## ΔS = nRln(v2/v1)

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

Philip Lee 1L
Posts: 30
Joined: Fri Sep 28, 2018 12:21 am

### ΔS = nRln(v2/v1)

During lecture, an equation for ΔS was derived using a previously given equation that relates entropy with degeneracy. The steps are as follows:

Given: S = kBlnW

1) ΔS = Sfinal - Sinitial

2) ΔS = kBlnW2 - kBlnW1

3) ΔS = kBln(W2/W1)

4) ΔS = kBln(V2/V1)

5) ΔS = nRln(V2/V1)

I am not sure how you get from step 4 to step 5. I know that the Boltzmann constant, kB = R/NA.
Why does kB get replaced with nR?

Anushi Patel 1J
Posts: 61
Joined: Fri Sep 28, 2018 12:19 am
Been upvoted: 1 time

### Re: ΔS = nRln(v2/v1)

I'm not sure, but I think it's because R is equal to kb multiplied by NA. Since the NA is actually the exponent within the natural log, you can take it out of the natural log and multiply it with Kb, which is equal to R. The n comes from the fact that since we used Avagadro's number we are calculating the entropy per mole, so we need to multiply it by the number of moles.