Derivation of Entropy Equation (changing temperature)

[Pauline Tze 3B]

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]

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!