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Thermodynamics of open soda can

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data
    C02 from a can of soda expands irreversibly against the atmospher. Assume the process is adiabatic and Pi = 3 bar. Assume C02 to be an ideal gas with Cp = 37 j/mol*K. Find the final temperature of CO2 after it has reached atmospheric pressure.

    Thats all I get...


    2. Relevant equations
    Adiabatic implies dq = 0
    constant Pext implies dw = -Pext dV
    Ideal gas implies dU = CvdT
    1st Law gives dU = -Pext dV
    we go from here

    3. The attempt at a solution

    nCvdT = -Pext dV

    integrating
    nCv(T2-T1) = -Pext (V2-V1)

    using PV=nRT the above equation reduces
    nT2(Cv+R) = nT1(Cv+Pext*R/P1)

    we can take Pext/T2 = P1/T1 ?? but this system does not yield a solution for T1, T2

    here is were I am stuck seeing as how I dont know T1 or T2 (obviously n's cancel out)

    If we take the can as the system
    the first law energy balance gives

    dU/dt = -dn_out/dt * H

    this reduces to the standard adiabatic equation

    (T2/T1)^Cp/R = Pext/P1

    an attempt with the concervation of mass yields
    dn/dt = -dn_out/dt we can sub in the ideal gas equation for n and get
    d(p/T)/dt = -dn_out/dt * R/nV but I dont think we know anything about n or dn_out/dt

    so I am stuck, help please!!

    Thanks
     
    Last edited: Feb 4, 2010
  2. jcsd
  3. Feb 4, 2010 #2
    I think it's before you integrate is your problem. Use ideal gas law to sub for pext.
     
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