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Cooling a ball of iron

  1. Sep 21, 2015 #1
    1. The problem statement, all variables and given/known data

    A boll of iron with the volume ##V=\frac{4 \pi 0.01^3}{3}## heats up to 1073 K in a chamber with vacuum, how long will it take until the iron is at 1063 K? The given data is this:
    ##\rho_{iron} = 7870 kg/m^3##
    specific heat.. ##c_i = 0.5 \cdot 10^3 J/(kg \cdot K)##


    2. Relevant equations
    Newtons law of cooling: ##T(t)=(T_1-T_0)e^{-\frac{k}{c}t}+T_0##

    3. The attempt at a solution

    Im stuck with that ##k## in the exponential. I know how to use the differential equation but i can't solve for ##t## as long as i have that unknown ##k## there, right? Can I approximate it or something?

    Can I do something else? Since they give me the volume and density I'm thinking that maybe i should go with some other approach?
     
  2. jcsd
  3. Sep 21, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Newton's law of cooling does not apply in a vacuum. How does energy transfer happen in a vacuum?
     
  4. Sep 22, 2015 #3
    Ofc, don't know what I was thinking. But hey, then I could just calculate the amount of heat needed to lower the temp. by 10 K and then use Stefan Boltzmanns law to solve for ##dt## right? Can I approximate it for a black body?
     
  5. Sep 22, 2015 #4
    The problem is solved! :)
     
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