One mole of an ideal gas with the adiabatic exponent `gamma` goes through a polytropic process as a result of which the absolute temperature of the gas increases `tau-fold`. The polytropic constant equal `n`. Find the entropy increment of the gas in this process.

Explanation

For the polytropic process with index `n`
`p V^n = constant`
Along this process (Sec 2.122)
`C = R((1)/(gamma -1) -(1)/(n - 1)) = (n - gamma)/((gamma -1)(n - 1)).R`
So `Delta S = int _(T_0)^(tau_(T_0)) C (dT)/(T) = (n - gamma)/((gamma - 1)(n - 1)) R 1n tau`.