Consider two containers A and B containing identical gases at the same pressure, volume and temperature. The gas in container A is compressed to half of its original volume isothermally while the gas in container B is compressed to half of its original value adiabatically. The ratio of final pressure of gas in B to that of gas in A is

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Consider the P−V diagram shown for the container A and container B.Both the process involves compression of the gas(i) Isothermal compression (Gas A) (during 1→2)P1​V1​=P2​V2​⟹P0​(2V0​)γ=P2​(V0​)γ⟹P0​(2V0​)=P2​(V0​)(II) Adiabatic compression (Gas B) (during 1→2)P1​V1γ​=P2​V2γ​⟹P0​(2V0​)γ=P2​(V0​)γ⟹P2​=(V0​2V0​​)γ     P0​=(2)γP0​Hence (P2​)A​(P2​)B​​= Ratio of final pressure =2P0​(2)γP0​​=2γ−1where, γ is the ratio of specific heat capacities for the gas.

Question Text	Consider two containers $A$ and $B$ containing identical gases at the same pressure, volume and temperature. The gas in container $A$ is compressed to half of its original volume isothermally while the gas in container $B$ is compressed to half of its original value adiabatically. The ratio of final pressure of gas in $B$ to that of gas in $A$ is
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