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Thermodynamics : Heat transfer question.

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant 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


    3. 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?
     
  2. jcsd
  3. Mar 17, 2012 #2
    Newton's law of cooling : dT/dt = -(4eσAT°3)ΔT/ms

    Please define your symbols.
     
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