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Homework Help: Heat transfering issue

  1. Mar 29, 2007 #1
    Hi all,

    First of all I'm a hardware engineer and therefore my phisycs knowladge is quite limited...
    Secondly my English is not well also so ... please forgive me.

    I have a heat body (copper) which I want him to heat from -30C to +7C.

    I supply it a constant power of let's say 7W (it has no matter for the discussion).

    The phenomenan I see is that (delta T)/(delta t) at low tempertures is much higher then in high tempertures. I mean that for example the time that takes from -30C to -20C is much faster than the time from 0C to 7C.

    a. What is the reason?
    b. I need to have some algorithm that will keep a constant and linear (delta T)/(delta t) so that the time from -30C to -29C will be the same time (lets say 1 minute) as from -3C to -4C. What are the formulas I need to know in order to do it?

    Thanks
     
  2. jcsd
  3. Mar 29, 2007 #2
    a. this may not be very technical but say, the temperature of the environment may also play a part in the heating factor?

    b. you could probably that your heat body is heated in an enclosed environment (don't know the thermodynamic terms), since i think the specific heat capacity of copper doesn't vary with temperature, at least not with such a small range (at very high temperatures you may experience difficulty due to black-body radiation)
     
  4. Mar 29, 2007 #3

    Mentz114

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    Gold Member

    You need Newton's 'law of cooling' which states that the amount of heat transferred between system A and system B is proportional to their temperature difference.

    [tex]\frac{dE}{dt} = K(T_a - T_b)[/tex]

    this accounts for the rapid transfer at low temperatures. It solves to an exponential for E(t).
     
  5. Mar 29, 2007 #4
    yes actually the answer should take account both reasons..deltaT and the radiation emmissions which vary propotional to T^4 and that's a lot of difference with a small temperature change. and the surrounding temperature of the environment.
     
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