# Help with English units. Specific Heat

1. Oct 4, 2013

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 $C_p = a + bT + cT^2 + dT^3$

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

2. Relevant equations

$C_p = a + bT + cT^2 + dT^3$

3. The attempt at a solution

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

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

Using this conversion factor I get $\frac{5442.3\frac{Btu}{lbmol*R}}{31.999\frac{lbm}{lbmol}}=170.1\frac{Btu}{lbm*R}$

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. Oct 5, 2013

### Simon Bridge

What are the dimensions of the Rankine?

3. Oct 5, 2013

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

4. Oct 5, 2013

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. Oct 5, 2013

### SteamKing

Staff Emeritus
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. Oct 5, 2013

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

Using this empirical heat equation, $\int_{800}^{1500}(a+bT+cT^2+cT^3)dT$, 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 $\int{C_p(T)}dT$.

My property tables book reads like this

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

This is where I was assuming my units for $5442.3\frac{Btu}{lbmol*R}$

Hopefully this clarified my dilemma.

Thanks again,
Mac

7. Oct 5, 2013

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. Oct 5, 2013

### Simon Bridge

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