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Posted by on Jun 2, 2011 in Physical Chemistry | 0 comments

The Thermodynamics of Weight Loss.

Imagine 10 of these on your belly

There are diets and fads galore out there, with one gimmick vying for another to take your money.  Such diets appeal to your desire to lose weight and your laziness to do it without effort: a quick and easy way to shed pounds, it is a big industry.

Thermodynamics is part of Physical Chemistry and Conservation of Energy is a basic law. The only way to lose weight is to eat less (less fuel) and exercise more (burn fuel).  Of course exercise is great for your health, but if you eat too much it is very difficult to burn off that excess fat by exercise alone.  It is much easier to eat less than exercise it away.

I will show this by working out how long it takes to burn off the energy from eating cookies that weight 100 grams (3.5 oz.) each.  Look at the cookie package and it tells you 100 g of cookies equals 150 Calories for example.

This means if you eat a cookie then when your body metabolizes it, 150 Calories of energy are produced. How do they know that?

Physical Chemistry again: The food company takes the cookies; grinds them up; puts a known amount, says 100 grams, in a bomb calorimeter with excess oxygen; and burns them. The heat released is measured and bingo, it is 150 Calories for 100 grams.

It does not matter if you burn cookies in your body or in a bomb calorimeter the energy change is the same. Energy is a state function because its value depends only on the initial state (cookies) and the final state (burned cookies).

Weight: Equilibrium, Gain and Loss

In the above figure, the “food-in” differs in a), b) and c).  In a) the food burned just equals what you need, so no weight change; in b) the “food-in” exceeds the bodies needs, so the excess is stored as fat; part c) weight is lost because not enough food is taken in, and so the body makes up the difference by burning fat.

Another way to ask the same question: suppose you have eaten all the food you need to keep your metabolism and daily activity going, but then you have one cookie too many.  How much fat will that put on you?

We need some information.  If you jog, let us suppose you burn 10 Calories per minute. Clearly it will take 15 minutes of jogging to burn 150 Calories from that cookie.

Notice that I have capitalized the word Calorie because in diet and on packages, they use “large” calories. The usual calorie is defined as the energy required to raise the temperature of one gram of water by 1 degree Celsius. This is quite small, so to save writing on the package 150,000 calories, they write 150 Calories. 1 Calorie = 1,000 calories.

A large Calorie is the heat required to raise one kilogram of water by 1 degree Celsius.

How much fat corresponds to one cookie? That is, if you eat it and do not jog for 15 minutes that energy is stored as fat. The energy of one gram of fat is about 9.4 Calories, so 150 Calories corresponds to about 16 grams (0.6 oz).

You will gain 0.6 oz. of fat. However you can jog for 15 minutes to work it off.  If you eat four cookies too many a day, you will gain 2.4 oz of fat unless you jog for an hour.  In one month those four extra cookies a day will pack onto you about 4.4 lbs (2 kg) unless you jog for an hour a day.

If you want to lose 1 lb (454 grams) of fat, you have to jog about 7 hours.

So the only effective diet is to eat less, and chose foods that do not have a high Calorie count (read the package).  Using Conservation of Energy and looking at the above figure, we can express all this as an equation,

[Energy into your body (eating)] minus [Energy out of your body by metabolism and your physical activity] equals Fat on your tummy.


E(in) – E(out) = Fat

In Figure a) Fat = 0 so equilibrium; in b) Fat >0 so weight gain; in c) Fat < 0 so weight loss.  This does not mean, of course, that I am knocking exercise.  Rather I am saying that you should not rely on exercise to compensate for overeating.  Of course exercise helps weight loss, but its benefits go far beyond weight loss.

The hard part about dieting is that you must eat a lot less so the extra energy you need is obtained by converting fat on your hips into energy. The formula above shows that.

Suppose you want to lose 2 kg (4.4 pounds) in a month.  That fat corresponds to about 18,800 Calories.  Now divide by 30 to get 627 Calories per day.  You simply have to look on the packages and calculate what to cut out so that you eat 627 fewer Calories a day.  A 12 oz can of soda (coke) has 150 Calories, so if you drink four cans a day, cut that out or only drink diet soda.  You can also cut out those four cookies a day.

The most important factor in losing weight, in my opinion, is motivation. If you really want to lose weight, set a goal, count Calories and stick to it.  Once you have lost the weight, keep it off by a life-style change regarding what you eat and how much.

There is a lot on the Internet about Calorie Counting and the energy in foods.

James Joule

A Calorie is not an SI unit of energy, the Joule is, after James Joule who did experiments in his father’s brewery lab.  He found the mechanical equivalent of work by dropping a weight which turned a paddle in a container of water (see image below).  The turning paddle heated the water, showing that mechanical energy can be converted into heat.  That is he showed that work and heat are different forms of energy and interchangeable, and so in honour of him, the SI unit of energy is the Joule with symbol J which is

1 J = 1 kg m2 s-2

The relationship to Calories is I Calorie = 4.184 kJ and 1 calorie = 4.184  J. Soon packages will have energy expressed in kilo Joules, kJ.

The mechanical equivalent of heat


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