Two sample `A` and `B` of a gas initially at the square at the same pressure and temperature are compressed from volume `V` to `V//2` (A isothermally and `B` adiabatically). The final pressure of `A` is

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)`