Help with English units. Specific Heat

In summary: Yes, I believe so. I didn't think the Rankine temperature scale had dimensions. Does Fahrenheit have dimensions, other than ^\circ{F}?http://en.wikipedia.org/wiki/Rankine_scale
  • #1

MacLaddy

Gold Member
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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
 
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  • #2
What are the dimensions of the Rankine?
 
  • #3
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
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
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
SteamKing said:
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
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
With no dimensions, the Rankine is a scale factor isn't it?
Oh you got there... well done ;)
 

What is the specific heat of a substance?

The specific heat of a substance is the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius.

How is specific heat measured?

Specific heat is measured in units of energy per unit mass per unit temperature, such as joules per gram per degree Celsius (J/g°C) or calories per gram per degree Celsius (cal/g°C).

Why do different substances have different specific heats?

Different substances have different specific heats because they have different molecular structures and compositions, which affect how much energy is required to raise their temperature.

How does specific heat relate to thermal conductivity?

Specific heat and thermal conductivity are both measures of a substance's ability to transfer heat. However, specific heat specifically refers to the amount of energy required to raise the temperature of a substance, while thermal conductivity refers to the rate at which a substance can transfer heat.

Can specific heat be changed?

Specific heat is an intrinsic property of a substance and cannot be changed. However, the specific heat of a substance can be affected by factors such as temperature, pressure, and phase changes.

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