An ideal gas with pressure P, volume V and temperature T is expanded isothermically to a volume 2V and a final pressure `P_i,` If the same gas is expanded adiabatically to a volume 2V, the final pressure `P_a.` The ratio of the specific heats of the gas is 1.67. The ratio `(P_a)/(P_1)` is .......

Answer

B

Explanation

For isothermal expansion
`PxxV=P_ixx2V rArr P_i=P/2`
For adiabatic expansion
`Pvgamma=P_axx(2V)gamma rArr P_a=P/(2^(gamma))=P/(2^(1.67))`
`:. (P_a)/(P_i)=P/(2^(1.67))xx2/P=2/(2^(1.67))=0.628`