The ends of a metal rod are kept at temperature -1 and -2 with -2 - -1- Then rate of flow of heat along the rod is directly proportional to

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Dimensional Analysis

The ends of a...

Question

The ends of a metal rod are kept at temperature $θ_{1}$ and $θ_{2}$ with $θ_{2} > θ_{1}$ . Then rate of flow of heat along the rod is directly proportional to

the length of the rod

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the diameter of the rod

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the cross-sectional area of the rod

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the temperature difference

(θ_{2} - θ_{1})

between the ends of the rod

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Solution

The correct options are
B the cross-sectional area of the rod
D the temperature difference $(θ_{2} - θ_{1})$ between the ends of the rod
The rate of heat flow is directly proportional to cross-sectional area of rod, and the temperature difference between the ends of the rod. It is inversely proportional to length of rod and directly proportional to square of diameter.
The rate of flow of heat is given by
$P = \frac{Q}{t} = \frac{K A (θ_{2} - θ_{1})}{l}$
Where $K$ is the thermal conductivity, $A$ is the cross-sectional area and l the length of the rod. Hence, the correct choice are $(c)$ and $(d) .$

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The ends of a metal rod are kept at temperature θ1 and θ2 with θ2>θ1. Then rate of flow of heat along the rod is directly proportional to

The ends of a metal rod are kept at temperature $θ_{1}$ and $θ_{2}$ with $θ_{2} > θ_{1}$ . Then rate of flow of heat along the rod is directly proportional to