What is the balloon's air pressure ?

[marz]

There is something confusing me about air pressure inside balloons. I got three questions:

Assume I am sitting at sea level, with a balloon. I fill it to 1/3 its capacity with air.
Then I place an absolute pressure sensor at its opening.
1- What pressure value do I read ?
Do I get the 1013 mbar which is the atmospheric pressure at sea level ? Because I read that the pressure inside the balloon must equal the outside pressure.

Now, I fill it to 2/3 its capacity with air.
2- What do I read now ? Is it double the pressure I got at question 1 or is it still the same ?
Remember, the outside atmospheric pressure did not change. It is still 1013 mbar. Also note the balloon has doubled its air mass.

Now, with 2/3 its capacity still filled with air, I move the balloon up to an altitude where the atmospheric pressure is half that at sea level.
3- What pressure value do I read there ?

Thanks.

 

[Delta2]

Whatever you doing the volume V of the balloon keeps changing according to the equation PV=nRT so that its pressure P always equals the atmospheric pressure. So for example when u double the n ( that is you put double air mass inside it) while keeping the atmospheric pressure the same (and assuming the temperature remains the same), the volume becomes double.

 

[jbriggs444]

Now, with 2/3 its capacity still filled with air, I move the balloon up to an altitude where the atmospheric pressure is half that at sea level.
3- What pressure value do I read there ?

Note that part 3 is a trick question.

 

[Chestermiller]

Whatever you doing the volume V of the balloon keeps changing according to the equation PV=nRT so that its pressure P always equals the atmospheric pressure.

This is not correct. The balloon membrane is under tensile stress, and this causes the pressure inside the balloon to be higher than the pressure outside (if the balloon is inflated). You can show this by doing a force balance on a small area of the curved balloon surface. If the pressure inside were the same as the pressure outside, it would take no effort to blow up the balloon.

Chet

 

[jbriggs444]

This is not correct. The balloon membrane is under tensile stress, and this causes the pressure inside the balloon to be higher than the pressure outside (if the balloon is inflated). You can show this by doing a force balance on a small area of the curved balloon surface. If the pressure inside were the same as the pressure outside, it would take no effort to blow up the balloon.

Although this is correct, it is also true that the gauge pressure inside a party balloon is typically only a small fraction of atmospheric pressure. The tensile stress can often be neglected and the absolute pressure in the balloon will be approximately equal to ambient.

 

[Chestermiller]

Although this is correct, it is also true that the gauge pressure inside a party balloon is typically only a small fraction of atmospheric pressure. The tensile stress can often be neglected and the absolute pressure in the balloon will be approximately equal to ambient.

Agreed.

Chet

 

[nasu]

This is not correct. The balloon membrane is under tensile stress, and this causes the pressure inside the balloon to be higher than the pressure outside (if the balloon is inflated). You can show this by doing a force balance on a small area of the curved balloon surface. If the pressure inside were the same as the pressure outside, it would take no effort to blow up the balloon.

Chet

If the problem refers to an elastic balloon, then it does not make sense to say that it is filled to 1/3 to its capacity. Such a balloon does not have a fixed "capacity". And how would you fill just a fraction of it?
What kind of balloon do you have in mind when you discuss this problem?

 

[marz]

If the problem refers to an elastic balloon, then it does not make sense to say that it is filled to 1/3 to its capacity. Such a balloon does not have a fixed "capacity". And how would you fill just a fraction of it?
What kind of balloon do you have in mind when you discuss this problem?

Weather balloon

 

[Delta2]

Note that part 3 is a trick question.

Why? I guess the temperature also drops as we move to higher altitude but something tells me this is not what u mean by tricky.

 

[jbriggs444]

Why? I guess the temperature also drops as we move to higher altitude but something tells me this is not what u mean by tricky.

If the balloon was at 2/3 capacity and ambient pressure is reduced by half without venting gas, what fraction of capacity is the balloon now at?

 

[Delta2]

4/3? This means it explodes?

 

[nasu]

Weather balloon

If it's one made of materials like cloth impregnated with polymers, I think a reasonable model will be to assume that the pressure can be more than atmospheric pressure (Pa) but not less. Once is filled to maximum volume its pressure can increase above the atmospheric pressure.
When it is partially filled, the pressure may be approximately equal to Pa. It may be a little more if the weight of the non-inflated part presses the gas.

 

[Vibhor]

Although this is correct, it is also true that the gauge pressure inside a party balloon is typically only a small fraction of atmospheric pressure. The tensile stress can often be neglected and the absolute pressure in the balloon will be approximately equal to ambient.

Hi jbriggs ,

In the case of party balloon we can neglect the tensile stress , but can we do the same in problems where an air bubble is given . I will take a problem for example sake .

An air bubble released at the bottom of the pond expand to four times its original volume by the time it reaches the surface .If atmospheric pressure is 100 KPa ,what is the absolute pressure at the bottom of the pond ? ( Answer comes out to be 400KPa )

In these type of problems also , why do we assume that pressure inside the air bubble is equal to the ambient pressure ( pressure of the water) ?

I think surface tension plays same role that tensile stress plays in case of party balloon . I guess the pressure difference between inside and outside of balloon is 4T/R ,where T is the surface tension and R is the radius of balloon .

Do we neglect pressure difference arising due to surface tension ?

Many Thanks

 

[Chestermiller]

Hi jbriggs ,

In the case of party balloon we can neglect the tensile stress , but can we do the same in problems where an air bubble is given . I will take a problem for example sake .

An air bubble released at the bottom of the pond expand to four times its original volume by the time it reaches the surface .If atmospheric pressure is 100 KPa ,what is the absolute pressure at the bottom of the pond ? ( Answer comes out to be 400KPa )

In these type of problems also , why do we assume that pressure inside the air bubble is equal to the ambient pressure ( pressure of the water) ?

I think surface tension plays same role that tensile stress plays in case of party balloon . I guess the pressure difference between inside and outside of balloon is 4T/R ,where T is the surface tension and R is the radius of balloon .

Do we neglect pressure difference arising due to surface tension ?

Many Thanks

For a 3 cm bubble released at the bottom of the pond, calculate the pressure difference arising from surface tension and see what the number comes out to be.

 

[Vibhor]

I think I was wrong in assuming that surface tension would be present in an air bubble .The air inside the bubble should be exactly at the same pressure as outside water . I guess an air bubble is not similar to a party balloon ( in terms of pressure ).

 

[Chestermiller]

I think I was wrong in assuming that surface tension would be present in an air bubble .The air inside the bubble should be exactly at the same pressure as outside water . I guess an air bubble is not similar to a party balloon ( in terms of pressure ).

You were right in the first place. Surface tension would have a small effect, unless the bubble were very small, in which case it could be much more important. In the case of a balloon, the rubber membrane would also have an effect, but not great.

Chet