Question

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What is the temperature at the plane where the wood meets the Styrofoam? Express your answer using two significant figures Constants A carpenter builds an exterior house wall with a layer of wood 3.2 cm thick on the outside and a layer of Styrofoam insulation 2.4 cm thick on the inside wall surface. The wood has k-0080w/(m·K), and he Styrofoam has k 0.010 W/(m K). The interior surface temperature is 20.0 °C, and the exterior surface temperature is-12.0 C T- OC You may want to review (Pages 565-572) Submit Request Answer For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Conduction through two bars in contact Part B What is the rate of heat flow per square meter through this wall? Express your answer using two significant figures. W/

Answer 1

Part A

Heat flow through wood is equal to heat flow through styrofoam.

k₁L₂(T - T₁) = k₂L₁ (T₂ - T)

here 1 is for wood and 2 is for styrofoam.

T = k₁L₂T₁ + k₂L₁T₂ /  k₁L₂ + k₂L₁

T = 0.080*0.024*(-12) + 0.010*0.032*20 / 0.080*0.024 + 0.010*0.032

T = -0.02304 + 0.0064 / 0.00224

T = -7.428 ⁰C

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Part B

Heat flow = 0.080 * (-7.428 - (-12)) / 0.032

Heat flow = 11.43 W/m²