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Homework Help: Gas expanding against a piston

  1. Sep 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider a cylindrical piston in which an ideal gas is kept. The gas is currently at pressure P1, volume V1, and temperature T. The temperature T is assumed to be constant throughout the experiment. The piston is massless and frictionless. On the piston is a block of mass M and this mass is not changed throughout the experiment. The block's cross-sectional area is A. Thus, the pressure of the block on the piston is Mg/A.

    Assume that initially P>Mg/A so that the gas begin to expand until its pressure equilibrates with the pressure of the block. Its final volume is V2.

    1) Throughout this process, is the pressure of the gas a constant?
    2) To calculate the work done by the gas, do you use the gas pressure P or the external pressure Mg/A.

    2. Relevant equations
    W = F*d
    PV = nRT

    3. The attempt at a solution

    1) As the gas expands, its pressure must decrease due to Boyle's law such that the product PV is a constant.
    2) My textbook says we use the external pressure to calculate work, but I can't understand this. My argument is that to calculate work done by the gas, you need to use the pressure of the gas since it is the gas which is responsible for the force applied in raising the piston.

  2. jcsd
  3. Sep 15, 2012 #2


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    Homework Helper

    The pressure of the gas is defined when the gas is in equilibrium. Expanding against the constant external force, the gas is not equilibrium with the surroundings, so pressure is not defined during the process. The gas molecules hit the piston, and exert force on the piston so it will raise, but that makes the molecules loose kinetic energy in the collision with the piston: the local pressure is lower near the piston than far from it. Calculate the work done on the gas by the external force. The negative of this work is done by the gas.

    Last edited: Sep 15, 2012
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