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Please check this problem

  1. Dec 5, 2005 #1
    Need to see if I worked this right.
    Hot air balloon floating in air has at 0 degrees C ( desnsity = 1.293kg/m^3). The mass of the balloon and passengers is 1650kg. If they want to stay at a constant height, estimate the required average temperature of the air in the balloon. Assume the volume of air in the balloon is 5000m^3 and the density of air varies with temperature according to the following information.
    -10 degrees C = 1.341 kg/m^3
    -5 degrees C = 1.316 kg/m^3
    0 degrees C = 1.293 kg/m^3
    +5 degrees C = 1.269 kg/m^3
    +10 degrees C = 1.247 kg/m^3
    MY SOLUTION:
    B = (1.293kg/m^3)(5000m^3)(9.81m/s^2) = 63422N Buoyant Force
    Weight of Balloon is (1650kg)(9.81m/s^2) = 16187N
    63422N-16187N=47235N
    47235N/9.81m/s^2 = 4815kg
    Density of air in balloon is 4185kg/5000m^3 = .963kg/m^3
    So here I would have to assume the Pressure is standard and is equal to 101325 so from row=P/RT it would give me a temp in degrees C of 93.5. I assume that pressure because it seems that was the value he used in the table to calculate the density for the temps from -10 to +10.
    Have I made any mistakes? Thanks
     
  2. jcsd
  3. Dec 6, 2005 #2

    Astronuc

    User Avatar

    Staff: Mentor

    That's about right. The answer may vary by +/- 1-2 K depending on the pressure, air density and gas constant used.
     
  4. Dec 6, 2005 #3
    Thanks for the response. Just worried that I made a mistake somewhere along the line of solving this problem.
     
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