Two rods A and B are of equal length. Each rod has its ends at temperatures T₁and T₂ What is the condition that will ensure equal rates of flow of heat through both the rods?

Solution

Rate of flow of heat through a rod of length l, cross-sectional area A whose ends are maintained at temperatures T₁ and T₂ (T₁ > T₂) is,

dQ over dT equals straight K fraction numerator left parenthesis straight T subscript 1 minus straight T subscript 2 right parenthesis over denominator straight ell end fraction

where K is the thermal conductivity of metal.
Therefore the rate of flow of heat through the above said rods will be same if,

straight K subscript straight A straight A subscript straight A equals straight K subscript straight B straight A subscript straight B

The above equation is the required condition.

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