Heat Transfer Problem: Finding Temperature Difference in Insulated System

[LHC_23]

Homework Statement

Two bodies of masses m_{1} and m_{2} and specific heat capacities s_{1} and s_{2} , are connected by a rod of length l and cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t=0, the temperature of the first body is T_{1} and the temperature of the second body is T_{2} (T_{2} > T_{1} ). Find the temperature difference between the bodies at time t.

Homework Equations

dQ/dt = KAdT/dx

dQ = msdθ

The Attempt at a Solution

I was able to set up 2 equations relating the amount of heat transferred through the rod in a time dt to the rise and fall of temperatures of the masses m_{2} and m_{1} respectively. I don't know how to proceed after this ?

 

[maajdl]

Since the heat capacity of the rod is neglected, the temperature profile in the rod is linear:

dT/dx = (T2-T1)/l

You need to write your second equation twice: once for m1 and once for m2.
Then you can simply solve the equations.