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Heat flow problem (copper pipe)

  1. Mar 20, 2014 #1

    A copper bar with a cross sectional area of 4.40 cm2 and a length of 0.62 m has one end at 1 °C and the other end at 97 °C. Find the heat flow through the bar if the thermal conductivity of copper is 385 W/(m·K)

    2. Relevant equations

    R = (λ*L)/A

    I = ΔT / R

    k = 1/λ

    R = resistance
    λ = thermal resistivity
    L = length of pipe
    A = cross sectional area

    I = thermal current
    ΔT = change in temperature

    k = thermal conductivity

    3. My attempt

    So first I converted the area 4.40 cm2 into 0.044 m2.

    Then I converted the thermal conductivity given in the problem to thermal resistivity

    k = 1/λ
    λ = 1/k
    = 1/385 W/(m·K) = 0.00259 mK/W

    Using this value, the area, and the length from the problem, I used R = (λ*L)/A

    R = (0.00259 mK/W)(0.62 m) / 0.044 m2
    R = 0.0366 K/W

    Now I plugged this R into the thermal current formula I = ΔT/R, where ΔT = 97 °C - 1 °C = 96 °C

    The ΔT is measured in Kelvin, but is still a difference of 96 units.

    I = 96K / 0.0366 K/W = 2622.95 W = 2622.95 J/s

    This is incorrect apparently. Does anybody know where I might have went wrong?

  2. jcsd
  3. Mar 20, 2014 #2


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    Homework Helper
    Gold Member

    Hello, BMcC. I haven't checked all of your numbers, but I did notice that you made a common mistake in converting 4.40 cm2 to m2.
  4. Mar 20, 2014 #3
    Ah wow how silly of me. That changes everything. Thanks TSny!

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