ΔS = nRln(v2/v1)

[Philip Lee 1L]

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 = k_BlnW

1) ΔS = S_final - S_initial

2) ΔS = k_BlnW₂ - k_BlnW₁

3) ΔS = k_Bln(W₂/W₁)

4) ΔS = k_Bln(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, k_B = R/N_A.
Why does k_B get replaced with nR?

[Anushi Patel 1J]

I'm not sure, but I think it's because R is equal to k_b multiplied by N_A. Since the N_A is actually the exponent within the natural log, you can take it out of the natural log and multiply it with K_b, 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.