Two different metal rods of the same length have their ends kept at the same temperatures $θ_{1}$ and $θ_{2}$ with $θ_{2}$ > $θ_{1}$ . If $A_{1}$ and $A_{2}$ are their cross-sectional areas and $k_{1}$ and $k_{2}$ their thermal conductivities, the rate of heat flow in the two rods will be same if

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$\frac{k_{1}}{k_{2}} = \frac{A_{2}}{A_{1}}$

Rate of heat flow is $\frac{Q}{t} = \frac{k A (θ_{2} - θ_{1})}{l}$
Since $(θ_{2} - θ_{1})$ and l are the same for the two rods, the rate of flow $\frac{Q}{t}$ will be the same if the product kA is the same for the two rods, i.e., if
$k_{1} A_{1} = k_{2} A_{2} \Rightarrow \frac{k_{1}}{k_{2}} = \frac{A_{2}}{A_{1}}$
Hence, the correct choice is (b).

Suggest Corrections

Similar questions

Two different metal rods of the same length their ends kept at the same temperatures $θ_{1}$ and $θ_{2}$ with $θ_{2}$ > $θ_{1}$ If $A_{1}$ and $A_{2}$ are their cross-sectional area and $K_{1}$ and $K_{2}$ their thermal conductivities, the rate of flow of heat in the two rods will be the same if

Two different metal rods of the same length have their ends kept at the same temperatures $θ_{1}$ and $θ_{2}$ with $θ_{2}$ > $θ_{1}$ . If $A_{1}$ and $A_{2}$ are their cross-sectional areas and $k_{1}$ and $k_{2}$ their thermal conductivities, the rate of heat flow in the two rods will be same if

Two different metal rods of equal lengths and equal areas of cross-section have their ends kept at the same temperatures $θ_{1}$ and $θ_{1}$ If $k_{1}$ and $k_{2}$ are their thermal conductivities, $ρ_{1}$ and $ρ_{2}$ their densities and $s_{1}$ and $s_{2}$ their specific heats, then the rate of flow of heat in the two rods will be the same if