An adiabatic cylinder fitted with an adiabatic piston at the right end of cylinder, is divided into two equal halves with a monoatomic gas on left side and diatomic gas on right side, using an imperme

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An adiabatic cylinder fitted with an adiabatic piston at the right end of cylinder, is divided into two equal halves with a monoatomic gas on left side and diatomic gas on right side, using an impermeable movable adiabatic wall. If the piston is pushed slowly to compress the diatomic gas to 3/4th of its original volume. The ratio of new volume of monoatomic gas to its initial volume would be

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Each gas is compressed reversibly and adiabatically, and the two pressures stay equal (movable wall). Initially both halves have the same pressure P 0 and volume V 0 . Diatomic (γ = 7/5): P = P 0 (4/3) 7/5 . Monoatomic (γ = 5/3): P = P 0 (V 0 /V m ) 5/3 . Equating: (V 0 /V m ) 5/3 = (4/3) 7/5 , so V m /V 0 = (3/4) 21/25 . Matches (c).

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