Newbie here with intro thermodynamics question

[diewlasing]

keep in mind this problem is on page 8 of my text (yes I'm already confused by the problem) and the ideal gas law was just introduced.

problem: Estimate the average temperature of the air inside a hot air balloon. Assume that the total mass of the unfilled balloon and payload is 500kg. What is the mass of the air inside the balloon?

That's all that's given. Thanks in advance.

 

[russ_watters]

Well...how do you find the mass of any volume of air?

 

[diewlasing]

I know how to do that, the density is 1000 kg/m^3 and you set it equal to m/v where v is the volume given. But I still don't see how that helps me much.

 

[yogi3939]

Since the mass of the baloon and payload is known then the mass of the air inside it must be equal to the mass of the air it displaces minus the mass of the baloon and payload. This is the same principle that let's a submarine maintain its depth. Compress the air from the balast tanks and let water in in its place and the sub goes lower. reverse the process and replace the water in the balast tanks with air and the sub rises. A hot air baloon works on the same principle of equilibrium. It just uses air with different temperatures instead of the water/air combo.

Start with an arbitrary figure for the total volume of the baloon and payload with the baloon inflated and figure the mass of free air at a particular altitude (barometric pressure) and temperature. Be as realistic as you can in the displacement volume figure. Then use that volume and its mass and subtract the mass of the baloon and payload from the total mass of the free air in the baloon if it were not heated. This will give you the mass of the air in the baloon needed to bring the total displacement mass of the baloon, payload, and hot air to the equilibrium point. This is the figure needed for the baloon to maintain its altitude. If you need to figure average temperature at this point you just figure it out from the gas laws you should already know.

Here are some links to use.

http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970106a.html

http://science.howstuffworks.com/hot-air-balloon.htm

http://van.physics.uiuc.edu/qa/listing.php?id=2122

http://www.Newton.dep.anl.gov/askasci/phy00/phy00435.htm