Entropy with Temperature and Volume

[Semi Yoon]

In a problem, if two initial and final values of temperature and volume are given in a problem in which two substances are mixed. Why would you need to solve for change in entropy using two equations (one with temperature and the other with volume) and add them together?

[Xuan Kuang 2L]

For those particular problems, you need to solve for a total change in entropy caused by both temperature and volume. I believe in those cases we are generally considering a reversible reaction, so we use two separate equations, one for temperature change (S=nCln(T2/T1)) and another for volume (S=nRln(V2/V1)). We are allowed to do this because we know entropy is a state property, so you can add the individual entropies of temperature and volume to get the total entropy.

[Faith Fredlund 1H]

For systems that undergo a temperature change and a volume change, it is difficult to calculate a change in entropy when those two actions are occurring simultaneously, so we consider these problems in two parts. You first calculate the change in entropy due to the change in volume ΔS= nRln(V2/V1) and then add that to the change in entropy due to the change in temperature ΔS= nCln(T2/T1) (using Cv= 3/2R).
Entropy is a state function so you can add these two entropy changes together making the problem much easier to solve that through considering simultaneous processes.