Can the Entropy of a System Always Be Expressed as dU/dT?

[Tio Barnabe]

Can we always express the entropy of a given system as $\partial U / \partial T$, i.e. as the variation of the internal energy of the system w.r.t. its temperature?

By always I really mean, in every discussion we are eventually engaged in. Like, when I want to talk about the evolution of the universe (in large scale), or when I want to talk about a container of gas.

 

[mishima]

As opposed to what? A definition involving multiplicity?

 

[Chestermiller]

Are you sure about the expression you gave for entropy?

 

[Tio Barnabe]

As opposed to what? A definition involving multiplicity?

Well, the definition I know for entropy does involve multiplicity. "The entropy is the logarithm of the multiplicity". So I'm not aware of an other definition which is opposed to the one I mentioned in the opening post.

Are you sure about the expression you gave for entropy?

I thought that would be the expression for the entropy, since we have $dU = S dT \ + \ ... \$.

 

[Chestermiller]

Well, the definition I know for entropy does involve multiplicity. "The entropy is the logarithm of the multiplicity". So I'm not aware of an other definition which is opposed to the one I mentioned in the opening post.

I thought that would be the expression for the entropy, since we have $dU = S dT \ + \ ... \$.

I think you mean TdS

 

[mishima]

Well, the definition I know for entropy does involve multiplicity. "The entropy is the logarithm of the multiplicity". So I'm not aware of an other definition which is opposed to the one I mentioned in the opening post.

Ok. So you're more asking if dU = TdS + pdV ever fails to be applicable?

 

[Tio Barnabe]

I think you mean TdS

yes, I'm sorry for the mistake

Ok. So you're more asking if dU = TdS + pdV ever fails to be applicable?

yes, exactly

 

[Chestermiller]

yes, I'm sorry for the mistake

yes, exactly

The equation $dU=TdS-PdV$ is really a physical property relationship that connects the changes in internal energy, entropy, and volume for a single-phase material between two closely neighboring thermodynamic equilibrium states at (U,S,V) and (U+dU, S+dS, and V+dV).