A polyatomic gas at pressure 'P', having volume 'V' expands isothermally to a volume ' 3 V ' and then adiabatically to a volume ' 24 V '. The final pressure of gas is (for moderate temperature changes)

Step-by-step solution

The gas undergoes isothermal expansion from volume V to 3V at constant temperature. Since PV = constant for isothermal processes, the pressure reduces from P to P₂ = P V 3V = P 3 . The subsequent adiabatic expansion from volume 3V to 24V follows PV^ = constant , with = 4 3 for polyatomic gases. Using P₂(3V)^ 4/3 = P₃(24V)^ 4/3 : P₃ = P 3 ( 3V 24V )^ 4/3 = P 3 ( 1 8 )^ 4/3 = P 3 1 2^ 3 (4/3) = P 3 1 16 = P 48 Final pressure: P 48