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 is container B is compressed to half of its original vlue adiabatically. The ratio of final pressure of gas of B to that of gas in A is

Explanation

Figure shows the P-V diagrams for two gases expanded from volume V to 2V. As an adiabatic is steeper than an isotherm, so the adiabatic expansion curve AB lies below the isothermal expansion curve AC.

Work done in adiabatic expansion = area ABDE Work done in isothermal expansion = area ACDE. As area ACDE `gt` area ABDE, work done is greater for adiabatic expansion