APFIVE Temperature-Dependent Thermal Conductivity
The thermal conductivity k of a material varies with temperature T according to the equation k = k₀(1 + αT), where k₀ and α are positive constants. A slab of this material has a thickness L, and its faces are maintained at constant temperatures T₁ and T₂, with T₁ > T₂. Which of the following expressions represents the rate of heat transfer per unit area through the slab?
A
k₀(T₁-T₂)/L
B
k₀(1 + αT₁)(T₁-T₂)/L
C
k₀(1 + α√(T₁T₂))(T₁-T₂)/L
D
k₀(1 + α(T₁+T₂)/2)(T₁-T₂)/L
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