An ideal gas with pressure P , volume V and temperature T is expanded isothermally to a volume 2 ~V and a final pressure P _ i . The same gas is expanded adiabatically to a volume 2 ~V , the final pressure is P _ a . In terms of the ratio o

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An ideal gas with pressure P , volume V and temperature T is expanded isothermally to a volume 2 ~V and a final pressure P _ i . The same gas is expanded adiabatically to a volume 2 ~V , the final pressure is P _ a . In terms of the ratio of the two specific heats for the gas ' ', the ratio P _i P _ a is

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Correct answer: B. 2^ -1

For isothermal expansion we have aligned & P ₁ ~V ₁= P ₂ ~V ₂ & P ₂= P ₁ V ₁ ~V ₂ = P ₁ 1 2 = P 2 & P _ i = P 2 aligned For adiabatic process: aligned & P ₁ ~V ₁^ = P ₂ ~V ₂^ & P ₂= P ₁ ( V ₁ ~V ₂ )^ = P ₁ ( 1 2 )^ = P 2^ & P _ a = P 2^ & P _ i P _ a = 2^ 2 =2^ -1 aligned

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