The rotational partition function for a symmetric top was used, i.e. (The translational partition function uses a #"1 atm"# standard state. All masses here are in #"amu"#, temperatures are in #"K"#, and the Boltzmann constant is #k_B ~~ "0.695 cm"^(-1)"/K"#. METHANE PARTITION FUNCTION + MOLECULAR INTERNAL ENERGYĪll of this is assuming the high temperature limit for translations and rotations. The actual number-chugging of this calculation is beyond the scope of what we need to get into, so I'll just place an example partition function and molecular energy expression here, and show the results. Where #> = E/N = k_B T^2 ((del ln (q//N))/(delT))_V# is the molecular internal energy.īy knowing the single-molecule partition function #q/N# for a given molecule at the particular temperature range of interest, the molecular entropy can thus be calculated all in one go.įor another, more tedious approach, see here. So, with some derivation (which is omitted for brevity), the molecular entropy can be written as ( Statistical Mechanics, Norman Davidson): Where #q = sum_i g_i e^(-betaepsilon_i)# is the microcanonical partition function for the system of particles, and #beta = 1//k_BT#.
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