Under pressure

[chiddler]

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At atmospheric pressure, air is 7 times heavier than helium. If a balloon rises in the atmosphere remaining in thermal equilibrium with surroundings, then the balloon will rise:

Until the pressure inside the balloon is seven times greater than the pressure of the surrounding atmosphere.

do not understand very well.

thanks.

 

[milski]

Helium under pressure of 7P will be 7 times as dense as helium under pressure P. But air under pressure P is also 7 times as dense as helium under pressure P. That means that helium under pressure 7P will be equally dense as air under pressure P. At that point you have no more buoyant force and the balloon will stop to rise.

The densities relationship comes from ideal gas law. Since density D=M/V, you can rewrite it as PM/D=nRT. For constant T, PM/D=const or P is proportional to D.

 

[ljc]

The balloon will rise until the densities are equal, which because air is 7 times more dense, will be when the balloon holds 7 times more particles than the air it displaced. In other words, when you have 7x as many helium particles in a set volume as you would have had in the air which that volume displaced. If you have 7 times as many particles, you have 7 times as much pressure.
We can see this from PV=nRT. V is always going to be the same for both air and helium, because the volume of the balloon is the volume of air displaced. Thus, knowing that we must have 7x as many molecules of helium as air, we can write:
PV=(7*n)RT
We just decided V was constant, R is always constant, and the question tells us T is constant. Thus, P must also go up by 7.

 

[chiddler]

The only time it will stop rising is when the external pressure is seven times less or internal pressure is seven times more as is agreed upon. I understand this.

But atmospheric pressure decreases with altitude. I'd think the more appropriate answer is that external air density is reduced 7x less. How is increase in internal pressure possible?

 

[milski]

The only time it will stop rising is when the external pressure is seven times less or internal pressure is seven times more as is agreed upon. I understand this.

But atmospheric pressure decreases with altitude. I'd think the more appropriate answer is that external air density is reduced 7x less. How is increase in internal pressure possible?

Normally, it would not be possible. But all the answer is saying is that it is 7 times greater than outside pressure. They don't say how that was achieved.

 

[chiddler]

Normally, it would not be possible. But all the answer is saying is that it is 7 times greater than outside pressure. They don't say how that was achieved.

oh man you're right. how frustrating...

thanks again.

 

[silverice]

Normally, it would not be possible. But all the answer is saying is that it is 7 times greater than outside pressure. They don't say how that was achieved.

Nvm

 

[chiddler]

Nvm

do you mean equilibrium as in its not floating or sinking? no if pressures are equal, then the less dense helium will rise.

 

[milski]

Nvm

Too fast this time. 😉

 

[silverice]

do you mean equilibrium as in its not floating or sinking? no if pressures are equal, then the less dense helium will rise.

Lol thx, I realized that right after i synthesized my q.

 

[silverice]

Too fast this time. 😉

Lol u saw again!