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msumner Group Title

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

  • one year ago
  • one year ago

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  1. msumner Group Title
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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.

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

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

    • one year ago
  4. abb0t Group Title
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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

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

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

    • one year ago
  7. abb0t Group Title
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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".

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

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

    • one year ago
  10. UnkleRhaukus Group Title
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    Standard Temperature and Pressure

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

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

    • one year ago
  13. UnkleRhaukus Group Title
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    yes

    • one year ago
  14. Tinman Group Title
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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

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

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

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

    • one year ago
  18. Tinman Group Title
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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

    • one year ago
  19. msumner Group Title
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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.

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

    • one year ago
  21. Tinman Group Title
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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.

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

    • one year ago
  23. msumner Group Title
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    @agreene

    • one year ago
  24. electrokid Group Title
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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. \(V_{\rm baloon}\propto {T\over P}\)

    • one year ago
  25. electrokid Group Title
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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

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

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

    • one year ago
  28. msumner Group Title
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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

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

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

    • one year ago
  31. msumner Group Title
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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

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

    • one year ago
  33. Preetha Group Title
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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.

    • one year ago
  34. msumner Group Title
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    I am homeschooled

    • one year ago
  35. Preetha Group Title
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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.

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

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

    • one year ago
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