# Help with English units. Specific Heat

Gold Member

## Homework Statement

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.

## Homework Equations

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

## 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

Simon Bridge
Homework Helper
What are the dimensions of the Rankine?

Gold Member
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

Gold Member
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.

SteamKing
Staff Emeritus
Homework Helper
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.

Gold Member
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.

Determine the enthalpy change of $\Delta{h}$ 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, $\int_{800}^{1500}(a+bT+cT^2+cT^3)dT$, 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

Gold Member
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

Simon Bridge