A non-linear polyatomic gas is heated to a temperature such that exactly two of its vibrational modes become active. According to the law of equipartition of energy, the ratio of specific heat capacities = C_p C_v for this gas is:

Step-by-step solution

For a non-linear polyatomic gas, the number of translational degrees of freedom is 3 and the number of rotational degrees of freedom is 3. According to the law of equipartition of energy, each translational and rotational degree of freedom contributes 1 2 R to the molar heat capacity at constant volume ( C_v ). Each active vibrational mode contributes R to C_v (since it has both kinetic and potential energy components). Given that there are 2 active vibrational modes: C_v = 3 2 R + 3 2 R + 2(R) = 3R + 2R = 5R The m