ΛE = Λq + ΛW
That is the equation to calculate the amount of energy (positive or negative) in a chemical reaction. E is total energy, q is the temperature of the system and W is the work done on or by the system.
To find q, you would need to know the substances you’re dealing with, their specific heat capacities, and what reactions they’re going through. If you’re applying more than one reaction, you need to take the equations for both reactions and add them together.
Furthermore, specific heat capacity only applies under given conditions. Most specific heat capacities will be tailored to standard laboratory conditions (ambient pressure ≈101.4 kPa, temperature ≈24°C), but heat capacity varies based on temperature (the heat capacity of water is 4.1855 [J/(g·K)] at 15°C and 2.259 [J/(g·K)] at 25°C), and the human body has an internal temperature of 36.6°C.
“But Setar, isn’t there a lot of energy in food? You know those labels say calories when they mean kcal, right?”
Oh, I know. There’s two problems with that:
1) The body expends energy to break the food down in the first place. Your digestive system is not run by a wizard (though that would be cool, and explain irregular bowels quite well), it needs energy just as much as the rest of your body does.
2) Obviously, not all of the food we eat is taken up by the body in the first place, otherwise I wouldn’t be talking about bowels at all.
3…wait, crap, let me start over again. Among the problems with saying that there’s a ton of energy in the food and therefore the first law of thermodynamics holds…
3) Not all of the energy is taken up in the same way, and the body manages how that is done quite well.
4) Remember how I said that the equation only applies to a single given reaction under set conditions? Well, nutrients go under a hell of a lot more reactions after they’re taken up. The most famous cycle is the citric acid or Krebs cycle, and to get the energy output, you’d need to add up the energy equations for ALL of the reactions in that cycle.
And then you’d need to add in the reactions from all the other cycles in the cell that help to convert the nutrients into usable energy, and you’d have the total energy output over that cycle of reactions. You’d then somehow need to tie the energy inputs to concentrations of nutrients, and trace those nutrients back to the food they came from, and figure out how much of the energy present in that food actually makes it to the cell.
Getting complicated yet? Because it gets worse.
If you do all that, you will get the food intake to energy output ratio…for one cell. In one part of your body, under one set of conditions. And the intake-output ratios will be vastly different over differing types of cells in your body, and different parts of your body. To get the intake and translate it into something meaningful like weight loss — such as fat deposits — you’d need to intensely monitor what you ate, figure out what it would get taken up as in the digestive system, and then monitor your body and see how it worked out and where all this food actually ended up. You’d also need to account for other confounding factors such as your genetic structure and general life. Then you’d need to figure out how much energy your body puts out over a given period of time — and that is a lot more than just exercising; you would probably want to use a given 24-hour period to cross a range of activities including sleep. And then you’d need to monitor how changing that affected your fat/muscle/energy distribution.
And then you’d figure out exactly how much fat you’ll put on by having that extra brownie or bigger slice of cake. My guess, however, is not much, and if you’re not willing to have that bigger slice of cake then I guess it just means more for me ^_^