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

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Homework Help Overview

The discussion revolves around the application of the grand partition function in thermodynamics, particularly in relation to heat flow and work done in a system of ideal gas molecules. Participants are examining the relationship between internal energy, heat, and work within the context of a grand canonical ensemble.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants are exploring whether heat flow can be considered zero in a grand canonical ensemble and questioning the validity of the equation U=Q-W. There are discussions about the definitions of heat flow and work done, as well as the implications of thermal equilibrium on these quantities.

Discussion Status

The discussion is active, with participants offering differing views on the equations relating internal energy, heat, and work. Some are questioning the assumptions made regarding the nature of heat flow and work in the context of the grand partition function, while others are clarifying the definitions of state functions versus non-state functions.

Contextual Notes

There is an ongoing debate about the correct formulation of the relationship between internal energy, heat, and work, with references to different equations seen in literature. The participants are also considering the implications of the system being in thermal equilibrium with its surroundings.

pivoxa15
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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?
 
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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?
 
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.
 
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.
 
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.
 

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