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)`1

Answer

A

Explanation

Consider the p-V diagram shown for the container A (isothermal) and for container B (adiabatic).

Both the process involving compression of the gas.
For isothermal process (GasA) (during 1`rarr`2)
`P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma)`
`rArrP_(0)(2V_(0))^(gamma)=P_(0)(V_(0))^(gamma)`
`rArrP_(2)=((2P_(0))/(V_(0)))^(gamma)P_(0)=(2)^(gamma)P_(0)`
Hence, `((P_(2))_(b))/((P_(2))_(A))=` RAte of final pressure
`=((2)^(gamma)P_(0))/(2P_(0))=2^(gamma-1)`
Whre, `gamma` is ratio of specific heat capacities for the gas.