[Schrödinger]

Hi!

I'm going through the 2nd law of thermodynamics and its application in material equilibrium in systems. So, I read this about the Helmholtz energy, A = U-TS : At contant T and V, for a closed system in mechanical and thermal equilibrium but NOT material equilibrium, we can say that dA < 0, which means equilibrium is attained only when A is minimized.

I just wanted to clarify my perception of the consequences of this statement. Does this mean, that no matter what you do to a system once it has attained this equilibrium, as long as you maintain T and V constant, you cannot effect any change? Let's say I am increasing/decreasing the pressure randomly, making sure that the T and V are constant (is that even possible?). This experiment of mine will not do anything to the system if it has already attained material equilibrium. Is this correct?

[curiouscat]

If A has a minimum shouldn't dA = 0?

[Schrödinger]

Only after the material equilibrium has been reached. dA < 0 until then

[curiouscat]

Couldn't that P change be compensated by an n change? Say a transformation of the form

A  2B

Or the gas could be non ideal in which case PV = nRT need not hold.

[Jorriss]

I just wanted to clarify my perception of the consequences of this statement. Does this mean, that no matter what you do to a system once it has attained this equilibrium, as long as you maintain T and V constant, you cannot effect any change? Let's say I am increasing/decreasing the pressure randomly, making sure that the T and V are constant (is that even possible?). This experiment of mine will not do anything to the system if it has already attained material equilibrium. Is this correct?

Do you know gibbs phase rule? If so, you know that a system is fully characterized by a finite number of variables. Helmholtz free energy is a function of T,V, N, so you can't just change the pressure at constant T, V, N and have it be uncoupled from the other variables. Further, if you start adjusting pressure in that way and treat it as an independent variable, then you are working with the gibbs free energy.