## Entropy Changes Based on Changes in Volume

Volume:
Temperature:

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):

However, entropy can have a negative value, if the volume decreases (i.e. ), 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 ).

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.