PPT Slide
Boltzmann Distribution and Helmholtz Free Energy
- We consider a thermodynamic system (S) in contact with a Reservoir (R) (Heat Bath), which has temperature T. S+R is an isolated system with U0 internal energy. We assume S<<R
- central problem: what is the probability that S will be is a given state :s (S is not an isolated system, and we cannot use the Ps=1/g results)?
- Since S+R is an isolated system, and thus we can apply our fundamental assumption for the probability of the states.
- When S is in state s with energy ?s, R will have an energy UR=U0- ?s with multiplicity gR(U0- ?s ).
- applying our fundamental assumption for the total isolated system and the relation between entropy and multiplicity, for two states (1 and 2) with energies ?1 and ?2 we get: