1
$\begingroup$

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

UPDATE

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

UPDATE 2:

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

$\endgroup$

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – John Rennie, jinawee, Valter Moretti, Brandon Enright, Kyle Kanos
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 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
2
$\begingroup$

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.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.