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Thermal Conductivity Problem

  1. Jan 10, 2012 #1
    1. The problem statement, all variables and given/known data
    One end of a metal rod is maintained at 100 degrees C, and the other end is maintained at 0 degrees C by an ice-water mixture. The rod is 60 cm long and has a cross-sectional area of 1.25 cm^2. The heat conducted by the rod melts 8.50 g of ice in 10.0 min. Find the thermal conductivity of the metal if 30% of heat is lost to the surroundings.

    2. Relevant equations
    (Q/t) = mLf/t
    where (Q/t) is the heat flow, Lf is the latent heat of fusion

    (Q/t) = KA(delta T)/L
    where K is the thermal conductivity of the metal, A is the area, delta T is the temperature difference, and L is the length.

    3. The attempt at a solution
    First, I solved the heat flow of the metal using the mass of the melted ice and the time it took to melt that amount of ice;

    (Q/t)= [8.5g(80cal/g)x.70]/600s = 119/150 cal/s

    Then I solved the K of the metal;

    119/150 cal/s = [K(1.25 cm^2)(100C-0C)]/60 cm
    K = 0.381 cal/cm.s.C

    BUT THEN..
    I saw a solution of my classmate that used something like this;

    (Q/t)={[8.5g(80cal/g)]/.70}/600s = 34/21 cal/s

    so his K is about 0.777 cal/cm.s.C

    that's where I'm confused. Should I divide or multiply the .70?
  2. jcsd
  3. Jan 10, 2012 #2
    Your friend is correct.
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