A fixed mass of gas (γ= 1.4) at 1 atm  is compressed adiabatically to 5 atm. and then allowed to expand isothermally to its original volume. The pressure at the end of the isothermal process will be

Let P1,V1 be the initial pressure and volume and P2,V2 those after adiabatic compression respectively. ThenP1V1γ=P2V2γ  or  V2/V1γ=P1/P2∴ V2V1=P1P21/γ=151/1⋅4log⁡V2V1=11⋅4[log⁡1−log⁡5]=11⋅4[0−0⋅6990]=−0⋅4993=1¯⋅5007V2V1=0⋅3167The gas now expands isothermally to original volume V1 . Let P3 be the pressure after this expansion. ThenP3V1=P2V2P3=P2V2/V1=(5atm.)×0⋅3167=1⋅58 atm