# Writing out expression for entropy

## Homework Statement

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.

## Homework Equations

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

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

## 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.

DrClaude
Mentor
DrClaude
Mentor
That comes from statistical mechanics...I'm talking about the entropy constitutive equations.
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.

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.

DrClaude
Mentor
Also, what you said so far doesn't answer my OP.

Is is correct to say S1 (absolute value of entropy of a gaseous system in state 1)= Cv*ln(T1)+R*ln(V1)?
I think I answered that quite clearly.

rude man
Homework Helper
Gold Member
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.

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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.

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"?

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

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.

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