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Suppose we put a very obese man inside a large air tight isolated room with a treadmill and he runs on the treadmill for 24 hours and at the end of the day he sees his weight has come down (mostly water weight, but also includes some fat), would the weight of the entire sealed room be decreased?

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up vote 3 down vote accepted

No, the room will stay the same weight.

I'm guessing that your question is really about the process of burning fat to create energy. You mention that the man loses water, but of course this just condenses on the walls of the room so no water is lost.

Strictly speaking it isn't fat that the man is burning to create the energy. Fat is used for energy storage by the body, and your body converts it to carbohydrate before burning it. The burning process is called respiration and is actually basically the same as just burning the carbohydrate on a fire. The overall reaction is:

$$ C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O $$

So you are just converting the carbohydrate to carbon dioxide and water. The atoms you end up with are the same as the ones you started with. They're just organised into different molecules.

If you measure very very carefully you'll find that the weight of the reaction products, $6CO_2 + 6H_2O$ is very slightly less than the weight of the carbohydate and oxygen $C_6H_{12}O_6 + 6O_2$. This is because some of the mass has been converted into energy in accordance with Einstein's famous equation $E = mc^2$. However for a chemical reaction the mass change is tiny. The enthalpy of combustion of glucose is about 2.8MJ/mol, so for every 180g of glucose burned about 30 picograms is converted to energy i.e the mass lost is 0.00000000001% of the carbohydrate burned.

If your room is really sealed, the energy produced goes into heating up the room, and this will increase the room's weight. So even allowing for matter turned into energy the room still stays the same weight.

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The room would not only have to be air-tight but also "energy-tight" to preserve identically the weight. If the room is not energy-tight, then it may gain a little weight (if the total room+treadmill+fatty is warmed up by the external environment) or it may lose a little weight (if the total is cooled off a little by the external environment). – mwengler Jul 1 '12 at 20:45

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