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Two rods have the same length and are kept with their ends at the same temperatures. Their cross-sectional areas are A₁ and A₂, thermal conductivities are K₁ and K₂, specific heats are c₁ and c₂, and densities are d₁ and d₂. If heat is conducted through both rods, then the ratio of the rates of heat flow in the two rods is

1. A₁/A₂ = -K₁/K₂
2. A₁/A₂ = K₁c₁d₁ / K₂c₂d₂
3. A₁/A₂ = K₁c₁ / c₂d₂
4. A₁/A₂ = K₂/K₁

Correct answer: A₁/A₂ = K₂/K₁

Solution

The correct option is based on Fourier's law of heat conduction, which states that the rate of heat flow is directly proportional to the cross-sectional area and the thermal conductivity of the material. Therefore, the ratio of the areas A₁ and A₂ is equal to the inverse ratio of their thermal conductivities K₂ and K₁.

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