question_answer

An ideal monatomic gas with pressure P, volume F and temperature T is expanded isothermally to a volume 2V and a final pressure \[{{P}_{i}}.\] If the same gas is expanded adiabatically to a volume 2V, the P final pressure is \[{{P}_{a}}.\]The ratio \[\frac{{{P}_{a}}}{{{P}_{i}}}\]is                                                                                                                                  [JEE ONLINE 26-05-2012]

A) \[{{2}^{-1/3}}\]                      

B)      \[{{2}^{1/3}}\]

C) \[{{2}^{2/3}}\]                       

D)      \[{{2}^{-2/3}}\]

Correct Answer: D

Solution :

[d] For isothermal process:

...(i)

For adiabatic process

( for monatomic gas )

or,                   [From (i)]