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`.

Answer

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

Explanation

We have `triangleW = intpdv and triangle U = intC_(v)dT ,for an ideal gas pV = RT`,
`therefore " " triangle W = overset(T+triangleT)underset(T)int(RT)/(V)dV = overset(T+triangleT)underset(T)int(RT^2)/(a)(-a/T^(2)dT)=-RtriangleT`
`triangleU = overset(T+triangleT)underset(T)int(R)/(gamma-1)dT = (RtriangleT)/(gamma-1)`
`therefore " " triangleQ = triangleU + triangleW =(RtriangleT)/(gamma-1)+(-RtriangleT) = ((2-gamma)RtriangleT)/(gamma-1)`