Question

Two identical square rods of metal are welded end to end as shown in figure (1), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (2), the same amount of heat will flow through the rods in

A. 1 minute
B. 2 minute
C. 4 minute
D. 16 minute

Answer 1

Hint:The rate of heat flow is defined as the amount of heat that is transferred per unit of time in any material. It is usually measured in watts (or joules per second). To solve this problem, we compare the rate of heat flow when the length of the material will double and when the area of the material will double.

Formula used:
Heat flow rate is given as,
\[\dfrac{{dh}}{{dt}} = k \times A \times \left( {\dfrac{{dT}}{{dx}}} \right)\]
Where k is the thermal conductivity, A is the boundary surface area and \[\dfrac{{dT}}{{dx}}\] temperature gradient.

Complete step by step solution:
As we know that the heat flow rate is given as,
\[\dfrac{{dh}}{{dt}} = \dfrac{{k \times A \times \Delta t}}{l}\]
As for the figure (1), with double length, we have
\[\dfrac{{20}}{4} = \dfrac{{k \times A \times \Delta t}}{{2l}}\] ……1
for figure (2), with double length, we have
\[\dfrac{{20}}{t} = \dfrac{{k \times 2A \times \Delta t}}{l}\] …….2
Now dividing equations 1 and 2, we get
\[\dfrac{t}{4} = \dfrac{1}{4}\]
\[\therefore t = 4\]
Time, t = 4 minute
Therefore, the same amount of heat will flow through the rods in 4 minutes.

Hence option C is the correct answer.

Note: Heat transfer is the process in which there is the exchange of heat from a high-temperature body to a low-temperature body. As kinetic energy is the parameter included by the particles in the system. When the temperature of a system increases then the kinetic energy of the particle in that system will also increase.