## Pages

### GIBBS CANONICAL ENSEMBLE

(SYSTEM IN CONTACT WITH A HEAT RESERVOIR)

Canonical ensemble describes those systems that are not isolated but are in contact with a heat reservoir.

The system under consideration together with a heat reservoir forms a closed system and then system of interest is taken as sub system of this closed system.

Any sub system of an isolated system in statistical equilibrium can be represented by a canonical ensemble.

The probability density of a canonical ensemble depends both on Energy 'E' and temperature 'T'

It is given by

Ď(E,T) = Ae-E/đ

Partition function for canonical ensemble

z=(1/h³âż.n!)∫exp(-E(q,p)/KTdÎ

The statistical energy of a system in a canonical ensemble is given by

đ = logZ  +(E/đ);  đ = logZ  +T[∂(log Z)/∂T]

Thermodynamical entropy 'S' of a system in a canonical ensemble is given by

S=Kđ

S=KlogZ + (E/T); U=KT2[∂(log Z)/∂T]

The entropy at absolute zero in a canonical ensemble can be expressed as

S=K.log g

gâ is statistical weight of ground state