Constructing A Mathematical Model To Predict The Effects of Temperature And Pressure Of A Balloon

- anonymous

Constructing A Mathematical Model To Predict The Effects of Temperature And Pressure Of A Balloon

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- anonymous

A scientist (at sea level) releases a balloon that contains 1 mole of Helium (He) gas, which is less dense than air. The skin of this balloon is made of a Star Trekien material that can be stretched or contracted to any size. In other words the balloon can shrink to zero size and expand to infinite size.
What do you think is going to happen to the volume of such a balloon if it allowed to rise to a height of 150 km. Articulate what you think will happen as a hypothesis.
1) Use atmospheric data in conjunction with Boyle's and Charle's Law to calculate the volume of a balloon at intervals of 10 km (starting from sea level) up to 150 km.
2) Use the Ideal Gas Law (PV = nRT) to predict the volume of the balloon as a function of its altitude (from sea level to 150 km in 10 km intervals).
3) Calculate the % deviation between the volume calculated in 1 and the volume calculated in 2
4) Use data from the CRC Handbook and Excel to do these calculation.
5) Plot the size of the balloon (as determined in 1 and 2) as a function of atmospheric height.
6) Write a conclusion in which you compare the calculated values for the balloon's volume with the predictions you made in your hypothesis.

- anonymous

I think this credit assignment is beyond my ability :( I am not even finished in algebra

- anonymous

if someone can guide me through this I would appreciate it very much

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## More answers

- abb0t

I think this should go in the chemistry section, but you might want to use the ideal gas law: PV = nRT

- UnkleRhaukus

do you know the volume of one mole at STP?

- anonymous

I was reading this on hyperphysics so I thought it is physics related too :( ?

- abb0t

The other thing that you might need need for your assignment is a table that gives you information about atmospheric pressure and temperature. You can get a tables from the web search on "STP".

- anonymous

is STP the same as ATM?

- anonymous

1 atm = 760 mmHg = 760 torr

- UnkleRhaukus

Standard Temperature and Pressure

- anonymous

273 Kelvin and 1 atm?

- anonymous

the information I see are beyond 8th grade omg

- UnkleRhaukus

yes

- anonymous

Correct me if I'm wrong but the lower you are the higher the pressure so if the balloon rises it will expand as the pressure decreases @abb0t

- anonymous

no the pressure is lower at higher altitude actually

- nincompoop

how do you know that the pressure at higher altitude is lower?

- abb0t

Yes. Look up the values for standard pressures at different altitudes.

- anonymous

Regions on the Earth's surface (or in its atmosphere) that are high above mean sea level are referred to as high altitude. High altitude is sometimes defined to begin at 2,400 metres (8,000 ft) above sea level.[4][5][6]
At high altitude, atmospheric pressure is lower than that at sea level. This is due to two competing physical effects: gravity, which causes the air to be as close as possible to the ground; and the heat content of the air, which causes the molecules to bounce off each other and expand.[7]
Because of the lower pressure, the air expands as it rises, which causes it to cool.[8][9] Thus, high altitude air is cold, which causes a characteristic alpine climate. This climate dramatically affects the ecology at high altitude
took this from Wikipedia

- anonymous

okay so how would you consider the temperature affecting the pressure inside the balloon? You're only giving the pressure outside the balloon.

- anonymous

I think this homework is going to make me want to pull my hairs off

- anonymous

the reason why the balloon expands is as a result of a pressure difference. this causes the balloon to expand in this case but as said above the temperature will decrease since the air expands.

- anonymous

guys correct me if I'm wrong

- anonymous

@agreene

- anonymous

we have
1. \(P_{\rm atm}\propto e^{-h}\)
2. T varies but non-unniformly with the height above sea-level
3. \(V_{\rm baloon}\propto {T\over P}\)

- anonymous

1) use atmospheric data that you are supposed to have to find P at height 150m.
2) use boyle's law \(\Large{P_h\over P_0}={V_h\over V_0}\) to find the new volume of gas in the baloon. If you are familiar with calculus and differentiation, this step will be easier that way.
3) Given that \(PV=nRT\implies V=\frac{nRT}{P}\), plug in the "P" (and mybe T, if provided) in-terms of height "h" and that answers the second piece.
4) % deviation of V2 from V1:
= (V2-V1) * 100 / V1
5) rest seem pretty straight forward

- anonymous

how do I begin with the information electrokid provided? @abb0t

- abb0t

It looks prety clear how you should start. Lol.

- anonymous

can I use google docs to create the excel? I don't know this yet … I am only algebra-beginner's level

- abb0t

You can use microsoft excel. I dont think you need to go thru google..

- anonymous

how much is an excel? I don't own one

- anonymous

I can't find any atmospheric data above 3km
I found this chart
http://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html
by following the formula, spreadsheet is only allowing me to calculate unto 40km

##### 1 Attachment

- anonymous

I don't even have the CRC Handbook… what is that?

- Preetha

That is why you have been given this problem. The math is simple. So your first task is to google around to get the table. Otherwise, your library will have a physical CRC Handbook.

- anonymous

I am homeschooled

- Preetha

http://usatoday30.usatoday.com/weather/wstdatmo.htm
You can calculate the pressure for any altitude. Make a table of altitude, and P and T and use that to calculate V.

- Preetha

This is a better table: http://www.engineeringtoolbox.com/standard-atmosphere-d_604.html

- anonymous

thank you all.
I will attempt this once more

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