Heat moving through the walls of a house

  1. A carpenter builds an exterior house wall with a layer of wood 3.2 {\rm cm} thick on the outside and a layer of Styrofoam insulation 2.4 cm thick on the inside wall surface. The wood has k=0.080 W/(m* K, and the Styrofoam has k= 0.010 W/ m* K)}. The interior surface temperature is 20.0C, and the exterior surface temperature is -12.0C.

    What is the temperature at the plane where the wood meets the Styrofoam?


    so i set up

    H=Ak(Tf-T0)/L

    H=Ak(Tf-T0)/L

    set them both equal so the A drops out

    .08(x-20)/.o32=.01(x+12)/.024

    and get 26.4 which is wrong, so where am i going wrong at?
     
  2. jcsd
  3. PeterO

    PeterO 2,319
    Homework Helper

    Your temperature difference on the LHS is wrong way round.

    x will be between 20 and -12, so the temp differences should be 20 - T, and T - (-12)

    Hopefully that fixes it up.
     
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