The volume of one mode of an ideal gas with adiabatic exponent `gamma` is varied according to the law `V = a//T`, where a is constant . Find the amount of heat obtained by the gas in this process, if the temperature is increased by `Delta T`.

Explanation

The differential work done by the gas
`dA = pdV = (vRT^2)/(a) (- (a)/(T^2)) dT = -vRdT`
`(as pV = vRT and V = (a)/(T))`
So, `A = -int_T^(T + Delta T) vRdT = - gamma R Delta T`
From the first law of thermodymics
`Q = Delta U + A (vR)/(gamma - 1) Delta T - vR Delta T`
=`v R Delta T. (2 - gamma)/(gamma -1) = R Delta T. (2 - gamma)/(gamma - 1)(for v = 1 "mole")`.