Calculating lifting power of heated gas

[vitekc45c]

So lets say i have a round balloon, 25cm in diameter, filled with helium thats heated to about 200C. How much lift (in N or kg) would it produce and how to calculate it?

[SgtSomeone]

I don't know the calculations off the top of my head, but additional information that you'll need is the altitude that you're launching it at and the outside temperature, as these can affect the air density. I've heard taking off in a Cessna at -40 feels like a fighter jet because of how dense the air is. 

[Gaarst]

Take the ideal gas law: pV = nRT, and rearrange it: n = pV / RT.

T is the temperature (473.15 K), R the ideal gas constant, V the volume of the balloon V = 4/3 * pi * 0.125³ = 0.008 m³ and p is the pressure, usually close to 1atm for your average balloon.

n = 1013.25*100 * 0.008 / 8.314 / 473.15 = 0.21 mol of He in your balloon, which corresponds to 0.82 g of He.

The same volume of air would weigh (at StdAtm): 1.225 * 0.008 = 9.8 g

Therefore, you balloon could lift about 9g, or 88 mN (milliNewtons) (actually a bit more since your payload doesn't have infinite density, unless you're trying to lift a black hole).

(I might have made a mistake so big I didn't see it, so this might as well be completely wrong)

Edited April 30, 2016 by Gaarst
Changed N to mN

[vitekc45c]

47 minutes ago, SgtSomeone said:

I don't know the calculations off the top of my head, but additional information that you'll need is the altitude that you're launching it at and the outside temperature, as these can affect the air density. I've heard taking off in a Cessna at -40 feels like a fighter jet because of how dense the air is. 

Altitule would be ground level (6-700m above sea level or so) with outside temperature somewhere between 10 - 20C

Gaarst

That seems sound, exept the 1 atm presure in balloon since that would make the pressure inside and outside same and the balloon would not inflate. I gues it should be around 1.2 or so but that doesnt change the result by that much.

[todofwar]

Heating the helium doesn't get you much more lift then leaving it room tempeeature. And your internal pressure will only be slightly higher than outside pressure to maintain structural integrity.

[AngelLestat]

Viteck, why you ask?  what you want to know exactly?
As @todofwar said, does not have much sense heat up helium or hydrogen, this may be more important if your external air pressure is low and cold (high altitude), so if you heat up your lifting gas (at 20000m) then the benefit is more notorious. 
Ok. I made the math, and even at higher altitude your lifting difference by heating helium or h2  does not worth it (pros: is harder to lose temperature at higher altitudes).
m3 of air at 20000 m (215k - 8000 pa) weight: 125 grams by m3
m3 of helium same conditions weight 18 grams by m3
m3 of helium +180 degres of ambient temperature weights 9.7 grams
It only increase a 7% your payload mass with a delta temperature of 180c.

5 hours ago, Gaarst said:

Take the ideal gas law: pV = nRT, and rearrange it: n = pV / RT.

T is the temperature (473.15 K), R the ideal gas constant, V the volume of the balloon V = 4/3 * pi * 0.125³ = 0.008 m³ and p is the pressure, usually close to 1atm for your average balloon.

n = 1013.25*100 * 0.008 / 8.314 / 473.15 = 0.21 mol of He in your balloon, which corresponds to 0.82 g of He.

The same volume of air would weigh (at StdAtm): 1.225 * 0.008 = 9.8 g

Therefore, you balloon could lift about 9g, or 88N (actually a bit more since your payload doesn't have infinite density, unless you're trying to lift a black hole).

(I might have made a mistake so big I didn't see it, so this might as well be completely wrong)

88N is equal to 8kg, you forget the to add milli-newtons.
But your answer is the most accurate and detailed..  cheers.

Edited May 1, 2016 by AngelLestat