Can heat flow and work done be determined using the grand partition function?

[pivoxa15]

Homework Statement

When modeling ideal gas molecules using a grand partition ensemble, is heat flow = 0? So if U=Q-W then in a grand canonical ensemble, U=-W?

The Attempt at a Solution

I think so as the system is in thermal equilibrium with the surroundings. So in this system the total energy is negative the work done by the particles in the system?

 

[lalbatros]

This equation is wrong: U=Q-W , if no further explanation is given.
And what do you call heat flow. Heat flowing from where to where?
And why particles in a system would be doing work on this system?

 

[pivoxa15]

I have seen U=Q+W in books but my one is U=Q-W.

Q is heat flow from the outside to inside the system.

W is work done by particles in the system. So it could be gas particles pushing on the boundaries of the system caused by random collision between the particles, in turn pushing each other leading them to randomly crashing to the boundaries.

U is the internal energy of the system.

 

[pivoxa15]

The grand partition function describes a system in a large heat bath so in fact U=Q-W where Q is non zero because U describes the energy of the system rather than the whole bath. So Q is non zero as it can fluctuate when not in thermal equilibrium.

 

[lalbatros]

Pivoxa15,

Remember that U is a state function while Q and W are no state functions.
Q and W are variations of internal energy under particular transformations.