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Temperature-Dependent Thermal Conductivity

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A material has thermal conductivity that varies with temperature according to k = k₀(1 + αT), where k₀ and α are constants. If a slab of this material has thickness L and faces at temperatures T₁ and T₂ (T₁ > T₂), which expression best approximates the heat transfer rate per unit area?

A

k₀(T₁-T₂)/L

B

k₀(1 + αT₁)(T₁-T₂)/L

C

k₀(1 + α(T₁+T₂)/2)(T₁-T₂)/L

D

k₀(1 + α√(T₁T₂))(T₁-T₂)/L

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