## Entropy Changes Based on Changes in Volume

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

Amy Luong 1L
Posts: 11
Joined: Fri Sep 26, 2014 2:02 pm

### Entropy Changes Based on Changes in Volume

In the equation for change in entropy (delta s)= nRln(V2/V1), when would you know whether or not there should be a negative sign in front of the "n"? Is it based on whether it's expansionary or not?

Neil DSilva 1L
Posts: 70
Joined: Fri Sep 26, 2014 2:02 pm

### Re: Entropy Changes Based on Changes in Volume

The equation for entropy is always written the same way (without a negative sign -- to see why there is no negative sign in the equation, look back in your course reader or review the lecture for how the equation is derived):
$\Delta S = nRln\frac{V_{2}}{V_{1}}$

However, entropy can have a negative value, if the volume decreases (i.e. $V_{2} < V_{1}$), since the ratio of the volumes would be a fraction between 0 and 1 and the natural log of a number between 0 and 1 is always negative (and a negative number times n and R would give you a negative value of $\Delta S$).

And this makes logical sense, because if you decrease the volume, the system has fewer possible states and the entropy has therefore decreased.

Justin Le 2I
Posts: 142
Joined: Fri Sep 26, 2014 2:02 pm

### Re: Entropy Changes Based on Changes in Volume

You will know if you need to use a negative sign depending on if you're measuring the delta S of the system or the surroundings. Look at Example 8.12 on page 312-313 for an example of where the book uses both the positive and negative equation.