How to Calculate Moles of Helium in a Balloon Using the Ideal Gas Law

[kensei3000]

I was wondering if any of you guys could solve this problem for me with complete solutions. I have been at it for a couple of hours and I am running out of pencil. I would really appreciate your help!

Problem:

A helium balloon is used to lift a load of 110 N. The weight of the balloon's skin is 50 N, and the volume of the balloon when fully inflated is 32 cubic meters. The temperature of the air is 0 degrees C and the atmos. pressure is 1 atm. The balloon is inflated with sufficient helium gas so that the net upward force on the balloon and its load is 30 N. Neglect changes of temperature with altitude.

(a) How many moles of a helium gas are contained in the balloon?
(b) At what altitude will the balloon be fully inflated?
(c) Does the balloon ever reach the altitude at which it is fully inflated?
(d) If the answer to (c) is affirmative, what is the maximum altitude attained by the balloon?


P.S: Does anybody know if a guy named Paul Tipler is in the forums?

 

[arcnets]

Originally posted by kensei3000
P.S: Does anybody know if a guy named Paul Tipler is in the forums?

Are you joking? Paul Tipler is the author of a popular textbook on physics.

Tipler, Paul A.: Physics for Scientists and Engineers,
Worth Publishers, Inc., NY

As for the problem
(a) Use Archimedes' law. You must put in so much helium that the balloon would weigh 190N more, if it was filled with air instead.
(b) Use the law of the ideal gas (pV = nRT, IIRC). There exist also formulae for p(h) and T(h) in the atmosphere. So you have 3 unknowns (p,T,h) and 3 formulae. Perfect.
(c) Archimedes again. Replace 32m^3 of helium (at h) with 32m^3 air (at h), the lift is the weight difference. If it's larger than 160N, then the answer is yes.
(d) Now use the same formula as in (c), but let lift = 160N, and find h.

 

[Ace-of-Spades]

Kids these days!
Too lazy too do their homework?
- Just get someone on the internet to do it for you lol

 

[kensei3000]

Thanks arcnets, Ill try that one out..

Yeah, I know who Paul Tipler is. The problem I just posted came from his book. I just thought that maybe he could be around the forums somewhere,.. hehe, what a slim possibility.

P.S. I am not really lazy, I just didnt have the time to do it.. Well, I never really thought that anyone would reply to my post, but I tried it anyway. Its a good thing that some people did.

 

[franz32]

Regarding to b.

Hello. I read that problem. Actually, I did find it very challenging.

In B, how are you going to use the formula for p(h) and T(h)? What are those by the way...

And how is that the ideal gas law is used in this solution? =)