Unknown thermochemical properties help please

[Mercaptan]

Hi all,
I've joined this forum as a last resort seeing no one else here knows (well, before maybe joining other forums?). I've been handed an old model of the iron ore plant I work at which was made in the 90s in excel (the model was made then, not the plant!). The metallurgist at the time was apparently secretive and didn't like to pass down information, so he's left out all formulae and explanations on what's what. I'm trying to bring it up to 2015 and make it useful again, and I've got most of it worked out, but I'm a chemist/geologist by trade. I was wondering if anyone's be able to help me?

I've attached the screenshot for the page on CaO, but there's a table for every oxide and gas that goes through the plant. I know the first column is std enthalpy, second is entropy, the last number is molecular weight, 3rd and 2nd last columns are T1 and T2. The rest was labelled a,b,c,d. These don't correspond to a Shomate equation either, and I think they're in kJ/mol. "s" and "l" are solid and liquid.

Anyway, have a go, see if you can decode it for me.

Peace,
Mercaptan

 

[Chestermiller]

Maybe they are constants in another heat capacity equation than that of Shomate. Try just a power series, and plot it up over each of the ranges. See if they join up at the transition points.

Chet

 

[Mercaptan]

Thanks Chet, I'll give it a go and get back to you.

 

[Mercaptan]

I've figured out the equation in which they are used in. This appears a number of times in the model, and often as sums, but the base of it is this:

A(T- Tref) + (B/2000)( T²- T²) – 100000C(1/T - 1/Tref) + D^-6/3(T³- Tref³)

Where T is any temperature (in one example it's the temperature of the ore feed, another example it's the different Ts, T1, T2, T3...),
Tref is the reference temperature the whole model is based on,
A,B,C and D are the constants.

Since writing the OP I've found that not all oxides and elements are carried through from start to finish, so I need to add them in at various stages in the model. This means I'll need the constants for the missing ones.

Does this look familiar to anyone?

 

[Quantum Defect]

I've figured out the equation in which they are used in. This appears a number of times in the model, and often as sums, but the base of it is this:

A(T- Tref) + (B/2000)( T²- T²) – 100000C(1/T - 1/Tref) + D^-6/3(T³- Tref³)

Where T is any temperature (in one example it's the temperature of the ore feed, another example it's the different Ts, T1, T2, T3...),
Tref is the reference temperature the whole model is based on,
A,B,C and D are the constants.

Since writing the OP I've found that not all oxides and elements are carried through from start to finish, so I need to add them in at various stages in the model. This means I'll need the constants for the missing ones.

Does this look familiar to anyone?

These look like expressions for the integral of CpdT using an analytical expression for the heat capacity at constant P.

 

[Mercaptan]

Thanks Quantum Defect. Coming from an analytical chem and Earth science background, my maths knowledge is very limited. Excuse the ignorance, what is CpdT? A derivative of Cp wrt temperature?

 

[Chestermiller]

I've figured out the equation in which they are used in. This appears a number of times in the model, and often as sums, but the base of it is this:

A(T- Tref) + (B/2000)( T²- T²) – 100000C(1/T - 1/Tref) + D^-6/3(T³- Tref³)

Where T is any temperature (in one example it's the temperature of the ore feed, another example it's the different Ts, T1, T2, T3...),
Tref is the reference temperature the whole model is based on,
A,B,C and D are the constants.

Since writing the OP I've found that not all oxides and elements are carried through from start to finish, so I need to add them in at various stages in the model. This means I'll need the constants for the missing ones.

Does this look familiar to anyone?

If looks pretty clear that this is an integrated form of the heat capacity equation to get the enthalpy. Oops. I see that QD has also noticed this. One indicator is that the leading term is linear in T. Another indication is the factor of 3 in the denominator of the D term (incidentally, those should be 1/T³'s, not a temperature difference cubed). So, the actual heat capacity is:

A + (B/1000)T+100000C/T² -D^-6?/T⁴

That's obviously absolute temperature in the equation.

We need to see of we can find this functional form in a book somewhere, or in NIST.

I found the following in a description of heat capacity equations: Cp = a + bT + c / T² + ……………

Chet

 

[Chestermiller]

In your equation, you don't know the units of the heat capacity. You need to plot up the heat capacity vs temperature using the values in the table, and compare the graph with corresponding results from a heat capacity parameterization in the literature (for which you know the units of the parameters) to ascertain the units in your table. The two plots will be offset by a constant factor (approximately) which will enable you to ascertain the units.

Chet

 

[Mercaptan]

They did leave me the units of the constants, J/molK.

Thanks for the actual heat capacity equation, I haven't done integration for years so I was going to wait until I got home and got the old textbook out.

 

[Chestermiller]

They did leave me the units of the constants, J/molK.

Still, just benchmark against another representation to make sure. That's what I would do.

Chet

 

[Mercaptan]

Good idea.

 

[Quantum Defect]

They did leave me the units of the constants, J/molK.

Thanks for the actual heat capacity equation, I haven't done integration for years so I was going to wait until I got home and got the old textbook out.

http://www.geol.ucsb.edu/faculty/hacker/geo124T/lecture.html

This lecture shows the integral with a similar expansion for Cp

The particular expansion differs only in the last term in the expansion from what is here (the "D" term).

I have started packing my books up for a move, but I think that the CRC Handbook has tables of coefficients for Cp in an expansion like this, they may (or may not) have the same expansion coefficients. Even if it is not exactly the same, the functional form for the dominant terms is the same, so you should have similar values for A, B, and C. You can also look in places like: the JANAF tables, J. Phys. Chem. Ref. Data, The NIST Webbook (as Chet notes), etc.

 

[Mercaptan]

Thanks Quantum Defect. I have a few old chemistry books here handed down from the old metallurgist and other chemists if I can't find them online.