A gas undergoes a change in which its pressure 'P' and volume 'V' are related as PV ^ n = constant, where n is a constant. If the specific heat of the gas in this change is zero, then the value of n is ( = adiabatic ratio)

Step-by-step solution

The molar specific heat for a polytropic process PV^n = constant is given by C = C_V + R 1-n , where C_V is the molar specific heat at constant volume, R is the universal gas constant, and n is the polytropic index. Given C_V = R -1 and that the specific heat for this process is zero, C = 0 : 0 = R -1 + R 1-n Dividing by R (since R 0 ): 0 = 1 -1 + 1 1-n Rearranging: 1 1-n = - 1 -1 1-n = -( -1) 1-n = 1- Subtracting 1 and multiplying by -1 : n = The value of n equals , corresponding to option D .