Can Absolute Entropy Be Calculated Directly from State Variables?

[Urmi Roy]

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]

What you are doing is not correct.

The entropy of a monatomic ideal gas is given by the Sackur-Tetrode equation.

 

[Urmi Roy]

What you are doing is not correct.

The entropy of a monatomic ideal gas is given by the Sackur-Tetrode equation.

That comes from statistical mechanics...I'm talking about the entropy constitutive equations.
See the bottom of http://hyperphysics.phy-astr.gsu.edu/hbase/therm/entropgas.html

 

[DrClaude]

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.

 

[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.

 

[DrClaude]

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]

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 anyone 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.

 

[Urmi Roy]

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 anyone 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]

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.