## Temp and reversibility

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

Payton Kammerer 2B
Posts: 49
Joined: Tue May 01, 2018 3:00 am

### Temp and reversibility

In section 4F.4 of textbook, the "how is that done?" section reads: "To calculate the entropy change in a system due to a temperature change, first note that Eq. 1 itself applies only when the temperature remains constant as heat is supplied to a system.--->Except in special cases, that is true only for infinitesimal transfers of heat, so the heating must be broken down into an infinite number of infinitesimal steps, with each step taking place at a constant but slightly different temperature, and then the infinitesimal entropy changes for all the steps are added together."

Eq 1 is the delta S=q/T equation

I am a really confused by the sentence I've labeled with an arrow. I don't even know where to begin explaining my confusion. Temp is only constant when it is broken down like that? But the rest of the section talks about temp changing and being broken down like that. The other cases didn't use derivatives at all to explain.

Sanjana Munagala_1j
Posts: 103
Joined: Sat Aug 24, 2019 12:17 am
Been upvoted: 1 time

### Re: Temp and reversibility

So if you are calculating entropy at a constant temperature, use the equation S=q/t. If you have changing temperatures then you would us the integral equation which can be simplified to S=nCln(T2/T1)

Hope that helps!