## connecting the boltzmann and macro/thermodynamic entropies?

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

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Sue Bin Park 2I
Posts: 52
Joined: Mon Jun 17, 2019 7:24 am

### connecting the boltzmann and macro/thermodynamic entropies?

so i'm reviewing prof. lavelle's lecture from feb 3rd and i'm following along with his derivation of the link between "accessible microstates and a macroscopic property" (specifically V). i understand most of it up until he basically replaces the boltzmann constant with nR in which n = moles of gas. why are we able to do this exactly?

Ryan Lee 1E
Posts: 50
Joined: Sat Aug 17, 2019 12:16 am

### Re: connecting the boltzmann and macro/thermodynamic entropies?

The boltzman equation at its base is to describe the entropy of a single molecule using its degeneracy of W. But, we usually deal with molecules in the quantity of moles, which means the equation of just Kb*ln(w) is not very useful to us. So, in order to find the entropy of one mole of molecules, we will have to multiply the entropy of one molecule 6.02*10^23 times, or Na times. This looks like this: NaKb*ln(w). If you multiply out Na and Kb together though, you will find that it equals 8.31, and the units is J/(K*mol). Then at that point, it's just the R gas constant which is why we just replace NaKb with R. Then, the n value is just a scaler. If we have 2 moles of molecules, then just put 2 for n since we have to multiply by even more molecules.

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