Answer to Question #311945 in Physical Chemistry for rup

Question

Using the "equipartion" of energy concept, estimate the ideal gas $c_p$ (not $c_v$) in units of $k_B$ for "low-temperature" where no vibrational modes are activated. (if you calculate $c_p = 42k_B$, enter 42 as your answer)

Answer 1

According to "equipartion" of energy concept the gas atom has three degrees of freedom and, therefore, will have an average total energy of 3/2 * K_b * T.

The equation of state for an ideal gas for N particles:

P * V = n * R * T = N * K_b * T.

According to the equation:

C * V * R = N * K_b.

C * V = N * K_b / R = N/N_A.