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Help with English units. Specific Heat

  1. Oct 4, 2013 #1

    MacLaddy

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    1. The problem statement, all variables and given/known data

    I have a problem that I've mostly solved using Ideal-gas specific heats for Oxygen. It has the form [itex]C_p = a + bT + cT^2 + dT^3[/itex]

    I am supposed to give the answer in English units of [itex]\frac{Btu}{lbm}[/itex], but I am having some difficulties in my conversion.


    2. Relevant equations

    [itex]C_p = a + bT + cT^2 + dT^3[/itex]


    3. The attempt at a solution

    After integrating to solve above I have the answer of [itex]5442.3\frac{Btu}{lbmol*R}[/itex]. These units are given to me via my property tables booklet.

    In trying to convert [itex]5442.3\frac{Btu}{lbmol*R}[/itex] to [itex]\frac{Btu}{lbm}[/itex] I am using the fact that Oxygen has a molar mass of [itex]31.999\frac{lbm}{lbmol}[/itex].

    Using this conversion factor I get [itex]\frac{5442.3\frac{Btu}{lbmol*R}}{31.999\frac{lbm}{lbmol}}=170.1\frac{Btu}{lbm*R}[/itex]

    I am getting the extra factor of Rankine in the denominator. My instructor has a solution video she's presented, and she doesn't even use the R in the original units from the property tables booklet, but it clearly shows it.

    Any clarification would be appreciated.

    Thanks,
    Mac
     
  2. jcsd
  3. Oct 5, 2013 #2

    Simon Bridge

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    What are the dimensions of the Rankine?
     
  4. Oct 5, 2013 #3

    MacLaddy

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    I didn't think the Rankine temperature scale had dimensions. Does Fahrenheit have dimensions, other than [itex]^\circ{F}[/itex]?

    http://en.wikipedia.org/wiki/Rankine_scale
     
  5. Oct 5, 2013 #4

    MacLaddy

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    Now I'm realizing that R may be the universal gas constant, not Rankine... Have to look at this in the morning when I have a brain.

    Insight is definitely still welcome.
     
  6. Oct 5, 2013 #5

    SteamKing

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    Your problem statement is not clear. You are supposed to give what answer in units of BTU/lbm? Those are the units of enthalpy or internal energy. Specific heat has units of Energy/unit mass/deg. Temp. The universal gas constant would not be incorporated into the units, anyway.
     
  7. Oct 5, 2013 #6

    MacLaddy

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    Yes, I apologize for being vague. It was a late night for me.

    The question reads like this.

    Using this empirical heat equation, [itex]\int_{800}^{1500}(a+bT+cT^2+cT^3)dT[/itex], I came up with the previous mentioned answer of 5442.3. The a, b, c, and d values were provided for me in my property tables booklet, and the solution of 5442.3 is verified from the instructors solutions. I believe the basic form of this is [itex]\int{C_p(T)}dT[/itex].

    My property tables book reads like this

    [itex]C_p = a + bT + cT^2 + dT^3[/itex]
    (T in R, [itex]C_p[/itex] in Btu/lbmol * R)


    This is where I was assuming my units for [itex]5442.3\frac{Btu}{lbmol*R}[/itex]

    Hopefully this clarified my dilemma.

    Thanks again,
    Mac
     
  8. Oct 5, 2013 #7

    MacLaddy

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    Ah, I had a Eureka moment.

    Those are the units for Specific heat, not the solution of enthalpy.

    $$C_pT=\frac{Btu}{lbmol*R}*R=\frac{Btu}{lbmol}$$

    Thanks all,
    Mac
     
  9. Oct 5, 2013 #8

    Simon Bridge

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    With no dimensions, the Rankine is a scale factor isn't it?
    Oh you got there... well done ;)
     
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