Problem 3: Starting with the expression derived in the lecture notes for the multiplicity of an ideal 1 n3N/2 (2m)³N/2 N! (3N/2)! h3N gas VNU3N/2 derive the Sackur-Tetrode expression for the entropy.

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Using molecular and system partition functions it is possible to derive the Sackur-Tetrode equation, which allows the computation of absolute entropy from molecular parameters: 2лmkвT S = {NkB + NkB In In [ (2TmkyT) 3/² V h² N In this equation, the quantity V/N is sometimes written as 1/p. = (a) Use this expression to compute the entropy due to translation for one mole of CO₂ gas at 400 K, for which mco2 = 44.01 Daltons, and its molar volume (pressure = 1 bar) is V 0.03326 m³. (Note: 1 Dalton = 1.66053 × 10-27 kg). Be careful with the computation- keep track of units and make sure that the argument of the LN function is unitless. Your answer should be between 100 and 200 J/K if you do everything correctly. (b) If the mass of neon were twice as large (88 instead of 44 Daltons), by how much would the extra mass affect its translational entropy? Report the ratio of the entropy with the heavier mass to that found in part (a).

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