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Finding thermal conductivity of an insulated metal bar

  1. Sep 2, 2014 #1
    1. The problem statement, all variables and given/known data

    One end of an insulated metal rod is maintained at 100∘C and the other end is maintained at 0.00 ∘C by an ice–water mixture. The rod has a length of 60.0cm and a cross-sectional area of 1.40cm2 . The heat conducted by the rod melts a mass of 7.15g of ice in a time of 15.0min .
    Find the thermal conductivity K of the metal.


    2. Relevant equations

    (Heat/time) = k(A)(ΔT/L)
    H(fusion) for water = 334 KJ/kg*K = 334000 J/kg


    3. The attempt at a solution

    Converting to SI units -> L=.6 m, A= .014 m^2, m(ice) = .00715 kg, time= 900s

    Q=heat/time, so heat = .00715 kg(334000 J/kg) = 2388 J, Q = 2388J/900s = 2.6533 J/s = 2.653W

    So, 2.653 W = k(.014 m^2)(100°C/.6m)

    2.653 W / ( .014 m^2 ) *.6m / 100 C ≈ 1.14 W/m*C OR 1.14W/m*K since K or C can be used interchangeably here.

    So, my answer kept coming up as 1.14, yet the correct answer was 114 W/m*K.

    I am confused as to why I'm getting the correct answer in a sense but with my order of magnitued off. It makes me wonder if I'm doing my math correctly or I made a careless mistake somewhere. Any and all help/advice will be greatly appreciatied.
     
    Last edited: Sep 2, 2014
  2. jcsd
  3. Sep 2, 2014 #2

    haruspex

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    Try that one again.
     
  4. Sep 2, 2014 #3
    Oh, I completely forgot to divide by 100 twice. I'm getting the right answer now, thanks!
     
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