Question

An electric room heater has a resistance of $40\Omega $ and operates at $220V$ for 10 min. Calculate the heat energy dissipated by it in kilojoule.

Answer 1

Hint: Heat energy dissipated by a resistance is given by a unique formula. This formula holds true for all types of resistances. It includes the power along with the time of usage. This formula remains constant for all temperatures.

Formula used:
$H=P\times t$
$P={{I}^{2}}R=\dfrac{{{V}^{2}}}{R}$

Complete answer:
The heat energy dissipated by a resistor is given by a basic formula:
$\text{Heat = Power}\times \text{ Time}$
This can also be written as:
$H=P\times t$ ------(i)
We know that the power dissipated by a resistor is given by the formula:
$P={{I}^{2}}R=\dfrac{{{V}^{2}}}{R}$ -------(ii)
Where, $P$ is the power dissipated, $I$ is the current through the resistor, $V$ is the voltage across the resistor and $R$ is the resistance of the resistor.
Here, we are given with the resistance of the resistor and the voltage across the resistor.
Hence, the power absorbed by the resistor is given by:
$P=\dfrac{{{220}^{2}}}{40}$ ------(iii)
Now, using equation (i), the heat energy absorbed by the resistor is given by:
$H=\dfrac{{{220}^{2}}}{40}\times 10\min $
$\Rightarrow H=\dfrac{{{220}^{2}}}{40}\times 10\times 60\sec $
$\Rightarrow H=726000joules$
$\Rightarrow H=726KJ$
Hence, the resistor absorbs $726KJ$ of heat energy when connected to a supply of $220V$ for 10 minutes.

Additional Information:
The quantitative measure of the hotness or coolness of a body is termed as temperature. Heat is defined as the net energy contained by the atoms or molecules moving in a given volume. Heat energy can be transferred from one body to another by any of these three methods: Conduction, Convection or Radiation. The flow of heat energy depends upon the difference in the temperature of the bodies.

Note: Heat energy is not equal to the power of the resistor. Heat energy is the product of the power and the time of usage. Do not miss out the time of usage while calculating the heat energy absorbed by a resistor. It is their product which gives the total heat energy consumed.