Boltzmann Equation for Entropy:
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Adding on to that, for this specific problem the number of states will be the number of orientations. In a, all of the molecules face the same way and therefore have only one possible orientation. In b, you will have four orientations so w = ln(4^# of molecules).
The problem asks us to calculate entropy and gives us the number of molecules and the number of arrangements. Using these 2 things, we an calculate the degeneracy(W). To calculate the degeneracy: (# of arrangements)^(# of molecules). For part (a), we know there are 64 molecules aligned in the same direction, so we get W = 1^64. And to calculate entropy from that, we have to plug it into the Boltzmann equation: S = kB*ln(W) = kB*ln(1^64).
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