A rod of length ℓ = 1 m and cross section area A = 1 cm 2 has a variable thermal conductivity given by k = α T , where α = 4 in SI units and T is temperature in kelvin. Two ends of the rod are maintai

Question

A rod of length ℓ = 1 m and cross section area A = 1 cm 2 has a variable thermal conductivity given by k = α T , where α = 4 in SI units and T is temperature in kelvin. Two ends of the rod are maintained at temperatures T 1 ​ = 100 K and T 2 ​ = 0 K . Heat current (in W ) flowing through the rod will be :-

TestHub · Accepted Answer

Heat current : i = − k A d x d T ​ i d x = − k A d T i ∫ 0 ℓ ​ d x = − A α ∫ T 1 ​ T 2 ​ ​ T d T ⇒ i ℓ = − A α 2 ( T 2 2 ​ − T 1 2 ​ ) ​ ⇒ i = 2 ℓ A α ( T 1 2 ​ − T 2 2 ​ ) ​ = 2 × 1 1 0 − 4 × 4 × 10 0 2 ​ = 2 W

Physics - Heat & Thermo Question with Solution | TestHub

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