An ideal gas goes through a polytropic process. Find the polytropic exponent `n` if in this process the coefficient
(a) of diffusion ,
(b) of viscosity ,
( c) of heat conductivity remains constant.

Explanation

(a) `D alpha V sqrt(T) alpha sqrt(p V^3)`
Thus `D` remains constant in the process `pV^3 = constant`
So polytropic index `n = 3`
(b) `eta alpha sqrt(T) alpha sqrt(pV)`
So `eta` remains constant in the isothermal process
`pV = constant, n = 1 here`
( c) Heat conductivity `k = eta C_V`
and `C_V` is a constant for the ideal gas
Thus `n = 1` here also.