## Derivation of Entropy Equation (changing temperature)

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

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Pauline Tze 3B
Posts: 57
Joined: Sat Jul 09, 2016 3:00 am
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### Derivation of Entropy Equation (changing temperature)

Hi,
Does anyone know how to mathematically derive the formula delta S = nR ln (T2/T1)?

I can't seem to work it out from PV = nRT and delta S = q(reversible)/T though I presume that it works out because T is directly related to V which has the equation delta S = nR ln (V2/V1)

Thank you in advance.

Mindy Zhang 3F
Posts: 10
Joined: Wed Sep 21, 2016 2:55 pm

### Re: Derivation of Entropy Equation (changing temperature)

Hi,

From my knowledge, you should be able to take the delta S = nR ln (V2/V1) and use the gas law that volume is directly proportional to the temperature in cases of constant pressure. (V2/V1)=(T2/T1) In this way, the formula delta S = nR ln (T2/T1) can be derived. Does anyone else have another explanation for this?

Hope this helped!

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