Understanding the Helmholtz energy.

[aaaa202]

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.

 

[emailanmol]

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)

 

[emailanmol]

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