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_(1)V_(1)/(V_2)= P_(1)(V_(1))/(V_(1)//2)=2P_(1)`
For gas in B, when compression is adiabatic,
`P'_(2)V'_(2)=P_(1)V_(1)^(gamma)`
`P'_(2)=P_(1)((V_(1))/(V'_(2)))^(gamma)= P_(1)((V_(1))/(V_(1)//2))^(gamma)= 2^(gamma)P_(1)`
`:. (P'_(2))/(P_(2))=(2^(gamma)P_(1))/(2P_(1))= 2^(gamma-1)`