# Conservation of Mass and weight loss

j
Sterling Heights, MI Icrontian

I have a question, and I can't seem to put all the pieces together.

Conservation of mass states that mass can not be created or destroyed. Applying this to food intake this means that if you eat 1 pound of butter you can not gain more than 1 pound of body weight.

The opposite is what if perplexing to me. In order to loss 1 pound of fat you have to expel this mass from you body some how. I under stand that calories are key to weight loss, but calorie is a unit of energy not mass. I know there is potential energy in fat, and the metabolic process breaks down the fats into different things that you body can use and the energy is used as well. But where does the mass go? no matter how small you body breaks down the fat. the sum of atomic masses remain the same(conservation of mass)

This question comes up because I weight myself before bed and then right when I get up. sometimes I'm 2 pounds less in the morning. I do think I sweat that much and I don't take any massive 2 pound turds during the night. So where did it go, how did it get expelled out of my body. Maybe I'm not accounting for fluid loss during the night.

They way I see it there is only 3 ways to expel mass. Crap, piss, or sweat. what else am I missing?

Heat does not count, that's energy, not mass. I would not think breathing, because gasses are not that heavy and I'm sure the mass in and out when I breath is equal.

So where does the mass go?

Conservation of mass states that mass can not be created or destroyed. Applying this to food intake this means that if you eat 1 pound of butter you can not gain more than 1 pound of body weight.

The opposite is what if perplexing to me. In order to loss 1 pound of fat you have to expel this mass from you body some how. I under stand that calories are key to weight loss, but calorie is a unit of energy not mass. I know there is potential energy in fat, and the metabolic process breaks down the fats into different things that you body can use and the energy is used as well. But where does the mass go? no matter how small you body breaks down the fat. the sum of atomic masses remain the same(conservation of mass)

This question comes up because I weight myself before bed and then right when I get up. sometimes I'm 2 pounds less in the morning. I do think I sweat that much and I don't take any massive 2 pound turds during the night. So where did it go, how did it get expelled out of my body. Maybe I'm not accounting for fluid loss during the night.

They way I see it there is only 3 ways to expel mass. Crap, piss, or sweat. what else am I missing?

Heat does not count, that's energy, not mass. I would not think breathing, because gasses are not that heavy and I'm sure the mass in and out when I breath is equal.

So where does the mass go?

0

## Comments

It's really not all that uncommon. My metabolism is so high that it dips by 4 pounds between my last meal and the AM (about 7 hours).

Edit - never mind. Thrax mentioned it, albeit briefly. I don't think he highlighted it enough, though. Personally, I tend to lose about 3 pounds per 8 hours of sleep and it's all water, because I always wake up feeling parched.

Point of thought: your lungs always expand and contract to roughly the same volumes. I have a quick proof that doesn't really get you anywhere. I attempted to try and come up with a criteria for weight gain or loss based ONLY on the pressure and temperature coming out of your lungs, but I got hung up. Props to anyone who wants to continue the work. Here we go:

Consider two ideal gases (inhalation and exhalation), governed by the equation PV = nRT. We know V_in = V_out. Through experiment, we can determine the ratio P_in/P_out and T_in/T_out. For the sake of the off-the-cuff calculation, let's assume that the only gases you breathe in are oxygen and nitrogen, and the only gases out are the same two, plus CO2. In addition, N2 is not converted. Thus, n_in = n_O2_in + n_N2 and n_out = n_O2_out + n_CO2 + n_N2.

I make another assumption for the sake of the calculation - from the time an oxygen molecule enters your body and exits as a CO2, the breaths you have inhaled are essentially interchangeable (equal in volume, temperature, pressure, etc). The same I assume for exhalation. This is not unreasonable for a human at rest in a well ventilated area.

By attacking PV = nRT in such a manner (let P1 and T1 be the before P and T; P2 and T2 will be the after)

P1 x V = (n_O2_in + n_N2) x R x T1

P2 x V = (n_O2_out + n_N2 + n_CO2) x R x T2

Divide the first equation by the second, rearrange a bit.

(P1 x T2) / (P2 x T1) = (n_O2_in + n_N2) / (n_O2_out + n_N2 + n_CO2)

We see that the ratio of pressures and temperatures must be equal to the ratio of MOLECULES won and lost by the body. Since we're talking mass, let's get this into our heads proper:

O2 weighs about 32 AMU. CO2 weighs about 44, and N2 around 28. I thus have a conversion rate that I can substitute into my stupid equation. Note that since n is in moles, I SHOULD multiply the lot of this by avogadro's number, but because we're talking ratios here, I don't need to (it'd cancel). Furthermore, let's consider the border situation - where weight in equals weight out exactly. Thusly, each amount of gas's contribution is as follows:

1 = (n_O2_in*32 + n_N2*28) / (n_O2_out*32 + n_N2*28 + n_CO2*44)

We see quite quickly that nitrogen's part in this will cancel (as we'd expected). With a little (read: shit-ton of) rearranging, this gives us the almost ENTIRELY useless expression:

(n_O2_in - n_O2_out) / n_CO2 = 44 / 32.

This is the criteria for absolutely no weight gain or loss through exhalation. Weight gain would require that the = become a <, and weight loss would require that the = become a >. Pretty damn useless, isn't it? I've been hacking at this for an hour, and that's the most useful expression I can come up with. I mean, you MIGHT be able to solve the last expression for n_CO2 or n_O2_out and put it into your P1T2/P2T1 equation, but you'd still have that other stuff to deal with.

Anyone who wants to continue this, I'd planned to use the mole fractions of oxygen and nitrogen to effectively eliminate the numerator in the P1T2 expression, but I never got that far.

tl;dr SCIENCE

1. I didn't take into account water vapor. This is just a simplified situation.

2. It's not safe to assume that n_O2_in = n_O2_out + n_CO2. It's not biochemically true (and if it were, then the answer would be 'yes, you ALWAYS lose weight upon exhale').

3. If you can turn that second to last expression into the right-hand side of the third to last expression, you WIN. I'm not very good at MAPLE, though.

jeff shits the bed.

it sounds like your saying mass is converted to energy? or are you saying the energy is released and the mass is expelled. The later I would say is true. I found an interesting thread that talks about the same thing.

http://www.physicsforums.com/showthread.php?t=239589

Looks like the mass that I was taking into consideration is being expelled in gas form, but over a long period of time. This would make sense.

PS

I only shi^t the bed on holidays