ln in Boltzmann Equation

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

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Joined: Fri Sep 29, 2017 7:04 am

ln in Boltzmann Equation

How is the ln derived in the Boltzmann equation?

klarratt2
Posts: 60
Joined: Fri Sep 28, 2018 12:16 am

Re: ln in Boltzmann Equation

In an isothermal system, ΔS = [integral(T1 to T2) dq/T]

Since q = nCΔT, dq = nCdT

So, you can substitute the original equation to make it ΔS = [integral(T1 to T2) nCdT/T]

You can pull the constants outside of the integral: ΔS = nC[integral(T1 to T2) 1/T dT]

Using the general rule for integrals (the integral from A to B of 1/X dX = ln(B/A)), you get the equation ΔS = nC[ln(T2/T1)]

The ln comes from integrating 1/T

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