The calorie and the food Calorie

Let's say we have a liter of water (1000 ml) at 5 degrees Celsius and we want to heat it up to boiling (100 degrees Celsius).  How many calories would this take?

1000 ml H2O at 5 degrees C + ? calories = 1000 ml H20 at 100 degrees C
 
Let's think about this:
Well, each ml of water requires one calorie to go up 1 degree Celsius, so this liter of water takes 1000 calories to go up 1 degree Celsius.  (There are 1000 ml, each of which needs to have its temperature raised.)

So, if we add only 1000 calories, we will end up with the liter of water at 6 degrees Celsius.  We will need to add 95,000 calories to raise the temperature of this liter of water all the way to the boiling point.

Another way of working this out:
How many degrees does each ml need to rise?  100 - 5 = 95 degrees.

So, how much energy does each ml need?  95 calories.

How many ml do we have?  1000 ml.

So we have 1000 little cubes of water 1 cm on a side, and each requires 95 calories.
We need 95 * 1000 = 95,000 calories.

How much is 95,000 calories?  It turns out a food Calorie is actually 1000 calories (also called a Kilocalorie).  So, a soda containing 150 Calories actually has 150,000 calories, more than enough to bring our liter of water from 5 degrees Celsius to 100 degrees Celsius.  The number of calories in food can be determined by burning the food and using the heat released to warm up a given quantity of water.  For instance, if you were to burn a teaspoon of peanut butter, the heat produced would heat a 1000 ml of water 35 degrees:  from this we would say that this amount of peanut butter has 35,000 calories (or 35 Calories) in it.
 

Now you try some examples:

How many calories would it take to heat 1 ml of water from 20 degrees C to 30 degrees C?

How many calories would it take to heat 100 ml of water from 20 degrees C to 30 degrees C?

If you added 150 calories to 5 ml of water at 10 degrees C, what would the final temperature be?

Try making up and answering some questions of your own.


© Appalachian State University
Science Education On-line
Dr. Leslie Bradbury and Mr. Jeff Goodman