# Writing out expression for entropy

1. Oct 17, 2013

### Urmi Roy

1. The problem statement, all variables and given/known data

So as a part of a very long question on homework for thermodynamics, I and some of my friends got into a debate about how to write an expression for entropy at a particular state.

2. Relevant equations

delS(state 1 to 2)= Cv*ln(T2/T1)+R*ln(V2/V1)

(from constitutive relation for entropy change in an ideal gas)

3. The attempt at a solution

Is is correct to say S1 (absolute value of entropy of a gaseous system in state 1)= Cv*ln(T1)+R*ln(V1)?

I don't think so, coz you can't really calculate the absolute value of entropy ...unless you take the absolute zero temperature as reference state...in which case the above expression would contain -(Cv*ln(T0)+R*ln(V0))...and you'd still be taking 'change' in entropy rather than an 'absolute value.

2. Oct 18, 2013

### Staff: Mentor

3. Oct 18, 2013

### Urmi Roy

4. Oct 18, 2013

### Staff: Mentor

What is that supposed to mean? Entropy is entropy, however you calculate it.

Take an ideal gas at $T_1$ and $V_1$ and calculate the entropy using the Sackur-Tetrode equation, which is correct, and compare to what you get with your equation. Do you get the same result? No? Then your equation is not valid.

5. Oct 18, 2013

### Urmi Roy

Well in the link you provided V and T don't even come in. Anyway, I haven't come across the 'Sackur-Tetrode' equation in my course, and I'd like to stick to my course-work. Also, what you said so far doesn't answer my OP.

6. Oct 18, 2013

### Staff: Mentor

I think I answered that quite clearly.

7. Oct 21, 2013

### rude man

This is done in e.g. steam tables where a given (T,p) coordinate is assigned zero entropy, then all other states do have an "absolute" entropy number. But there is no meaning attached to any one number; it's only the difference between two numbers at different states that is significant.

And forget about absolute zero. You're delving ito some pretty fancy quantum mechanics there which I would avoid.

8. Oct 21, 2013

### Urmi Roy

rude man: Exactly what I was talking about. So you agree that we can't just write :
S1=Cv*ln(T1)+R*ln(V1)?

Interestingly, in the Sackur Tetrode equation, the entropy at a given state is given as a function of the volume and internal energy at the given state...so does that contradict your statement that "; it's only the difference between two numbers at different states that is significant"?

9. Oct 21, 2013

### rude man

Yes. Absolutely!
As I said, there you're dealing with quantum mechanics. There are good reasons not to get "involved" with that equation. It only applies to a monatomic ideal gas, only under limited conditions, and it predicts negative infinity for the entropy at absolute zero.

http://en.wikipedia.org/wiki/Sackur–Tetrode_equation

Stay away from such irrelevancies at the introductory physics level and even at the undergraduate heat & thermodynamics course level. Entropy differences are all that matter.