I used the Ideal Gas Law PV = nRT where

P is the pressure of the gas P = 1.033 kgf/cm squared

V is the unknown volume of the gas

n is the amount of substance of gas (also known as number of moles) n = 40.7 mole

R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant. R = 8.3145

T is the temperature of the gas T = 298.15 K

incorrect work snipped


figured it out.

I used some of the work found here: http://www.newton.dep.anl.gov/askasci/phy99/phy99471.htm

and then used ideal gas law against his answer to derive a volume of 266 gallons

I then used density = mass / volume against his answer and achieved similar results so as to feel confident that 266 gallons is correct at SATP


Here's a calculator specifically for this problem http://keyvanfatehi.com/balloon

You can find the source code here: https://github.com/keyvanfatehi/balloon

It uses https://www.npmjs.org/package/gas-density-calculator and https://www.npmjs.org/package/archimedes-principle


closed as off-topic by John Rennie, jinawee, Valter Moretti, Brandon Enright, Kyle Kanos Mar 22 '14 at 16:28

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  • 2
    $\begingroup$ It is advisable to FIRST convert all quantities to the proper units that you want to end up with, and then do the calculation. You also seem to have some numbers wrong ($R=8.3145$, for instance). $\endgroup$ – Danu Mar 22 '14 at 9:09
  • $\begingroup$ Thanks, updated. Also this is not homework, I am not in school--I just want to use math instead of using trial and error, and build some open source JavaScript code to help people understand factors at play.... $\endgroup$ – keyvan Mar 22 '14 at 9:25
  • $\begingroup$ That doesn't matter; the homework pertains to a certain type of question rather than the motivation of the asker ;) $\endgroup$ – Danu Mar 22 '14 at 9:53
  • $\begingroup$ Well this question is "On Hold" but I've solved it myself in two ways. One way was with Ideal Gas Law, the other was by applying this equality: density = mass / volume against this answer newton.dep.anl.gov/askasci/phy99/phy99471.htm . At SATP it will take 266 gallons to lift 1kg $\endgroup$ – keyvan Mar 23 '14 at 2:53
  • $\begingroup$ github.com/keyvanfatehi/archimedes-principle $\endgroup$ – keyvan Apr 5 '14 at 11:18

The simplest way to approach this is to note that the molar volume of an ideal gas (helium and air are close to ideal at STP) is $22.4$ litres. This means that $22.4$ litres of helium weighs $4$g and similarly $22.4$ litres of air (average $M_W = 28.8$) weighs $28.8$g.

Archimedes' principle tells us that the upthrust is equal to the weight of fluid displaced, so when $22.4$ litres of helium displaces $22.4$ litres of air the net upthrust (weight of air - weight of helium) is $28.8 - 4 = 24.8$g.

From this you should be able to work out what volume of helium is required to produce an upthrust of $1$kg.


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