Calculating Heat Released by Heating Filament

The question asks us to determine the amount of heat released by a heating filament given its power rating and the time it is operational. This involves understanding the relationship between power, energy (heat), and time.

Understanding the Concepts

• Power (P): Power is the rate at which energy is transferred or converted. In electrical circuits, power is the rate at which electrical energy is converted into other forms of energy, like heat or light. The unit of power is the Watt (W), which is equivalent to Joules per second (J/s).
• Energy (E) / Heat (Q): Energy is the capacity to do work or produce heat. When current flows through a resistor like a heating filament, electrical energy is converted into heat energy due to the resistance. The unit of energy is the Joule (J).
• Time (t): This is the duration for which the heating filament is operating. The unit of time is typically seconds (s).

The fundamental relationship between power, energy, and time is given by the formula:

\( \text{Power} = \frac{\text{Energy}}{\text{Time}} \)

Rearranging this formula to find the energy (or heat released), we get:

\( \text{Energy (Heat)} = \text{Power} \times \text{Time} \)

Applying the Formula

We are given the following values for the heating filament:

• Power (P) = 24 W
• Time (t) = 6 seconds

Now, we can substitute these values into the formula to calculate the heat released (Energy):

\( \text{Heat (Q)} = \text{P} \times \text{t} \)

\( \text{Q} = 24 \, \text{W} \times 6 \, \text{s} \)

\( \text{Q} = 144 \, \text{J} \)

Since 1 Watt is equal to 1 Joule per second (1 W = 1 J/s), multiplying Watts by seconds gives us Joules (J). Therefore, the heat released by the heating filament is 144 Joules.

Conclusion

The heat released by the heating filament rated 24 W when it is kept on for 6 seconds is 144 Joules.

Revision Table: Power, Energy, and Time

Additional Information on Electrical Heating

The heat produced by a heating element when electric current flows through it is often referred to as Joule heating or resistive heating. The amount of heat produced is also related to the current (\( I \)), voltage (\( V \)), and resistance (\( R \)) of the filament.

• Using Ohm's Law (\( V = I \times R \)), we can express power in different ways:
• \( P = V \times I \)
• \( P = I^2 \times R \) (This form, \( I^2R \), is directly related to Joule's Law of heating)
• \( P = \frac{V^2}{R} \)

The heat released (\( Q \)) over time (\( t \)) can thus also be expressed using these forms of power:

• \( Q = V \times I \times t \)
• \( Q = I^2 \times R \times t \)
• \( Q = \frac{V^2}{R} \times t \)

In this specific problem, we were directly given the power (\( P \)) and time (\( t \)), making the calculation \( Q = P \times t \) the most straightforward method.