# Homework Help: Entropy, reversible process

1. Aug 17, 2010

1. The problem statement, all variables and given/known data
An ideal gas is taken from an initial temperature Ti to a higher final temperature Tf along two different reversible paths: Path A is at constant pressure; Path B is at constant volume. The relation between the entropy changes of the gas for these paths is
a) delta S(A) > delta S(B)
b) delta S(A) = delta S(B)
c) delta S(A) < delta S(B)

2. Relevant equations

delta S = delta Qr / T
Qr = heat transferred to system while the system is going along a reversible path

3. The attempt at a solution
This is one of those checkpoint questions in the chapter and the answer is given as choice a (delta S(A) > delta S(B)).

I'm confused though because in this book, it says that entropy is a state variable and as such, it only depends on the endpoints and is therefore independent of the actual path taken from A to B. But here, we're taking two different paths and yet we're getting that the change in entropy going from one path is different than when we take the other path.

I think the answer should be choice b (delta S(A) = delta S(B)).

It would seem that if you're only dependent on the endpoints, then regardless of the path taken, if you're going from A to B in multiple ways, that the entropy should be the same for all cases.

Where am I going wrong in my thought process? Thanks a lot ahead of time.

2. Aug 17, 2010

### Hurkyl

Staff Emeritus
Remind me -- does state include pressure and volume too? Or does the state involve temperature alone?

3. Aug 17, 2010

### vela

Staff Emeritus
The final states are different. Though they end at the same temperature, the two paths end at different pressures and volumes.

4. Aug 17, 2010