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Homework Help: Pressure Cooker Problem

  1. Jan 30, 2009 #1
    1. The problem statement, all variables and given/known data

    A pressure cooker is a sealed pot designed to cook food with the steam produced by boiling water somewhat above 100 C. Consider a pressure cooker with a weight of mass m covering the only hole (which has a diameter d = 0.003 m) on top of it. What should m be in order to cook food at 120 C. Assume the atmospheric pressure outside the cooker is 1 atm.

    2. Relevant equations

    Pressure = Force/Area
    Saturated vapor pressure of water at 120 C = 1.99 x 10^5 Pa

    3. The attempt at a solution

    Since P = F/A, F = AP. F must then at least equal the weight mg of the weight at the top of the pressure cooker in order to lift it and let steam escape. So m = AP/g. The result I get from this approach is incorrect. Any help would be greatly appreciated.
     
  2. jcsd
  3. Jan 30, 2009 #2

    rl.bhat

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    Will you please show your calculation?
     
  4. Jan 30, 2009 #3
    PA = mg

    m = PA/g

    where P is the pressure inside the cooker, A is the area of the hole, and m is the mass of the weight.

    [tex]m = \frac{(1.99)(10^{5})(\pi)(0.003^{2})}{(9.8)} = 0.574 kg[/tex]
     
  5. Jan 30, 2009 #4

    rl.bhat

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    Have you taken into account the atmospheric pressure?
     
  6. Jan 30, 2009 #5
    Yes, I tried to include the difference in pressures (199,000 Pa - 101,300 Pa) as P in the equation, but still came up with an incorrect answer.
     
  7. Jan 30, 2009 #6

    rl.bhat

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    Area = pi*d^2/4
     
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