# Thermal Equilibrium

1. Jan 29, 2008

### nicksauce

1. The problem statement, all variables and given/known data
Two objects A and B, with an equal number, N, of molecules are brought into thermal contact. The first has entropy $$S_A = Nkln(U_A/N)$$ and the second has entropy $$S_B = 3/2 * Nkln(U_B/N)$$. What is the final temperature?

2. Relevant equations
$$\frac{1}{T} = \frac{\partial S}{\partial U}$$

3. The attempt at a solution
My process would be to take
$$\frac{\partial}{\partial U}Nkln((U_A + \Delta U) / N) = \frac{\partial}{\partial U}3/2 * Nkln((U_b - \Delta U)/N)$$

And solve for delta U. Is this the best way to approach the problem?

2. Jan 30, 2008

### siddharth

I think your way is mostly right. As you said, the criteria at equilibrium is,

$$\left( \frac{\partial S}{\partial U} \right) |_{U_A + \Delta U} = \left( \frac{\partial S}{\partial U} \right) |_{U_A - \Delta U}$$

Find $\Delta U$, and from that, the final temperature.