Extremum of thermodynamic potentials: confusion

AI Thread Summary
The discussion centers on the confusion surrounding the minimization of the internal energy (U) of a thermodynamic system when temperature and entropy are held constant. It highlights the relationship between changes in energy, entropy, and volume, specifically referencing the equation dU = TdS - pdV. Participants note that if both volume and entropy are constant, U should remain unchanged, raising questions about the conditions under which U can be minimized. Two different formulations of the second law are presented, one from Steven Blundell's book, which includes a derivation involving availability, and another that does not specify volume as a constant. This discrepancy leads to a deeper inquiry into the conditions necessary for minimizing thermodynamic potentials.
Dazed&Confused
Messages
190
Reaction score
3
An alternative formulation of the second law is that the energy of the system U is minimised if the temperature and entropy of the system are held constant.
However, dU= TdS -pdV
which means that U is presumably constant if the volume V and the entropy S are kept constant. How then can U change so that it is minimised?
 
Physics news on Phys.org
The formulation doesn't say anything about keeping volume constant.
 
Thanks for replying. I have seen two versions. One is in Steven Blundell's book where he derives the availability which satisfies
dA= dU + p_0dV -T_0dS \leq 0 where the subscripted variables are the reservoir ones. He then states that if V, S are constant then dA = dU \leq 0 so that U is minimised.

The other version uses a completely different approach but crucially no mention is made of V being constant as you say.
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'average velocity as a weighted mean'

Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »

Similar threads

Chemistry How to derive 2nd law extremum principles for U, A, G, and H?
Replies
1
Views
2K
I Understand the Thermodynamic Identity: Is This Correct?
Replies
3
Views
2K
I Minimization of the Gibbs energy when number of molecules varies
Replies
16
Views
2K
Chemistry Show that book levitation by absorption of heat violates 2nd law
Replies
13
Views
2K
Work done in reversible and irreversible processes
Replies
4
Views
3K
Microcanonical ensemble generalized pressure
Replies
2
Views
964
Entropy and the Helmholtz Free Energy of a Mass-Piston System
Replies
8
Views
2K
Chemistry What does the differential of U mean in an irreversible process?
Replies
11
Views
1K
I Change of Variables in Thermodynamics
Replies
4
Views
2K
What Happens to Kinetic Energy of the Piston in an Isothermal System?
Replies
21
Views
2K

Hot Threads

Recent Insights

Back
Top