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

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Presentation Transcript

Q = -QR

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

(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

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