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Isochoric Process with Unknown Ideal Gas

  1. Feb 14, 2015 #1
    I was assigned a problem in my Engineering Thermodynamics class as follows:
    Problem:
    An ideal gas in a rigid closed container undergoes isochoric heating from T1 = 27 C to T2 = 77 C. Initial gage pressure is 300 kPa, pressure of surroundings is 1 atm.
    Find the final gage pressure.

    The way to go about solving the problem seems straight forward, as I will show my train of thought below. The only thing I am stuck up on is what R value to use for this particular ideal gas, since the gas itself is not specified, nor it's volume, nor it's specific volume, nor it's mass.

    Relevant Equations:
    Pv = RT

    Attempted Solution:

    Here's how I attempted it:

    Knowns: T1 = 27 C, T2 = 77 C, Pgage1 = 300 kPa, Psurround = 1 atm
    Trying to find: Pgage2

    For an ideal gas, Pv = RT, where v = specific volume (m3/kg) and R = specific gas constant (J/kgK). If I know what R value to use, I can solve for v:

    v = (RT1)/P1 where P1 = Pgage1+Psurround (in Pa)

    Then, because volume V is constant, and the unknown arbitrary mass m is constant, so is v
    by the relationship

    v = V/m

    Then I would find P2:

    P2 = (RT2)/v

    It follows,

    Pgage2 = P2 - Psurround (in Pa)

    That's all folks. Maybe I am missing something rather obvious here, or taking the wrong approach. Again, the only thing I am stuck on is what the specific gas constant R should be. I can not solve for it with it's definition since R = R/M = nR where R is the universal gas constant (8.314 J/molK), M is molar mass of the gas, and n is moles of the gas. I have consulted Tables in the back of my text, and R is given for monatomic or diatomic ideal gas as is to be expected, but again, I'm not given those specifics in the problem. Any help is appreciated! :)

    - Preston
     
  2. jcsd
  3. Feb 14, 2015 #2

    Bystander

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    Why?
     
  4. Feb 14, 2015 #3
    Why solve for v, or why am I justified in saying that?

    v = (RT1)/P1 and everything on right hand side is known (if I know what R to use). Why am solving for v in the first place--

    I can use the fact that v is constant through the process (remember, the system is a constant volume closed container) to solve for P2 (absolute, not gage)

    P2 = (RT2)/v again, everything on the right is known at this point. Knowing the final absolute pressure allows me to solve for final gage pressure

    Pgage2 = P2 - Psurround

    The last two equations were in my original post, but I hope this clarifies my thought process for you.
     
  5. Feb 14, 2015 #4

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    Think.
     
  6. Feb 14, 2015 #5
    True or false: The values of n, R, and V are the same in the initial and final states of the gas.

    Chet
     
  7. Feb 14, 2015 #6
    Chet, that is true. Bystander, I see what you are getting at now!

    In both cases, (Pv)/RT = 1

    so (P1v)/(RT1) = P2v/RT2 and R and v will cancel out of each side showing that the following relationship is independent of them:

    P1/T1 = P2/T2 and now I can solve. Thats what I get for still being up at 3 am when I woke up 6:30 am. Ha.

    Thanks so much!
     
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