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Need help on this gas flowing into a vessel problem

  1. Nov 22, 2011 #1
    1. The problem statement, all variables and given/known data

    An evacuated rigid vessel is filled adiabatically through a valve from a large constant pressure source of a certain gas, until the pressures inside and outside are equal. If the P-U-V relation for the gas is given by the equation:
    U = 831 + 2PV where U is joules, P is pascals, and V is m^3
    Find the ratio of the initial and final volumes of the gas which enters.
    (Hint: This is an application of the non-steady flow energy equation)

    2. Relevant equations
    So we need to use the Non-steady flow energy equation. Does that mean I use the equation
    dE/dt = Q - W + (dm/dt)*(h2-h1) + .5*(dm/dt)*(V1^2 - V2^2)
    In this case, kinetic and potential energy contributions would be negligible and I'm guessing the equation reduces to:
    ΔU = Q - W + (dm/dt)*(h2 - h1)

    3. The attempt at a solution
    Also since the process is adiabatic, then Q = 0 and W = 0 for the process so the above equation simplifies to:
    dU/dt = (dm/dt)*(h2-h1)
    I also think that the internal energy of the system is 831 since the initial pressure and volume are both 0. In other words, U(0,0) = 831, but I don't know how to figure out the rest of the problem. Please let me know if I'm doing this right or not.
  2. jcsd
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