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Homework Help: Thermodynamics - Irreversible Adiabatic expansion

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Closed system made of a cylinder containing air, compressed by a piston with weights on top of it. The piston is frictionless and its weight can be neglected. The system contains initially 10 kg of air at 27 °C and a pressure of 10 ata. The weights are suddenly halved. Considering the process adiabatic and air an ideal gas, calculate:

    1) The temperature of air at the final state
    2) The work done on the surrounding
    3) The entropy increase of the air
    4) The isentropic efficiency of expansion.
    2. Relevant equations
    pV = m Rspecific T
    delta U = Q - W
    delta U = Cv delta T

    3. The attempt at a solution

    p2 = p1 / 2 = 5 ata = 490,3 kPa
    v1 = m Rspecific T / p1 = 0,88 m^3
    Since the process is adiabatic, Q = 0 and delta U = - W

    I'm stuck at question one already. How am I supposed to find T2 ?
    I tried to use
    T2 = p2 V2 / Rspecific
    but can't because I don't have V2;
    I tried using the first law for an adiabatic process of an ideal gas
    Cv ( T2 - T1) = -Pextern ( V2 - V1)
    but can't because I don't have V2;

    Can't use the reversible adiabatic equation
    T2 = (p1/p2)^((1-γ)/γ) * T1
    because the weights are removed suddenly and thus it's not reversible..

    How am I supposed to solve this?
  2. jcsd
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