An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and final pressure `P_(I)`. The same gas is expanded adiabatically to a volume 2V and final pressure in this case is `P_(A)`. In terms of the ratio of the two specific heats for the gas `gamma`, the ratio `P_(I)//P_(A)` is

Options

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

Answer

A

Explanation

For a isothermal process,
PV=constant
`:.PV=P_(1)2V`
`P_(1)=P/2`…….i
For an adiabatic process
`PV_(gamma)=` cosntant
`:.PV^(gamma)=P_(A)(2V)^(gamma)`
or `P_(A)=P/(2^(gamma))`……….ii
Divide I by ii we get
`(P_(1))/(P_(2))=(2^(gamma))/2=2^(gamma-1)`