A rod of length l with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as K x = α T (here α is a positive constant). The ends of the rod are kept at temperature T 1 and T 2 ( T 1 T 2 ). Find the heat current per unit cross-sectional area in the rod

Question

A rod of length l with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as K x = α T (here α is a positive constant). The ends of the rod are kept at temperature T 1 and T 2 ( T 1 > T 2 ). Find the heat current per unit cross-sectional area in the rod, α l l n T 1 + T 2 T 1, α l l n T 1 T 2, α l l n 2 T 1 T 1 + T 2, α l l n T 1 + T 2 T 2

MARKS App · Accepted Answer

d Q d t = - K A T x + d x - T x d x ⇒ I 0 = - α T A d T d x ⇒ ∫ 0 l I 0 A α d x = - ∫ T 1 T 2 d T T ∴ I 0 l A α = l n T 1 T 2 ⇒ I 0 A = α l l n T 1 T 2

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