Question

If the radius and length of a copper rod are doubled, at the rate of heat flow along the rod increases to
A. 4 times
B. 2 times
C. 8 times
D. 16 times

Answer 1

Hint: In order to solve this problem we need to understand the rate of heat transfer. The rate of flow of heat is the amount of heat that is transferred per unit of time. Here, using the formula for heat flow we are going to find the solution.

Formula Used:
To find the heat flow the formula is,
\[Q = KA\dfrac{{\Delta T}}{L}\]
Where, A is a cross-sectional area, \[\Delta T\] is the temperature difference between two ends of a copper rod, L is the length of the cylinder and K is the thermal conductivity.

Complete step by step solution:
Suppose the radius and length of a copper rod are doubled, then we need to find how the rate of heat flow along the rod varies. We know the formula for the heat flow is,
\[Q = KA\dfrac{{\Delta T}}{L}\]
Since the K and \[\Delta T\] are constant, then, for the first rod and second rod is,
\[{Q_1} \propto \dfrac{{{A_1}}}{{{L_1}}}\]and \[{Q_2} \propto \dfrac{{{A_2}}}{{{L_2}}}\]
If the radius and length are doubled then, we can write as,
\[\dfrac{{{A_1}}}{{{L_1}}} = 2\dfrac{{{A_2}}}{{{L_2}}}\]
Then, we can write the thermal conductivity as,
\[{Q_1} = 2{Q_2}\]
Therefore, the rate of heat flowing along the rod increases by 2 times.

Hence, option B is the correct answer.

Note:Here in the given problem it is important to remember the formula of the rate of flow of heat transfer and on which factors it depends suppose if the radius and length are doubled how the rate of flow changes.