C_v for monoatomic gases is equal to(where, R = gas constant)

ANS:B - 1.5 R

The specific heat capacity at constant volume (𝐶𝑣Cv​) for monoatomic gases can be calculated using the equipartition theorem from statistical mechanics. According to this theorem, for each degree of freedom, a monoatomic gas has 12𝑘𝐵𝑇21​kB​T of energy, where 𝑘𝐵kB​ is the Boltzmann constant and 𝑇T is the temperature. For a monoatomic gas, such as helium (He), neon (Ne), or argon (Ar), there are three translational degrees of freedom and no rotational or vibrational degrees of freedom. So, the molar specific heat capacity at constant volume (𝐶𝑣Cv​) for a monoatomic gas is: 𝐶𝑣=32𝑅Cv​=23​R where 𝑅R is the gas constant. Therefore, the correct option is: 𝐶𝑣=32𝑅Cv​=23​R