Consider two containers A and B containing identical gases at the same pressure, volume and temperature. The gas in container A is compressed to half of its original volume isothermally while the gas in container B is compressed to half of its original value adiabatically. The ratio of final pressure of gas in B to that of gas in A is

Options

A. `2 ^(gamma-1)`
B. `(1/2)^(gamma-1)`
C. `(1/(1-gamma))^2`
D. `(1/(gamma-1))^2`

Answer

A

Explanation

When the compression is isothermal for gas in `A P_2 V_2 = P_1 V_1`
`P_2=(P_1V_1)/V_2=P_1=V_1/(V_1//2)=2P_1`
For gas in B, when compression is adiabatic
`P_2V_2^gamma =P_1V_1^(gamma)`
`P_2=P_1(V_1/(V_1//2))^gamma=2^(gamma)P_1`
So `P_2/P_1 =(2^(gamma)P_1)/(2P_1) = 2^(gamma-1)`