Consider one mole of helium gas enclosed in a container at initial pressure P 1 and volume V 1 . It expands isothermally to volume 4 V 1 . After this, the gas expands adiabatically and its volume becomes 32 V 1 . The work done by the gas during isothermal and adiabatic expansion processes are W iso

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Consider one mole of helium gas enclosed in a container at initial pressure P 1 and volume V 1 . It expands isothermally to volume 4 V 1 . After this, the gas expands adiabatically and its volume becomes 32 V 1 . The work done by the gas during isothermal and adiabatic expansion processes are W iso and W adia , W iso W adia = f ln 2 , then f is _________ .

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Correct answer: A. A

∴ γ = 5 3 In isothermal process, W 1 = n R T ln 4 V V = 2 n R T ln 2 In adiabatic process, T ( 4 V ) γ - 1 = T ' ( 32 V ) γ - 1 ⇒ T ' = T ( 8 ) 1 - γ = T × 8 - 2 3 = T 4 W 2 = - n 3 2 R T ' - T = + 3 2 nR 3 T 4 = 9 8 n R T W 1 W 2 = 2 n R T ln 2 9 8 n R T = 16 9 ln 2 = f ln 2 f = 16 9 = 1 . 78

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