Solve Thermal Equilibrium Homework Problem

[nicksauce]

Homework Statement

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?

Homework Equations

$$\frac{1}{T} = \frac{\partial S}{\partial U}$$

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?

 

[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.