Question

A player gets 400 kilocalories energy from the daily food. His power will be
A) Zero
B) 1.93 watt
C) 19.3 watt
D) 193.5 watt

Answer 1

Hint: We can find the value of energy in joules from the given value in calories, similarly the time can be calculated in seconds the both of the respective quantities can be substituted in the formula of power so as to obtain its value.

Formula used:
$P = \dfrac{E}{T}$ where P is power, E is the energy and T is the time.
For conversions, remember:
1kg = 1000 g
1 gcal = 4.184 J
1 hr = 3600s $\left( {60 \times 60} \right)$

Complete step by step answer:
It is given that the energy he gets from the food is 400 kilocalories (cal), in joules )J) it can be written as:
$400{\text{ }}kilo{\text{ }} = \left( {400 \times 1000} \right)g$ $\left( {\because 1kg = 1000g} \right)$
1g calorie is equal to 4.184 J then:
$\left( {400 \times 1000} \right)gcal = \left( {400 \times 1000 \times 4.184} \right)J$
If it is the energy he’s getting on a daily basis, it means that the time involved is 24 hours as a day comprises 24 hours.
24 hours in terms of seconds can be written as:
$
24hrs = \left( {24 \times 60 \times 60} \right)s \\
\left(\Rightarrow 1hr = 60\min \\
60\min s = 60\operatorname{s} \\
\Rightarrow 1hr = 60\min s \times 60s \\ \right) \\
 $
Now, the power is defined as the energy consumed per unit time and can be given mathematically as:
$P = \dfrac{E}{T}$ here the calculated values are,
Energy (E) = $\left( {400 \times 1000 \times 4.184} \right)J$
Time (T) = $24hrs = \left( {24 \times 60 \times 60} \right)s$
Substituting the values, we get:
\[
  P = \dfrac{{\left( {400 \times 1000 \times 4.184} \right)J}}{{\left( {24 \times 60 \times 60} \right)s}} \\
\Rightarrow P = 19.3W \\
 \]

So, the correct answer is “Option C”.

Note:
We made the respective conversions because, while calculating, we have to use the SI units of the respective quantities while performing calculations and get the required answer. The important SI Units for this question are:
Energy – Joules (J)
Time – Seconds (s)
Power – Watt (W)
We describe power as the energy per unit time because unit means 1 ad when the denominator in its formula becomes 1, it becomes equal to the numerator which is energy.