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Homework Help: Thermal Conductivity of a Metal Rod

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data

    One end of an insulated metal rod is maintained at 100^\circ C and the other end is maintained at 0.00 ^\circ {\rm C} by an ice–water mixture. The rod has a length of 75.0 cm and a cross-sectional area of 1.40 cm^2. The heat conducted by the rod melts a mass of 7.85 g of ice in a time of 15.0 min. Find the thermal conductivity k of the metal.


    2. Relevant equations

    H=dQ/dt=kA(T2-T1)/L

    3. The attempt at a solution

    I tried to solve for k using the formula for heat transfer and since H was not given, I substituted it with dQ/dt. Then in stead of dQ I used the equation for heat transformation Q=mL where m=mass of ice melted and L=333kj/kg which is the heat of fusion for water, if I'm not mistaken. I put everything in SI units and solved but I got the wrong answer. Did I make a wrong assumption somewhere?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 26, 2009 #2

    Delphi51

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    Homework Helper

    That all sounds good but the devil is in the details. What answer did you get?
     
  4. Jan 26, 2009 #3
    I got the answer 0.0022796947 w/(m*K)
     
  5. Jan 26, 2009 #4
    is there anyone else who can help me find out where I went wrong?
     
  6. Jan 27, 2009 #5

    Astronuc

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    Staff Emeritus
    Science Advisor

    Please show one's work, particularly, the value obtained for heat flux. If one is off by 4-orders of magnitude, look at the value for cross-sectional area given in cm2 and make sure it is properly converted to m2.

    I obtain a value on the order of the thermal conductivity of a metal. Thermal conductivity of Al is about 200 W/m-K, and that of Cu is about 385 W/m-K.

    Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html#c1
     
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