Thermodynamics : Heat transfer question.

[AlchemistK]

Homework Statement

A solid body X of heat capacity C is kept in an atmosphere whose temperature is 300K. At t=0 temperature of X is 400K. It cools according to Newton's Law of cooling.
At time t1 its temperature is found to be 350 K .
At this time,the body X is connected to a large box Y at atmospheric temperature through a conducting rod of length L, cross sectional area A and thermal conductivity K.
The heat capacity of Y is so large that any vibration in its temperature rod is small compared to the surface area of X.
Find temperature of X at time t=3t1

Homework Equations

Newton's law of cooling : dT/dt = -(4eσAT°³)ΔT/ms

On integrating to calculate the time it takes for the body to reach a temperature T2 from T1:
t=(ms/4eσAT°³) ln ((T1 - T°)/ (T2 - T°))

H = KA/L dT

The Attempt at a Solution

Now first, the box reaches the temperature of T=350K in t1 time

So, ti = (ms/4eσA°*300³) ln ((400 - 300)/ (350 - 300))
= (ms/4eσA°*300³) ln 2

Now after this, a rod is connected to it, at this point I don't know if I have to consider only heat transfer through the rod, or also by radiation into the atmosphere.

Also, how do I proceed in either case?

 

[LawrenceC]

Newton's law of cooling : dT/dt = -(4eσAT°3)ΔT/ms

Please define your symbols.