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Ideal Gas Help

  1. Dec 5, 2005 #1
    Here is my problem.

    A vertical cylinder of cross-sectional area .04m^2 if fitted with a frictionless piston with a mass of 13kg. Assume acceleration of gravity is 9.8 m/s^2. If there is 1 mol of an ideal gas in the cylinder at 315 K, find the pressure in the cylinder. Assume the system is in equilibrium.

    Here is what I've been doing.

    P=Force/Area Force= Pressue * Area

    Since it is in equilibrium, the downward force of the piston should equal the upward force of the gas.

    PA = (Piston mass)(gravity)

    P(.04) = (13)(9.8)
    P = 3185 Pa

    3185 is not the right answer according to my online answer checker. What am I doing wrong?
     
  2. jcsd
  3. Dec 5, 2005 #2
    Questionable Solution

    Okay, I found why my answer is wrong. Apparently I need to at 101300 Pa (1 atm) to my answer. If anyone can explain why I add one atmosphere, that would be greatly appreciated.
     
  4. Dec 5, 2005 #3

    Astronuc

    User Avatar

    Staff: Mentor

    Assume the piston seals the vertical cylinder. The piston has a mass (13 kg) but also, there is atomspheric pressure outside the cylinder, i.e. the air in which we live, and that pressure is 1 atm = 14.7 psia = 101325 Pa or 101.325 kPa. At equilibrium, the pressure inside the cylinder must equal the pressure applied from the outside which is the sum of the (weight of the piston)/(area of piston), or (13 kg)(9.8 m/s2)/(0.04 m2) + the atmospheric pressure 101325 Pa.

    mg = force = N if m (kg) and g (m/s2).

    Pressure = force/area = N/m2 = Pa.
     
    Last edited: Dec 5, 2005
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