Question

A Big Mac hamburger from McDonald's contains $540$ calories.
(a) How many kilojoules does a big Mac contain?
(b) For how many hours would the amount of energy in a big Mac light a $100$ watt light-bulb ($1watt = 1J{s^{ - 1}}$).

Answer 1

In the above question we have been given the content of the burger in the form of calories. Calorie is the unit of energy and it is smaller than that of joules. As per our knowledge we know that $1calorie = 4.184J$ and we have to use this conversion to solve this problem.

Complete step by step answer:
Let us use the given information that the big Mac hamburger contains $540$ calories then
We have,
$1calorie = 4.184J$
$\therefore 540calories = 540 \times 1calorie$
$= 540 \times 4.184J$
$= 2259.36J$
We have been asked the content in the form of kilojoules
Now, we know that the ${10^3}grams = 1kilo$
$\therefore 540calories = 2.259 \times {10^3}J$
$= 2.259kJ$
Hence the big Mac contains $2.259kJ$
Now, we have been asked about the time in hours the amount of energy in a big mac burger can light a $100$ watt light bulb.
Here, we already have found out how much energy a big Mac contains in the (a.) part of this question.
Energy $= 2.259kJ$
$1watt = 1J{s^{ - 1}}$ $\Rightarrow 100watt = 100J{s^{ - 1}}$
$1hour = 3600s$
This is the given data and we have to make use of this data to find out the answer of this question.
Now, for hours $(T)$ taken to light the lightbulb is given as follows:
$T = \dfrac{{2.259J}}{{100J{s^{ - 1}}}} \times \dfrac{{1hour}}{{3600s}}$
$\Rightarrow T = \dfrac{{2.259{J}}}{{100{J}{{{s}}^{ - 1}}}} \times \dfrac{{1hour}}{{3600{s}}}$
On solving, this gives the answer as
$\Rightarrow T = 6.276 \times {10^{ - 3}}hours$
Hence, the time to light up the bulb is $6.276 \times {10^{ - 3}}hours$ with the energy that contains the Mac.

Note:
We must be careful about the conversion of the units as we did in the above answering procedure. It needs good calculation and conversion knowledge to do this type of problem. Energy, power, hour all are interdependent values and need to be aware about their units.