Question

An immersion heater is rated $418W$. It should heat a litre of water from ${10^ \circ }C$ to ${30^ \circ }C$ in nearly
A. $40s$
B. $21s$
C. $24s$
D. $16s$

Answer 1

Heat or thermal energy is the form this energy possesses when it is being transferred between systems and surroundings. This flow of energy is referred to as heat. To solve the given question, we will first list the data needed and then apply the formula of heat developed in a body and equate it with power.

Formula used:
$C = \dfrac{Q}{{m\Delta T}}$
$P = \dfrac{Q}{t}$

Complete step-by-step answer:
When we supply heat to a body, its temperature increases. The amount of heat absorbed by the body depends upon its mass, the change in body depends upon the material of the body as well as the surrounding conditions, such as pressure.
Mathematically, we write the equation as
$Q = ms\Delta T$ $- - - (i)$
Where $\Delta T$ is change in temperature, $m$ is the mass of the body and $Q$ represents the heat supplied, $s$ represents the specific heat capacity of the substance.
Additionally, we also know that thee rate of heat produced by the heater will be given by,
${\text{Rate of heat produced}} = \dfrac{P}{t}$ $- - - (ii)$
Where is $P$ the power of the heater and $t$ is the time for which the heater works.
Given: \eqalign{ & P = 418W \cr & {T_1} = {10^ \circ }C \cr & {T_2} = {30^ \circ }C \cr & \Rightarrow \Delta T = {T_2} - {T_1} \cr}
Now, we know that the heat absorbed by $1l$ water to raise the temperature from ${10^ \circ }C$ to ${30^ \circ }C$ must be equal to the rate of heat produced by the heater. So, equating equation $(i){\text{and }}(ii)$ we get,
$\dfrac{P}{t} = ms\Delta T$
$\Rightarrow t = \dfrac{P}{{ms\Delta T}}$
$\Rightarrow t = \dfrac{{418}}{{(1)(1)(30 - 10)}}$ ; $s = 1$ is taken for water
$\Rightarrow t = \dfrac{{418}}{{20}} = 20.9 \approx 21s$

So, the correct answer is “Option B”.

Note: Power is the amount of energy transferred or converted per unit time. In the international system of units, the unit of power is taken in Watt, which is equal to one joule per second.