An ideal gas undergoes a process where its pressure and volume vary according to the relation p = kV . The molar heat capacity of the gas for this process is given by

Step-by-step solution

The equation of the process is given by p = kV , which can be written as pV⁻¹ = constant . This represents a polytropic process of the form pV^n = constant , where n = -1 . The molar heat capacity for a polytropic process is given by C = C_V + R 1-n . Substituting n = -1 , we get: C = C_V + R 1 - (-1) C = C_V + R 2 Alternatively, using the ideal gas law pV = RT (for one mole) and p = kV , we get kV^2 = RT . Differentiating both sides, 2kV dV = R dT , which gives 2p dV = R dT , so p dV = R dT 2 . From the first law