A monoatomic gas at pressure ' P ' having volume ' V ' expands isothermally to a volume 2 ~V and then adiabatically to a volume 16 ~V . The final pressure of the gas is ( = 5 3 )

Step-by-step solution

For isothermal process: P ₁ ~V ₁= P ₂ ~V ₂ P ₂= P ₁ ~V ₁ ~V ₂ = P ₁ 2 For adiabatic process: P ₂ ~V ₂^ = P ₃ ~V ₃^ aligned & P ₃= P ₂ ( V ₂ ~V ₃ )^ = P ₂ ( 2 ~V 16 ~V )^ = P ₁ 2 ( 1 8 )^ 5 / 3 & = P 2 1 32 = P 64 aligned