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Pressure problem: He or O2?

  1. Sep 12, 2009 #1

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    1. The problem statement, all variables and given/known data
    A 2-ft[tex]^{3}[/tex] closed tank is filled with 0.30 lb (Weight) of gas, which is thought to be either oxygen or helium. A pressure gage attached to the tank reads 12 psi at a temperature of T=80F. Is it He or O[tex]_{2}[/tex]? Why? Jeopardizing safety?


    2. Relevant equations

    [tex]\gamma[/tex]=weight/volume

    [tex]\gamma[/tex]=[tex]\rho[/tex]*g

    where [tex]\rho[/tex] is the specific density.

    [tex]\rho[/tex]=p/RT

    where p is pressure, R is engineering gas constant, and T is temperature in Rankine.

    3. The attempt at a solution

    In this case, I'm looking for R. I know R[tex]_{oxygen}[/tex]=1554 ft-lb/slug*Rankine and R[tex]_{helium}[/tex]=12419 ft-lb/slug*Rankine.

    So I know [tex]\gamma[/tex], which is 0.30-lb/2-ft[tex]^{3}[/tex]=0.15-lb/ft[tex]^{3}[/tex]

    so, since [tex]\gamma[/tex]=[tex]\rho[/tex]*g=Pg/RT

    and T(R) = 539.6 Rankine

    R=Pg/[tex]\gamma[/tex]T=((32.2 ft/s[tex]^{2}[/tex])*(12psi*144 lbs/ft[tex]^{2}[/tex]/psi))/((0.15-lb/ft[tex]^{3}[/tex])*539.6 Rankine)

    R=477.391 ft[tex]^{2}[/tex]/(s[tex]^{2}[/tex]*Rankine)

    _____________________________________
    I'm not sure where I'm going wrong with this, but it should either be 1554 or 12419... Oh, and my units are off too.
     
  2. jcsd
  3. Sep 12, 2009 #2
    Yes, your units are way off. However, the answer lies inside the units. One unit for the gas constant is;

    (psia*ft^3)/(lbm*R)

    Compare these units to the ones stated in your problem and try for the solution again using the ideal gas equation.

    Also, you don't need to convert 0.30 lbs to slugs.

    Thanks
    Matt
     
    Last edited: Sep 12, 2009
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