1 / 4

# The canonical ensemble - PowerPoint PPT Presentation

The canonical ensemble. Q = -Q R. Consider system at constant temperature and volume. adiabatic wall. System . Heat Reservoir R. T=const. We have shown in thermodynamics that system with (T,V)=const . in equilibrium is at a minimum of the Helmholtz free energy, F.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' The canonical ensemble' - elias

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Q = -QR

Consider system at constant temperature and volume

System

Heat Reservoir R

T=const.

We have shown in thermodynamics that

system with (T,V)=const. in equilibrium is at

a minimum of the Helmholtz free energy, F

(T=const, V=const.)

We use a similar approach now in deriving density function and partition function

System can exchange energy with the heat reservoir:

Find maximum of S under the constraint that average (internal) energy is given

under constraints

found by maximizing

Using again Lagrange multiplier technique

Partition function of the and partition function

canonical ensemble

with

Next we show

@ V,N constant

From the constraint

With the equilibrium distribution

back into the entropy expression

With and partition function

and

@ V,N constant

Using

we find

With

Gives meaning to the Lagrange parameter