Question Video: Conversion between Kilocalories and Kilojoules Using the Energy Consumption of the Adult Human Body

Video Transcript

It is estimated that the average
adult should consume around 2000 kilocalories per day to maintain a healthy
lifestyle. What is this value in units of
kilojoules?

2000 kilocalories is an amount of
energy, and kilojoules is another unit of energy. So we can ignore the per day. We can break down a kcal into k and
cal. The k corresponds to kilo, which
means 1000 of something, and cal stands for calorie or small calorie. So kilocalorie refers to 1000
calories. Meanwhile, the symbol for
kilojoules is kJ. The J corresponds to joule. Our starting unit and our final
unit both have kilo in them, so we don’t need to focus in on that. What we do need to remember is the
relationship between calories and joules. It takes about one calorie to warm
one milliliter of water one degree Celsius. But officially, one calorie is
defined as 4.184 joules. If we scale both sides by 1000, we
end up with the same numerical relationship between kilocalories and kilojoules.

Now we have all the information we
need to convert our kilocalories to kilojoules. We start by multiplying our 2000
kilocalories by 4.184 kilojoules per kilocalorie. So our answer is 8368
kilojoules. Alternatively, you could have done
it in steps, first, by converting from kilocalories to calories by multiplying by
1000 calories per kilocalorie, then convert it to joules by multiplying by 4.184
joules per calorie, and then finally convert it to kilojoules by multiplying by 10
to negative three kilojoules per joule. If we cancel common terms along
this route, we end up with exactly the same conversion factor. So regardless of the route, 2000
kilocalories is the equivalent of 8368 kilojoules.