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Two rods of thermal conductivities K₁ and K₂, cross-sections A₁ and A₂, and specific heats S₁ and S₂ are of equal lengths. The temperatures of two ends of each rod are T₁ and T₂. The rate of flow of heat at the steady state will be equal if:

1. K₁ / A₁S₁ = K₂ / A₂S₂
2. K₁A₁ = K₂A₂
3. K₁S₁ = K₂S₂
4. A₁S₁ = A₂S₂

Correct answer: K₁A₁ = K₂A₂

Solution

In the steady state, the rate of heat flow depends on the thermal conductivity and cross-sectional area of the rods. For the heat flow rates to be equal, the product of thermal conductivity and cross-sectional area must be the same for both rods, i.e., K₁A₁ = K₂A₂.

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