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Standard XII

Physics

Conduction Law

A rod of leng...

Question

A rod of length $l$ and cross section area A has a variable thermal conductivity given by $k = α T$ where $α$ is a positive constant and $T$ is temperature in Kelvin. Two ends of the rod are maintained at temperature $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ . Heat current flowing through the rod will be

\frac{A α (T_{1}^{2} - T_{2}^{2})}{l}

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\frac{A α (T_{1}^{2} + T_{2}^{2})}{l}

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\frac{A α (T_{1}^{2} + T_{2}^{2})}{3 l}

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\frac{A α (T_{1}^{2} - T_{2}^{2})}{2 l}

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Solution

The correct option is D $\frac{A α (T_{1}^{2} - T_{2}^{2})}{2 l}$

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A rod of length l and cross section area A has a variable thermal conductivity given by k=αT where α is a positive constant and T is temperature in Kelvin. Two ends of the rod are maintained at temperature T1 and T2 (T1>T2). Heat current flowing through the rod will be

The correct option is D Aα(T21−T22)2l

The correct option is D $\frac{A α (T_{1}^{2} - T_{2}^{2})}{2 l}$