# Entropy calculation

1. Aug 9, 2009

### <---

1. The problem statement, all variables and given/known data
Find the entropy change of the system.

1kg of water is heated reversibly by an electric heating coil from 20C to 80C($$c_{p}=4.18 X 10^{3}Jkg^{-1}K^{-1}$$).

2. Relevant equations

$$dU=TdS-PdV$$

3. The attempt at a solution

dV=0
$$dS=\frac{dU}{T}$$.............

I think I'm stuck on how to handle the heat capacity. If someone could just point me in the right direction so I know what to go over and learn to complete this problem that would be very helpful.

Last edited: Aug 10, 2009
2. Aug 9, 2009

### Redbelly98

Staff Emeritus
Since no work is done, dU is the same as dQ.

Use the formula relating heat Q, mass, Cp, and temperature change.

3. Aug 10, 2009

### Geezer

Ditto.

DU = DQ...

So, what equation do you have for DQ that relates to heat capacity?

4. Aug 10, 2009

### <---

Thanks for the replies, it may take me awhile to get back to this but I do appreciate the help.

Correct me if I'm wrong but it seems you are getting at using,

$$du=c_{p}dT=dq$$

$$dS\equiv\frac{dQ}{T}=C_{p}m\frac{dT}{T}$$

$$\Rightarrow \Delta S=C_{p}mln(\frac{T_{2}}{T_{1}})=4180ln(\frac{353}{293})=779JK^{-1}$$

This was the first thing I tried and is not right. Where did I go wrong?

5. Aug 10, 2009

### Physics Fern

If you're doing Carter problem 6-2 (a), the 1074 J/K answer in the back of the text is wrong. I did it the same was as you and got 778.35 J/K.

6. Aug 10, 2009

### <---

Thanks, that is indeed the problem I'm working on. And while I always like to think it's the book that's wrong it rarely turns out to be the case. If somebody(s) else could please confirm/disprove this I would feel better about letting this problem go.

7. Aug 10, 2009

### Physics Fern

Yeah...in thermo I often feel I've got a problem right, but for some frustrating reason or other my solution turns out to be quite wrong. I think you're alright on this one though, as before posting earlier I had referred to my text so see that that particular answer was indeed on the list of errata my prof pointed out. We can wait for a second opinion though

8. Aug 10, 2009

### <---

Ahh thank you very much, that's certainly good enough for me. I don't even want to say how much time I spent over complicating this trying to get the book's answer....
Is that list online anywhere that you know of? I couldn't find it in the five minutes I spent looking. It may be of help later. :)

9. Aug 10, 2009

### Physics Fern

I don't believe Carter has put out a list; I haven't been able to find one online either. Our prof didn't provide us with an official list either--he sometimes just gives us a heads up if one of the text answers may be incorrect. Also, when students bring up questions in our tutorials he works through some of them as examples. We haven't gotten too far through the text, but here are some of the "corrections" that have come up so far:

4-1 (c) 2312.5 Jkmol-1K-1
6-2 (a) 779 JK-1
6-3 0.127 JK-1