hw_4_solutions - 1 Two walls are constructed on made of...

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1. Two walls are constructed, on made of copper with thermal conductivity of 400 ௠௄ and the other made of wood with thermal conductivity of 0.1 ௠௄ . How much more heat is lost by the copper wall assuming a temperature differential of 50°C. You may assume the walls are identical in every way excepting the material. Solution We can set up the conduction equation for the two scenarios: ݍ ஼௨ = −݇ ஼௨ ܣ ∆ܶ ∆ܺ = −400 × ܣ × 50 ∆ܺ ݍ ௪௢௢ௗ = −݇ ௪௢௢ௗ ܣ ∆ܶ ∆ܺ = −0.1 × ܣ × 50 ∆ܺ To determine how much more heat the copper wall would lose, we can take the quotient ೎ೠ ೢ೚೚೏ by dividing the two equations: ݍ ஼௨ ݍ ௪௢௢ௗ = −400 × ܣ × 50 ∆ܺ −0.1 × ܣ × 50 ∆ܺ Since the two walls are identical in every way we can eliminate A and ∆ܺ in the equation and we get: ݍ ஼௨ ݍ ௪௢௢ௗ = −400 × 50 −0.1 × 50 = 4000 Thus, we can surmise that the copper wall tends to lose heat 4000 times as much as the wooden wall.
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