Two samples, A and B of a gas at the same initial temperature and pressure are compressed from volume V to V/2, A isothermally and B adiabatically. The final pressure of A will be

Options

A. greater than the final pressure of `B`
B. equal to the final pressure of `B`
C. less than final pressure of `B`
D. twice the final pressure of `B`

Answer

C

Explanation

c. For isothermal process
`P_(1) V = P'_(2) (V)/(2) implies P'_(2) = 2 P_(1)`
For adabatic process
`P_(1) V^(gamma) = P_(2) ((V)/(2))^(gamma)`
`implies P_(2) = 2^(gamma) P_(1)`
Since `gamma gt 1, P_(2) gt P'_(2)`