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Conservation of mass would prevent any outcome other than the scale showing you getting lighter.
No household scale would be precise enough for this experiment though.
No, scales don't measure mass but weight, it is completely possible to lose weight and have the scale show a larger number because of buoyancy. For example, grab a helium balloon capable of holding up a 1kg mass mid-air and the scale would show 1kg less than when you release it. This is very simple to understand, how much would the scale show for a 1kg object tied to that balloon? 0 of course, the object is not even touching the scale, and a slightly heavier object would only be making that slight weight difference of pressure on the sensors, not the remaining 1kg.
So conservation of mass has nothing to do with the question here. It's all to do with whether farts are denser than air while inside your body.
They are.
Are you sure? It's made mostly of Nitrogen, Hydrogen and Methane, all of which would be lighter than air because they're at a higher temperature than the air outside.
I think that, theoretically, if someone's flatus contained an abnormally high amount of lighter-than-air gases, like hydrogen and methane, they might get very slightly heavier. Having a gas like that inside of you would, I think, provide a bit of a buoyant force lifting you away from the scale that would make your weight read lower, and releasing that gas would sort of drop your full weight onto the scale.
In practice, methane and hydrogen are only part of a fart, and other gases and such in the mix are heavier than air, so at best you might break even.
Probably a few caveats to that about temperature and pressure and such, and it's doubtful that anyone's gut produces enough of the right kinds of gas for that to happen.
That would assume the digestive system isn't under pressure, but I think it is slightly?
What if you had eaten something that created a bunch of hydrogen gas (and lived somehow)? Wouldn't standing on a precision scale at sea level, in a sea level atmospheric pressure and composition, show you getting heavier as you expel the hydrogen.
I'm not sure it would, unless the person's volume also changes considerably.
Buoyant force comes from a displaced volume of fluid (the outside air in this case)
My volume changes a lot. When I'm full of gas, I look like I'm pregnant.
Well your guts and skin and other tissues do have some elasticity, I suppose it is possible that a large gas bubble might be able to expand your abdomen slightly.
We're very much into spherical cows in a vacuum territory here. I don't think there's any way this would be realistically measurable,just fun to think about.
It would have to expand your abdomen slightly, assuming you don't have access to a fourth dimension.
Conservation of mass is not what would be effected here. They said weight not mass. Weight is an object measured in situ, effected by gravity and the atmosphere above.
They would lose mass, but they'd become more dense. If that gas was less dense than the atmosphere then the slightly increased density would make the weight of everything above the scale slightly higher. Vice versa if it was more dense.