- #1

tanaygupta2000

- 208

- 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

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

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) ?