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Air pressure

  1. Dec 31, 2014 #1
    1. The problem statement, all variables and given/known data
    Car mechanics use compressed air tools to open bolts. Instead of using an air compressor one can also use a tank of pressurized air. There is an air tank with a volume of 50 L to work with. The pressure of the tank is 50 bars when it is stored indoors at 20 °C. The bolt wrench needs at least 10 bar pressure to operate.

    2. Relevant equations
    How long can the mechanics use the bolt wrench outdoors at -20 °C if it consumes 200 L/min of air at normal pressure ? the normal pressure is 1.0 bar.

    3. The attempt at a solution
    R = 8.314E-2 L bar/(mol K)
    the tank holds this many moles
    n = PV/RT = 50(50) / (8.314E-2 * 293) = 102.6 mol of air
    at -20° the pressure will be
    P = nRT/V = 102.6(8.31E-2)(253)/50 = 43.174 bar
    How many moles can be delivered from 43.174 bar down to 10 bar, the lower limit?
    all else being equal, moles are proportional to pressure
    X mol / 102.6 mol = 10 bar / 43.174 bar
    X mol = 23.76 mol (useful amount of gas)
    How much does the wrench use per minute?
    n = PV/RT = 1.0 (200) / (8.314E-2 * 253) = 9.508 mol per minute
    finally
    23.76 mol / 9.508 mol/min = 2.499 or 2.5 min to 2 sig figs or 150 s

    Is the solution correct ?
     
  2. jcsd
  3. Dec 31, 2014 #2

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    Your X mol seems to be the amount of gas left in the tank when the wrench stops working, not the amount of gas used.
     
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