Help with English units. Specific Heat

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MacLaddy
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Homework Statement



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.


Homework Equations



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


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
 

Answers and Replies

  • #2
Simon Bridge
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What are the dimensions of the Rankine?
 
  • #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
 
  • #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.
 
  • #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.
 
  • #6
MacLaddy
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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.

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

The question reads like this.

Determine the enthalpy change of [itex]\Delta{h}[/itex] of oxygen, in Btu/lbm, as it is heated from 800 to 1500 R, using the empirical specific heat equation as a function of temperature

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
 
  • #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
 
  • #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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