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msumner

  • one year ago

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

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  1. msumner
    • one year ago
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    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.

  2. msumner
    • one year ago
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    I think this credit assignment is beyond my ability :( I am not even finished in algebra

  3. msumner
    • one year ago
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    if someone can guide me through this I would appreciate it very much

  4. abb0t
    • one year ago
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    I think this should go in the chemistry section, but you might want to use the ideal gas law: PV = nRT

  5. UnkleRhaukus
    • one year ago
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    do you know the volume of one mole at STP?

  6. msumner
    • one year ago
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    I was reading this on hyperphysics so I thought it is physics related too :( ?

  7. abb0t
    • one year ago
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    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".

  8. msumner
    • one year ago
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    is STP the same as ATM?

  9. msumner
    • one year ago
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    1 atm = 760 mmHg = 760 torr

  10. UnkleRhaukus
    • one year ago
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    Standard Temperature and Pressure

  11. msumner
    • one year ago
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    273 Kelvin and 1 atm?

  12. msumner
    • one year ago
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    the information I see are beyond 8th grade omg

  13. UnkleRhaukus
    • one year ago
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    yes

  14. Tinman
    • one year ago
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    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

  15. Tinman
    • one year ago
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    no the pressure is lower at higher altitude actually

  16. nincompoop
    • one year ago
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    how do you know that the pressure at higher altitude is lower?

  17. abb0t
    • one year ago
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    Yes. Look up the values for standard pressures at different altitudes.

  18. Tinman
    • one year ago
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    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

  19. msumner
    • one year ago
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    okay so how would you consider the temperature affecting the pressure inside the balloon? You're only giving the pressure outside the balloon.

  20. msumner
    • one year ago
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    I think this homework is going to make me want to pull my hairs off

  21. Tinman
    • one year ago
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    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.

  22. Tinman
    • one year ago
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    guys correct me if I'm wrong

  23. msumner
    • one year ago
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    @agreene

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

  25. electrokid
    • one year ago
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    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

  26. msumner
    • one year ago
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    how do I begin with the information electrokid provided? @abb0t

  27. abb0t
    • one year ago
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    It looks prety clear how you should start. Lol.

  28. msumner
    • one year ago
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    can I use google docs to create the excel? I don't know this yet … I am only algebra-beginner's level

  29. abb0t
    • one year ago
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    You can use microsoft excel. I dont think you need to go thru google..

  30. msumner
    • one year ago
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    how much is an excel? I don't own one

  31. msumner
    • one year ago
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    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

  32. msumner
    • one year ago
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    I don't even have the CRC Handbook… what is that?

  33. Preetha
    • one year ago
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    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.

  34. msumner
    • one year ago
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    I am homeschooled

  35. Preetha
    • one year ago
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    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.

  36. Preetha
    • one year ago
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    This is a better table: http://www.engineeringtoolbox.com/standard-atmosphere-d_604.html

  37. msumner
    • one year ago
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    thank you all. I will attempt this once more

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