An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and f number of vibrational modes. If the ratio of heat capacities C_P/C_V of the gas is 8/7 , then the value of f is :

Step-by-step solution

The internal energy of one mole of the polyatomic gas is given by the equipartition theorem. Each translational and rotational degree of freedom contributes 1 2 RT to the internal energy, while each vibrational mode contributes RT (since it has both kinetic and potential energy components). U = 3 ( 1 2 RT ) + 3 ( 1 2 RT ) + f(RT) = (3+f)RT The molar heat capacity at constant volume is: C_V = dU dT = (3+f)R The molar heat capacity at constant pressure is: C_P = C_V + R = (4+f)R The ratio of heat capacities is given