An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure P_(1). The same gas is expanded adiabatically to a volume 2V, the final final pressure is P_(A). In terms of the ratio of the two specific heats for the gas gamma, the ratio P_(I)//P_(A) is

An ideal gas with pressure P, volume V and temperature T is expanded i

1.	An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure P_(1). The same gas is expanded adiabatically to a volume 2V, the final final pressure is P_(A). In terms of the ratio of the two specific heats for the gas gamma, the ratio P_(I)//P_(A) is
Answer» <P>`2^(gamma - 1)` `2^(1- gamma)` `2^(gamma)` `2gamma` Solution :For an isothermal PROCESS, PV = CONSTANT `:. PV = P_(I) 2V` or `P_(I) = (P)/(2)` …(i) For an adiabatic process, `PV^(gamma)` = constant `:. PV^(gamma) = P_(A) (2V)^(gamma)` or `P_(A) = (P)/(2^(gamma))` …(ii) Divide (i) by (ii), we get `(P_(I))/(P_(A)) = (2^(gamma))/(2) = 2^(gamma - 1)`