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

The gas in container A is comprssed isothermally,
`therefore P_(1)V_(1)=P_(2)V_(2)` ltbr. Or `P_(2)=(P_(1)V_(1))/(V_(2))=P_(1)(V_(1))/(V_(1//2))=2P_(1)`
Again the gas in container B is compressed adiabatically,
`therefore P_(1)V_(1)^(gamma)=P_(2)(V_(2))^(gamma)`
`P_(2)=P_(1)(V_(1)^(gamma))/((V_(2))^(gamma))=P_(1)((V_(1)/(V_(1)//(2))=2^(gammaP_(1)`
Hence `(P_(2))/(P_(2))=(2^(gammaP_(1))/(2P_(1))=2^(gamma-1)`