Question

The heat produced by a heater of $100W$ in 7 minutes?
(A) ${10^4}cal$
(B) ${10^5}cal$
(C) $1.2 \times {10^4}cal$
(D) $\dfrac{1}{2} \times {10^4}cal$

Answer 1

Hint:In this question, we need to evaluate the heat produced by the heater of rating 100 watts in 7 minutes. For this, we will first calculate the heat produced by a heater in the joules by using the relation between heat, power and time and then convert the joules into the calories to find the answer.

Formula Used:
$H = P \times t$ and $1cal = 4.2J$. $1cal = 4.2J$
Where $P$ is the power of heater and $t$ be the time.

Complete step by step answer:
In the given example, the power of the heater is $100W$.
We need to find the heat produced by the heater in 7 minutes.
Let $P = 100W$ where $P$ is the power of the heater.
Let $t$ be the time which is equal to 7 minutes.
Now, let us convert the time in seconds.
Therefore,
$
t = 7 \times 60 \\
\Rightarrow t= 420\sec $
Now, the heat produced by the heater in 7 minutes, that is, in 420 seconds can be calculated by taking the product of the power of the heater and the time.
$
  H = P \times t \\
\Rightarrow H = 100 \times 420 \\
\Rightarrow H = 42000J $
Therefore, the heat produced by the heater in 7 minutes is $42000J$. Now, we need to convert Joules to Calories.
$1cal = 4.2J$
Let $x$ be the heat produced by the heater in 7 minutes in calories.
$
x{\text{ }}cal = 42000J \\
\Rightarrow x{\text{ }}cal = \dfrac{{42000}}{{4.2}} \\
\Rightarrow x{\text{ }}cal = 10000 \\
\therefore x{\text{ }}cal = {10^4}
$
Hence, we can conclude that the heat produced by a heater of $100W$ in 7 minutes is equal to ${10^4}cal$.

So, option A is the correct answer.

Note: Students must know that the unit of energy is the joule, the unit of power is the watt, and the unit of time is the second. This enables them to convert the time from minutes to seconds.Students should understand that to find the answer in calories, they must first find the answer in the joules. They must also know that $1cal = 4.2J$. Then only the problem like above can be solved.