# Weight and buoyancy in air

1. Jun 15, 2013

### parsec

I was having a discussion with a friend and we could not come to an agreement on the following:

If you were to weigh yourself on a very sensitive set of scales, would you register the amount of air that you breathe in as an increase in measured weight?

The way I see it is, you can make one of two assumptions. If you assume your body's external volume doesn't increase at all when inhaling, and lung volume increases due to the compression of your diaphragm, then mass is being added to the system and should register on the scales.

If your external volume increases by the same amount that your lung volume increases, the increased buoyant force on your body cancels the increased mass in your lungs and no change in the measured weight will be observed.

I assume that the inhalation process is some combination of the two, where the measured increase in weight will be an underestimate of the true weight of the air inhaled, since the body's volume increases by some amount less than the increase of the lungs' volume.

Is this correct? He was arguing that there will be no measurable change in the weight measured.

2. Jun 15, 2013

### Staff: Mentor

Why would you assume that? That's a serious question, not a rhetorical one - it's what's behind your disagreement with your friend

However, before you go too far down that path, you might want to try calculating total mass of the air in one inhalation, compare it with the mass of a typical human. That will give you an upper bound on how much the measured weight might vary with breathing. That's important too, because if you read a few scientific papers you'll see that experimenters do not say things like "we measured it and it didn't change". Instead, they say things like "given the sensitivity of our instruments and the uncertainties in our experimental setup, we can say that if it does change, the amount of the change cannot be greater than (some really small number)".

3. Jun 15, 2013

### parsec

The assumption is based on my person experience with how much my chest moves when I breathe, and how much I estimate the volume of one breath to be. It's not something I have measured, it's a guess.

It's not the source of the disagreement, because his argument is that the mass would not change in both scenarios; if the external body volume remains fixed or if it increases.

I'm not concerned with the experimental practicalities. The hypothetical assumes a scale with a large dynamic range that is sensitive enough to measure very small changes in weight (say micrograms for arguments sake, if you want a value). I estimate the weight of a breath to be in the order of a gram (a litre or so of air).

4. Jun 15, 2013

### phinds

I find it sometimes useful when thinking about such thing to take things to an extreme, if possible. For some reason, I have difficulty "seeing" this problem in air, so I moved it to water and I think the conclusion would be the same.

If, to make things simple, you add weights so that you totally sink in water, you will weigh X pounds. If you were to fill your lungs with water before jumping in the pool, I believe you would STILL weigh X pounds because the buoyancy of the water in your lungs is exactly the same as that outside your body. SO ... if you emptied your lungs and THEN jumped in and filled your lungs with water, I STILL see you as weighing X pounds.

SO, my conclusion is that taking a breath does not change your weight.

I'm not 100% sure I haven't overlooked something, but so far that's my story and I'm sticking with it

5. Jun 15, 2013

### parsec

I don't believe this to be correct, if you make the assumption that your external volume does not change by the volume of the water ingested (as a result of your internals compressing to make room for it). By your logic, if you were to fill a submarine with water, it would have the same weight as when it is filled with air. As far as I understand, the volume you displace in the water determines your buoyancy. Any addition or subtraction of mass from within the body changes the weight acting against this buoyancy, regardless of the density of that substance.

6. Jun 15, 2013

### phinds

By that logic, a cubic foot of lead would have exactly the same buoyancy as a cubic foot of balsa wood. Do you see the flaw in that?

7. Jun 15, 2013

### parsec

It does. The displacement is what determines the buoyant force. Assuming both objects are completely submerged, the buoyant force on each would be the same. The weight of the lead is much higher than that of the wood though, so it only comes into equilibrium when it sinks.

8. Jun 15, 2013

### parsec

I think we might be confusing terms here. When I say "buoyancy", I'm referring to the gross force resulting from the displacement of the fluid, not the net force that acts on the object as a result of both its buoyancy and weight.

9. Jun 15, 2013

### phinds

Yes, and you are right. I was thinking sloppily. Thanks.

10. Jun 15, 2013

### Staff: Mentor

Neither your lungs or other parts of your body pressurize when you breathe, so the weight and buoyancy changes are the same.

11. Jun 15, 2013

### parsec

Doesn't the diaphragm have to compress to some extent to perform its action? As far as I'm aware, it's a combination of this contraction of the diaphragm and the expansion of your chest that form the breathing function.

12. Jun 15, 2013

### Staff: Mentor

Yes, there has to be a slight pressure differential to cause air to flow in and out, but this differential is very small and equalizes very quickly - I would be surprised to here that there was any practical way of measuring the tiny changes in buoyancy that result. I' also would expect that other influences (random air currents in the room where we're doing the measurements? temperature and moisture content changes? ...?) further obscure the effect. So when your friend "...was arguing that there will be no measurable change in the weight measured" he's almost certainly right. In theory, might there be a change in weight measured?

- If an object increases its volume, and the increased volume is filled with air at the pressure and density as ambient, there will be no change in net weight; the weight of the added air will be exactly offset by the added buoyancy from the air displaced by the added volume.
- If the increased volume is filled with higher pressure/density air, then there will be a net increase in weight. Phinds suggested that you consider an extreme case; so imagine that you're standing on the scale and holding a scuba tank. Pump it full of high pressure air and the weight will go up - vent it to the air until the pressure as equalized and the wight will go down as we lose mass while maintaning the same volume.
- Likewise, if the increased volume is filled with lower pressure/density air, there will be a net decrease in weight. The extreme example might be standing on the scale while holding a balloon that is being slowly inflated with helium - with a large enough balloon the reading on the scale will fall to zero and you'll float away.

13. Jun 15, 2013

### parsec

Thanks. I was just checking to see if my reasoning was correct.

As for the practicalities, I think it's possible. I'm not sure that temperature and moisture content will be a huge problem since they don't really fluctuate very quickly. Air currents might be, but that effect could be minimised with due diligence.