Question

The quantity of heat conducted through a metal rod kept at its ends at 100°C and 120°C is 5 J/s. If the ends are kept at 200°C and 220°C, then the quantity of heat conducted in 10 seconds is:

• A. 5 J
• B. 25 J
• C. 10 J
• D. 100 J
• E. 50 J

Hint:

The quantity of heat conducted is directly proportional to the temperature difference when all other conditions remain constant. So, if the temperature difference remains the same, the heat conducted remains constant.

Answer 1

Answer: (E)

The quantity of heat conducted through a rod is governed by the formula for thermal conduction:
\[ Q = \frac{Q_1}{\Delta T_1} = \frac{Q_2}{\Delta T_2} \] where: - \( Q_1 \) is the heat conducted in 1 second with the temperature difference \( \Delta T_1 = 120^\circ C - 100^\circ C = 20^\circ C \),
- \( Q_2 \) is the heat conducted in 1 second with the temperature difference \( \Delta T_2 = 220^\circ C - 200^\circ C = 20^\circ C \).
Given that \( Q_1 = 5 \, {J/s} \), the heat conducted in 1 second is 5 J for a temperature difference of 20°C.
When the temperature difference is also 20°C (from 200°C to 220°C), the heat conducted per second will remain the same, which is 5 J.
Now, the total heat conducted in 10 seconds is: \[ Q_{{total}} = 5 \times 10 = 50 \, {J} \] Thus, the quantity of heat conducted in 10 seconds is: \[ \boxed{50 \, {J}} \]