question archive A carpenter builds an exterior house wall with a layer of wood 3
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A carpenter builds an exterior house wall with a layer of wood 3.2cm thick on the outside and a layer of Styrofoam insulation 2.3 cm thick on the inside wall surface. The wood has k=0.080W/(m⋅K), and the Styrofoam has k= 0.010 W/(m⋅K). The interior surface temperature is 20.0 ?C , and the exterior surface temperature is -11.0 ?C .
What is the temperature at the plane where the wood meets the Styrofoam?
Answer:
T = (k1 L2 T1 + k2 L1 T2)/(k1 L2 + k2 L1)
T = ((0.08)*(0.023)*(-11)+(0.010)*(0.032)*(20))/((0.08)*(0.023)+(0.010)*(0.032))
T = -6.41 C