Entropy, chemical potential, temperature

In summary, there exists a function called entropy in a thermodynamic system, denoted as S(U,N,V), with other variables such as temperature and chemical potential defined in terms of partial derivatives of S with respect to U and N. It is understood that these partial derivatives only consider the explicit dependence on U and N, and not any potential dependence on these variables. This arises from the distinction between independent variables in the entropy and energy representations.
  • #1
aaaa202
1,169
2
For a thermodynamic system there exists a function called entropy S(U,N,V) etc.
We then define for instance temperature as:
1/T = ∂S/∂U
μ = ∂S/∂N
etc.
When taking these partial it is understood that we only take the derivative of S wrt the explicit dependece on U,N etc. right? Because couldn't U carry an N dependence? I mean it does not for me make physical sense that the energy of the system should not be related to the number of particles in it. Actually it seems also a bit weird that there should be an explicit U dependence. Does this come from the fact that we are given the mean value of the internal energy of the system?
 
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  • #2
aaaa202 said:
When taking these partial it is understood that we only take the derivative of S wrt the explicit dependece on U,N etc. right?

Yes, that is the definition of a partial derivative as opposed, e.g. to a total derivative.
 
  • #3
aaaa202 said:
For a thermodynamic system there exists a function called entropy S(U,N,V) etc.
We then define for instance temperature as:
1/T = ∂S/∂U
μ = ∂S/∂N
etc.
When taking these partial it is understood that we only take the derivative of S wrt the explicit dependece on U,N etc. right? Because couldn't U carry an N dependence? I mean it does not for me make physical sense that the energy of the system should not be related to the number of particles in it. Actually it seems also a bit weird that there should be an explicit U dependence. Does this come from the fact that we are given the mean value of the internal energy of the system?
'

In the entropy representation U,V,N are independent variables. On the other hand in the energy representation S,V,N are independent variables. One should not mix the two representations in the same time.
 

1. What is entropy in chemistry?

Entropy is a measure of the disorder or randomness in a system. In chemistry, it is often used to describe the tendency of a system to move towards a state of maximum disorder.

2. How does entropy relate to chemical reactions?

In chemical reactions, the change in entropy is related to the change in disorder of the reactants and products. A reaction that results in an increase in disorder (entropy) is more likely to occur spontaneously.

3. What is chemical potential?

Chemical potential is the energy required to add or remove a molecule from a system. It takes into account factors such as temperature, pressure, and concentration.

4. How does temperature affect entropy and chemical potential?

As temperature increases, the disorder (entropy) of a system also increases. This can lead to a decrease in chemical potential, as the system becomes more disordered and molecules are more likely to move freely.

5. How do entropy, chemical potential, and temperature relate to each other?

Entropy and chemical potential are both affected by temperature, as temperature can influence the amount of disorder in a system. They are also related through the Gibbs free energy equation, which takes into account temperature, entropy, and chemical potential to determine the spontaneity of a reaction.

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