(a) Predict Cv and gamma for helium gas at room temperature using equipartition. (b) Do the same for nitrogen at room temperature. (c) At 3000 K, nitrogen's measured Cv approaches (7/2) R - explain. Solution: (a) He is monatomic: f = 3, Cv = (3/2) R = 12.5 J/(mol K), gamma = 5/3 = 1.67. (b) N2 is diatomic with vibrations frozen: f = 5, Cv = (5/2) R = 20.8 J/(mol K), gamma = 7/5 = 1.40. (c) At 3000 K, kT becomes comparable to the vibrational energy spacing, so the 2 vibrational modes unfreeze: f = 7, Cv = (7/2) R = 29.1 J/(mol K).