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We all know the trick of breathing in a helium balloon to get a funny squeaky voice! When you do this, would it be correct to say you lose weight?

On the one hand, the helium should make you more buoyant in the surrounding air, similar to how taking a big lungful of air when swimming helps you to float better, so it would seem that you are decreasing in weight.

On the other hand, you are taking more matter inside your body so you must obviously increase in mass.

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Do you really mean the weight of our body? – ACuriousMind Aug 11 '14 at 20:25
Yes. I think this is an interesting action because you apparently lose weight and gain mass. – wim Aug 11 '14 at 20:29
Definition of weight: "the weight of a body is the product of its mass and the acceleration due to gravity" I don't understand your reasoning. – ACuriousMind Aug 11 '14 at 20:30
An alternate definition of weight is what some call "apparent weight", the quantity measured by an ideal spring scale reads. That's how "weight" is defined in a few introductory physics texts and also in a number of more advanced general relativity texts. It appears that this is the concept of weight about which wim is asking. – David Hammen Aug 11 '14 at 21:12
Yes @ACuriousMind it seems he's talking about what a scale on earth would read, not some scale in an atmosphere-evacuated earth, if you know what I mean. – Andres Salas Aug 11 '14 at 22:13

This is one of those situations where you could argue on and on about definitions so let's answer it in all three meanings of the word weight that people might have.

Does your mass $m$ increase when you inhale helium?

When you fill your lungs with helium, you transfer $\approx1g$ of matter, which is several times less, but roughly of the same order of magnitude as when you fill your lungs with air. Those amounts are relatively negligible for all practical purposes, but strictly speaking, when you fill your lungs with helium you do gain mass compared with you having empty lungs (obviously).

Does your weight $F_g=mg$ increase when you inhale helium?

Obviously, for the same reasons as above, but still negligible.

Do you "feel" lighter, or more precisely, does your weight scale read a smaller number when you inhale helium?

This is where we take into account that we're not in vacuum, we're surrounded by air and we have to account for buoyancy. But since the buoyancy force is equal in magnitude to the weight of the displaced fluid, it doesn't matter whether we inhaled air or helium, because in both cases we've displaced air. The number on the (extremely precise) weight scale will go down (in comparison with you having inhaled air!!), but for the exact same reason as in the previous two situations and it will also be negligible!

This might sound wrong because "helium floats", but think about it... When you're hugging a huge helium balloon, you're increasing your total volume (you + balloon) so you're displacing a significant amount of air without adding any significant mass. In that case the number on your weight scale should drop. (It would have to be a pretty huge balloon, but you get the point).

If this still doesn't sound right, consider a situation in which all of your internal organs, tissue, bones and everything except a thin layer of a skin is replaced by helium with the same total mass (disturbing, I know, sorry about that!). Assuming your body temperature was somehow the same and not being worried about the fact that the pressure inside your body would be several thousand times higher than atmospheric pressure, your weight would be exactly the same, and so would your scale reading. Why? Because the thing that matters when considering buoyancy is the density of the fluid displaced and that's always simply the air around you.

I hope this helps, any suggestions for improving the answer or comments are welcome :)

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A well thought out reply. So yes, you will weigh less than you would if you didn't inhale anything, and you will also gain mass. – Andres Salas Aug 11 '14 at 22:11
Strangely, when you exhale completely (you would increase your density since you no longer have the volume of filled lungs), you have less mass then with your lungs filled (even with helium). – LDC3 Aug 12 '14 at 1:34

When you breath in helium, you gain mass, volume, and buoyancy, but lose density and weight.

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If you gain mass, you cannot also lose weight: weight = mass x gravity. So mass, weight, volume and buoyancy go up, and density goes down. – Karnivaurus Jan 22 at 1:32
@Karnivaurus - While standing on a scale, if someone hands you a helium balloon, your weight goes down. Weight measured by a bathroom scale = mass * gravity - buoyancy - centripetal force due to the Earth's rotation. – Nick Jan 22 at 20:01

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