
${P_1}V = {P_2}\frac{V}{2} \Rightarrow {P_2} = 2{P_1}$
and $B$ is compressed adiabatically, hence
${P_1}{V^\gamma } = {P_2}\,{\left( {\frac{V}{2}} \right)^\gamma } \Rightarrow {P_2} = {(2)^\gamma }{P_1}$
Since $\gamma > 1$, hence ${P_2}' > {P_2}$or ${P_2} < {P'_2}$
${P_1}V = {P_2}\frac{V}{2} \Rightarrow {P_2} = 2{P_1}$
and $B$ is compressed adiabatically, hence
${P_1}{V^\gamma } = {P_2}\,{\left( {\frac{V}{2}} \right)^\gamma } \Rightarrow {P_2} = {(2)^\gamma }{P_1}$
Since $\gamma > 1$, hence ${P_2}' > {P_2}$or ${P_2} < {P'_2}$
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