Pressure in canonical ensemble

Click For Summary

Discussion Overview

The discussion revolves around the behavior of pressure in a canonical ensemble, specifically addressing why pressure does not remain constant despite fixed volume and temperature. Participants explore the implications of fluctuations in a thermodynamic system characterized by a constant number of particles, volume, and temperature.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how pressure can fluctuate in a canonical ensemble where volume and temperature are constant.
  • Another participant clarifies that while pressure is an average quantity, the forces exerted by particles on the walls of the system fluctuate, leading to variations around the average pressure.
  • A participant notes that in a canonical ensemble, temperature can also fluctuate, suggesting that pressure could similarly be viewed as fluctuating around an average value.
  • There is a question raised about defining a canonical ensemble with changing temperature and the conditions that would apply.
  • A participant provides a link to external resources regarding temperature fluctuations in canonical ensembles, indicating that this may be a recognized phenomenon.

Areas of Agreement / Disagreement

Participants generally agree that pressure can fluctuate in a canonical ensemble, but there is no consensus on the implications of these fluctuations or how they relate to temperature changes.

Contextual Notes

Participants mention that while N and V can remain constant, the average values of pressure and temperature may still experience fluctuations, highlighting the complexity of thermodynamic systems.

SchroedingersLion
Messages
211
Reaction score
56
Greetings,

I am having a hard time in understanding intuitively how pressure does not automatically stay constant in a canonical ensemble (=NVT ensemble).

Pressure in a closed system is the average force of particles hitting against the wall of said system. The obvious way to manipulate pressure in a closed system is to either shrink the volume so the particles would have less space and collide with the boundary more often, or to increase the temperature so the average momentum of the particles would increase and thus the force they hit the boundary with.
But both V and T stay constant in the canonical ensemble.

So how come pressure fluctuates?

Regards
SL
 
Physics news on Phys.org
A canonical ensemble represents the possible states of a thermodynamic system which is characterized by a fixed number of particles and a fixed volume and which is allowed to exchange heat with a huge heat bath at a "fixed" temperature T. Hence, the energy of such a system can fluctuate when considering its behaviour in course of time.
 
As you stated, the pressure is an average quantity. The forces with which the particles hit the walls are, at the microscopic level, wildly fluctuating quantities. What you control from outside is the volume, and if the volume and the temperature are held constant, then the average pressure is a constant. There are always fluctuations about the average value, along with the energy, as pointed out by Lord Jestocost above.
 
Thanks guys.

I was under impression that the three 'constant' quantities, like N,V,T in the canonical ensemble or N,V,E in the microcanonical ensemble can also fluctuate around a constant average (N and V can even be constant all time). For example, when learning about how to simulate a thermostat in a molecular dynamics simulation, it was said that even in a canonical ensemble, T can fluctuate and only the average stays constant.
If it is the same with p, then one could call the N,V,T ensemble also a N,V,T,p ensemble, right?
 
How would one define a canonical ensemble with changing temperature? What are the conditions?
 

Similar threads

Undergrad How Can Internal Energy of the Canonical Ensemble Change (Fluctuate)?
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Concept of Thermal Equilibrium in the Context of Canonical Ensemble
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Number of particles in canonical ensemble
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Connecting the microcanonical with the (grand) canonical ensemble
  • · Replies 37 ·
2
Replies
37
Views
6K
Graduate On the notion of pressure in the canonical ensemble
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Flow of air through an open tube with a balloon
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Can a Super Grand Canonical Ensemble Exist?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Grand Canonical Ensemble: N operator problem
  • · Replies 38 ·
2
Replies
38
Views
6K
Graduate Microcanonical vs canonical vs grand canonical ensemble
  • · Replies 1 ·
Replies
1
Views
37K
Graduate Bernoulli, lift and cause & effect
  • · Replies 30 ·
2
Replies
30
Views
5K