Consider two rods of same length and different specific heats ( $S_{1}$ and $S_{2}$ ), conductivities $K_{1}$ and $K_{2}$ and areas of cross section ( $A_{1}$ and $A_{2}$ ) and both having temperature $T_{1}$ and $T_{2}$ at their ends. If the rate of heat loss due to conduction is equal, then

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Solution

The correct option is A

According to problem, rate of heat loss in both rods is equal, i.e.,

${(\frac{d Q}{d t})}_{1}$ = ${(\frac{d Q}{d t})}_{2}$

$\Rightarrow \frac{K_{1} A_{1} Δ θ_{1}}{l_{1}}$ = $\frac{K_{2} A_{2} Δ θ_{2}}{l_{2}}$

$∴$ $K_{1} A_{1}$ = $K_{2} A_{2}$ [As $Δ θ_{1}$ = $Δ θ_{2}$ = $(T_{1} - T_{2})$ and $l_{1}$ = $l_{2}$ given]

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