An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume `2V` and a final pressure `P_i`. If the same gas is expanded adiabatically to a volume `2V`, the final pressure is `P_a`. The ratio of the specific heats of the gas is `1.67`. The ratio `p_a//p_i` is _______.

Answer

`0.628`

Explanation

Under isothermal conditions, pV= constant
`:." "(p_i)(2V) = pV rArr p_i = p//2`
Under adiabatic conditions,
`pV^gamma` = constant where `gamma = 1.67 " ":." "(pa)(2V)^(1.67) rArr pa = p//(2)^(1.67)`
Therefore, the ratio `pa//p i = (2//2^(1.67)) = 0.628`