## C versus R

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

Randon_Zahlout_3B
Posts: 16
Joined: Wed Sep 21, 2016 2:57 pm

### C versus R

Why in the equation with a change in volume do we use the Gas Constant but when we calculate Entropy with a change in Temperature we use C? Just curious and for some reason cannot seem to figure it out ...

Josh Ku 3H
Posts: 25
Joined: Wed Sep 21, 2016 2:59 pm

### Re: C versus R

Based off of the course reader, I think it is because of the equations that they are derived from. For the entropy equation involving volume, it is derived from the work equation (w = -nRTln(V2/V1) ) which has the R constant. As for the equation that involves temperature, it is derived from the expression delta S = q / T. The derivative of q is nCp(delta)T which is where the C term comes from. Both of the derivations are shown in the course reader.

I hope this helps!