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Two rods of same length and area of cross-section A₁ and A₂ have their ends at the same temperature. If K₁ and K₂ are their thermal conductivities, c₁ and c₂ are their specific heats and d₁ and d₂ are their densities, then the rate of flow of heat is the same in both the rods if

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$\frac{A_{1}}{A_{2}} = \frac{- k_{1}}{k_{2}}$

$\frac{A_{1}}{A_{2}} = \frac{k_{1} c_{1} d_{1}}{k_{2} c_{2} d_{2}}$

$\frac{A_{1}}{A_{2}} = \frac{k_{2} c_{1} d_{1}}{k_{1} c_{2} d_{2}}$

$\frac{A_{1}}{A_{2}} = \frac{k_{2}}{k_{1}}$

answer is D.

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Detailed Solution

$\frac{Q}{t} = K_{1} A_{1} \frac{d θ}{d x} = K_{2} A_{2} \frac{d θ}{d x}$

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