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Consider two containers A and B containi...

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

A

`2^(gamma-1)`

B

`(1/2)^(gamma-1)`

C

`(1/(1-gamma))^2`

D

`(1/(gamma-1))^2`

Text Solution

Verified by Experts

The correct Answer is:
A

Both the process involves compression of the gas.
Isothermal compression (gas A) during 1 `to` 2
`P_1V_1=P_2V_2`
`P_0(2V_0)^gamma=P_2(V_0)^gamma`
`therefore P_0(2V_0)=P_2(V_0)` from graph-1
`P_2=2P_0` …(1)
Adiabatic compression (gas B) during `1 to 2`
`P_1V_1^gamma =P_2V_2^gamma`
`P_0(2V_0)^gamma=P_2(V_0)^gamma` from graph -2
`therefore P_2=((2V_0)/V_0)^gamma P_0`
`therefore P_2=2^gamma P_0`...(2)
Ratio of equ. (2) and equ. (1)
`P_2/P_1=(2^gamma P_0)/(2P_0)`
`therefore P_2/P_1=2^(gamma-1)`
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