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.