Entropy Calc: 1kg Water Heated from 20C to 80C

[<---]

Homework Statement

Find the entropy change of the system.

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

Homework Equations

$$dU=TdS-PdV$$

The Attempt at a Solution

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

The answer is 1074J/K

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.

 

[Redbelly98]

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

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

 

[Geezer]

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

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

Ditto.

DU = DQ...

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

 

[<---]

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?

 

[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.

 

[<---]

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.

 

[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

 

[<---]

I had referred to my text so see that that particular answer was indeed on the list of errata my prof pointed out.

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. :)

 

[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
7-2 Not too sure about this question...answer is possibly 704 JK^-1 (instead of 660 JK^-1).
7-11 311 ms^-1

There may be others... Students have also pointed out typos in units and a couple other things (e.g. questionable atomic weight in 4-5), but I'm sure you'll realize those when doing the problems.

 

[Redbelly98]

I agree with the 779 J/K answer.