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.