One mole of an ideal diatomic gas undergoes a thermodynamic process described by the equation PT = constant , where P is pressure and T is absolute temperature. The molar heat capacity of the gas for this process is:

Step-by-step solution

The given process equation is PT = constant . From the ideal gas equation, T = PV nR . Substituting this into the process equation gives: P ( PV nR ) = constant P^2V = constant ' P V^ 1/2 = constant '' Comparing this with the standard polytropic process equation PV^x = constant , we get the polytropic index x = 1 2 . The molar heat capacity for a polytropic process is given by: C = C_v + R 1-x For a diatomic gas, the molar heat capacity at constant volume is C_v = 5 2 R . Substituting the values of C_v and x : C =