# Deriving entropy change equation from Boltzmann’s principle

1. The problem statement, all variables and given/known data

Show using Boltzmann’s principle (S=k.lnW), show that with respect to changes in V and T:

$dS=k.N.\frac{dV}V{}+\frac{C.dT}V{T}$

Where $W=T^{\frac{C}k{}}V^{N}$

3. The attempt at a solution

$S=k.lnT^{\frac{C}k{}}V^{N}=k.lnT^{\frac{C}k{}}+klnV^{N}$

$S=C.lnT+N.lnV$

Now I know that the differential of lnV is 1/V and lnT is 1/T but I’m unsure on how to do the final step required to get to the equation. My maths is a bit rusty, I’ve tried taking partial derivatives but couldn’t get to the right answer.

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