 #1
tanaygupta2000
 204
 14
 Homework Statement:
 System A has N particles and infinite energy levels 0, ε, 2ε, 3ε, ... is kept in thermal contact with system B having N particles and two energy levels 0 and ε, till they reach equilibrium. The total energy of system A is Nε and that of system is 3Nε/4. What is the sign of equilibrium temperature?
 Relevant Equations:

Partition function, Z = ∑exp[E(j)/kT]
Total energy, E = NkT^2 d[ln(Z)]/dT
First I found partition functions of both the systems and hence total energies of them using above formulas.
Z(A) = (1  e^{ε/kT})^{1} and Z(B) = (1 + e^{ε/kT})
Then I equated these values to the given values of total energies.
I got:
For System A, T(A) = ε/kln(2) > 0
For System B, T(B) = ε/kln(3) < 0
Now how do I find the equilibrium temperature when these systems are kept in thermal contact?
Do I have to take the average values of T(A) and T(B) ?
Z(A) = (1  e^{ε/kT})^{1} and Z(B) = (1 + e^{ε/kT})
Then I equated these values to the given values of total energies.
I got:
For System A, T(A) = ε/kln(2) > 0
For System B, T(B) = ε/kln(3) < 0
Now how do I find the equilibrium temperature when these systems are kept in thermal contact?
Do I have to take the average values of T(A) and T(B) ?