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Thermo: A Tire and a Gas Tank

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data

    We have a tank of air at 7 atm, 30 L, and 293 Kelvin(20 Celsius), and a flat tire with 1atm, 10 L (Constant), also at 293 K (20 C). The valve is opened quickly and closed quickly when the pressure in the tank reaches 6 atm. Using the Ideal gas assumption and taking the heat capacity of the air as Cp = 3.5 R...

    Determine: the temperature of the air in the tire and the tank immediately after filling, and the eventual pressure in the tank and tire after equilibration with room temperature.


    2. Relevant equations
    PV = RT

    T2/T1 = (V2/V1)^ (1-[tex]\gamma[/tex])

    dU = dW (Adiabatic)

    dQ = 0 (Adiabatic)

    dW = - [tex]\int[/tex]PdV

    Cv = Cp-R

    [tex]\gamma[/tex] = Cp/Cv = 1.4

    3. The attempt at a solution

    The first thing I did was assume that the problem was a closed, adiabatic system, with a constant volume. For the first part, I assumed that "immediately after filling" meant the split second you close the tank, implying that each portion of the system is "open" to each other. Intuitively, I also know that a tire tends to warm up when air is pumped in, so I also hoped that my answer might coincide with that conclusion.

    However I looked at the tank first. I said that T2/T1 = (V2/V1)^ (1-[tex]\gamma[/tex]), and plugged these sets of numbers in:

    T2/293K = (40L/30L)^(-.4)
    T2(tank) = 261.15K, -11.84 C (in the tank)

    T2/293K = (40L/10L)^(-.4)
    T2 (tire) = 168.28 K, -104.71 C (in the tire)

    This, of course goes against my initial belief that a tire usually warms slightly when you compress it. Is my process for the first part correct?
     
    Last edited: Sep 13, 2009
  2. jcsd
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