An ideal gas, ( C _ v = 5 2 R ), is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is (298 ~K ) and (5 ~atm ), respectively then the final temperature is ____

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An ideal gas, ( C _ v = 5 2 R ), is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is (298 ~K ) and (5 ~atm ), respectively then the final temperature is _______ ( K ) (nearest integer). [ ( C _ v ) is the molar heat capacity at constant volume]

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aligned & U = q + w ( q =0) & nC _ V T =- P _ ext ( V ₂- V ₁ ) & V ₂=2 ~V ₁ & nRT ₂ P ₂ = 2 nRT ₁ P ₁ & P ₁=5, ~T ₁=298 & P ₂= 5 ~T ₂ 2 298 & n 5 2 R ( T ₂- T ₁ )=-1 ( nRT ₂ P ₁ - nRT ₁ P ₁ ) aligned Put T ₁=298 and P ₂= 5 ~T ₂ 2 298 Solve and we get T₂=274.16 ~K T ₂ 274 ~K

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