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Rate of heat transfer passing from the boiling water to the ice bath

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data
    A copper rod of length 0.20 m and cross-sectional area 6.00 10-2 cm2 is connected to an iron rod with the same cross section and length 0.28 m (the figure below). One end of the copper is immersed in boiling water and the other end is at the junction with the iron. If the far end of the iron rod is in an ice bath at 0° C, find the rate of heat transfer passing from the boiling water to the ice bath. Assume there is no heat loss to the surrounding air.


    What equation do I need to solve this could someone help?
     
  2. jcsd
  3. Dec 6, 2011 #2

    PeterO

    User Avatar
    Homework Helper

    Check this explanation

    http://hop.concord.org/h1/phys/h1pm.html

    which ends with a formula

    OR [pasted from another site.

    Basic Theory
    The rate at which heat is conducted
    through a material is proportional
    to the area normal to the heat flow
    and to the temperature gradient
    along the heat flow path. For a one
    dimensional, steady state heat flow
    the rate is expressed by Fourier’s
    equation:

    Q = kA ΔT/d

    Where:
    k = thermal conductivity, W/m-K
    Q = rate of heat flow, W
    A = contact area
    d = distance of heat flow
    ΔT = temperature difference

    The trick with the two rods is that the rate of heat flow in each must be the same, so the temperature at the Cu/Fe junction will NOT be 50 degrees.
    Given that Copper conducts heat much better than Iron it will be closer to 100.
    If, for example, copper conducts 9 times as well as Iron, the temp would be 90 degrees.
    heat flow through copper with a 10 degree difference [100 - 90] would equal heat flow through Iron with a 90 degree difference [90 - 0].
     
  4. Dec 7, 2011 #3
    Q/ Time = (Thermal conductivity) x (Area) x (Thot - Tcold)/Thickness

    thermal conductivity of copper = 401 W/m K
    thermal conductivity of iron = 80 W/m K

    For copper heat conduction:
    Q/t = 401 * .0006 m^2 * (100C - 0C) / .20 m thickness
    Q/t = 120.3 watts conduction heat loss up to iron junction

    For iron conduction:
    Q/t = 80 * .0006 m^2 * ( 100C - 0C) / .28 cm = 17.1 watts heat conduction from junction to ice bath.

    Is my work correct??? I dont know what to do after?
     
  5. Dec 7, 2011 #4
    The temperature difference of 100C is across both rods. You do not know the temperature at the junction of the copper and the iron.... call it ∅.
    The temp difference for the copper is then (100 - ∅).... put this in your copper equation.
    The temp difference across the iron is (∅-0) =∅...put this in the iron equation
    You will then have 2 equations for heat flow through copper and iron. These are equal so find ∅ then substitute back to find heat flow.
    I got ∅ = 87.5C and rate of heat flow 1500W
     
  6. Dec 8, 2011 #5
    How did you solve for ∅?
     
  7. Dec 8, 2011 #6
    For the copper
    dQ/dt = 401 x 0.0006^2 x (100-∅)/0.2

    For the iron
    dQ/dt = 80 x 0.0006^2 x (∅ -0)/0.28
    These 2 equations are equal
    Can you do the algebra to find ∅?
    If not ask and I will do the next step
     
  8. Dec 9, 2011 #7
    Can you do the next step please
     
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