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
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?