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

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This equation is always applicable, regardless of the discussion being about the evolution of the universe or a container of gas. In summary, the equation ##dU=TdS-PdV## is a universal expression for the entropy of a given system, and is not opposed to the definition involving multiplicity.
  • #1
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.
 
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  • #2
As opposed to what? A definition involving multiplicity?
 
  • #3
Are you sure about the expression you gave for entropy?
 
  • #4
mishima said:
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.
Chestermiller said:
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 \ + \ ... \ ##.
 
  • #5
Tio Barnabe said:
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
 
  • #6
Tio Barnabe said:
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?
 
  • #7
Chestermiller said:
I think you mean TdS
yes, I'm sorry for the mistake
mishima said:
Ok. So you're more asking if dU = TdS + pdV ever fails to be applicable?
yes, exactly
 
  • #8
Tio Barnabe said:
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).
 

1. What is entropy?

Entropy is a measure of the disorder or randomness in a system. In other words, it is a measure of how spread out or dispersed energy is within a system.

2. How does entropy change in different cases?

The change in entropy depends on the specific case and the energy exchanges that occur. Generally, when energy is added to a system, the entropy increases, and when energy is removed, the entropy decreases. However, there are exceptions to this rule.

3. How does entropy relate to thermodynamics?

Entropy is a fundamental concept in thermodynamics and is related to the second law of thermodynamics. This law states that the total entropy of a closed system will always increase over time, or remain constant in ideal cases where the system is in equilibrium.

4. What is the significance of entropy in chemistry?

In chemistry, entropy plays a crucial role in determining the direction and spontaneity of chemical reactions. Reactions that increase in entropy are more likely to occur spontaneously, while reactions that decrease in entropy are less likely to occur without external energy input.

5. How does entropy impact our daily lives?

Entropy is present in many aspects of our daily lives, from the way heat flows to how our food digests. It also plays a role in larger-scale systems, like climate change and the growth of cities. Understanding and managing entropy is crucial for maintaining order and efficiency in our world.

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