Understanding the Helmholtz energy.

In summary, the conversation discusses the concept of obtaining free heat from the environment in certain systems and how this is related to the increase in entropy. The speaker also mentions their confusion with the derivations and physical meaning of equations in Physical Chemistry. They also mention the idea of subtracting TΔS to account for the change in entropy of the surroundings. Additionally, the conversation touches on the relationship between entropy and temperature, and how temperature can remain constant or decrease when entropy increases. The speaker also brings up the example of free expansion, where entropy increases due to an increase in volume.
  • #1
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I'm having some trouble understanding this concept. Why is it that you sometimes can get heat for free from the environment? Like suppose you have a system, on which you make an energyconsuming proces which creates entropy. Then you subtract TΔS because apparently heat can enter when the entropy increases - why is that? Does the temperature drop, when we increase the entropy?
Can you guys please explain in terms of microstates too, as it is that way I feel I understand it the best.
 
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  • #2
Although I may not have a complete solution to your problem
I too have a lot of doubts in the derivations.I refer to Physical Chemistry by Atkins and the way they derive the equation and then extract the physical meaning out of results is puzzling. Like while deriving we consider, they ssume to be having V constant and T constant and later after the expression comes they say its the maximum expansion work a system can erform. If V is constant how can expansion work be performed.?

Coming to your query
From what I know ( I maybe wrong)
TdS is actually the heat change of surrounding.
Whenever we calculate the net change in entropy we calculate for the universe.
If the entropy of system increase entropy of surrounding should decrease as if heats flows into system the surrounding loses heat).
I think subtacting is done for that issue.

(NOTE: I maybe wrong.I am still in high school. I am just trying to share an idea or point out a speculation)
 
  • #3
Also in general its not neccesary that temperature should rise when entropy increases.
It can remain contstant and can decrease too.
Its like providing heat to an ideal gas.
Providing heat increases its entropy.
Now if the added heat cam change its Internal energy or be used to do work or a combination of both.
So we can't really .However, since heat was provided entropy increases.


A classic example is free expansion where T remains same but entropy changes due to volume increase (and therefore more freedom in movement
 

What is the Helmholtz energy?

The Helmholtz energy, also known as the Helmholtz free energy, is a thermodynamic potential that represents the maximum amount of work that can be extracted from a system at a constant temperature and volume. It is denoted by the symbol A and is defined as A = U - TS, where U is the internal energy, T is the temperature, and S is the entropy of the system.

Why is the Helmholtz energy important?

The Helmholtz energy is an important concept in thermodynamics as it helps us understand the behavior of a system at a constant temperature and volume. It is particularly useful in studying systems that are not in equilibrium, such as chemical reactions, and in predicting the direction of spontaneous processes.

How is the Helmholtz energy related to other thermodynamic potentials?

The Helmholtz energy is related to other thermodynamic potentials through Legendre transformations. For example, the internal energy U can be obtained by taking the Legendre transform of the Helmholtz energy with respect to volume, and the enthalpy H can be obtained by taking the Legendre transform with respect to pressure.

How is the Helmholtz energy used in practice?

In practice, the Helmholtz energy is often used in conjunction with the Gibbs free energy to determine the spontaneity of a process. By comparing the values of A and G, we can determine whether a process will occur spontaneously at a constant temperature and pressure.

What are the limitations of the Helmholtz energy?

The Helmholtz energy is not always applicable to all systems. It assumes that the temperature and volume of the system are constant, which is not always the case. Additionally, it does not take into account the effects of external factors such as pressure and magnetic field, which may affect the behavior of the system.

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