How to calculate spcific heat capacity 3

[treddie]

Hello.

My ignorance is showing here with this question. It has been awhile since my college chem days, but here is my question. Is there a way to calculate specific heat capacity of a polyatomic gas mixed with another polyatomic gas or vapor when only chemical reactants, temperature and pressure are known?

For instance in a rocket engine thrust chamber where O2 is the oxidizer and C12H26 is the fuel, the mix is burning at a given temperature and pressure, so what is the average specific heat? The empirical equation for the reaction was easy enough to work out: C12H26 + 12.5O2 --> 12CO + 13H2O.
The general equation, Q = c*m*deltaT, where (Q) = heat, (c) = specific heat capacity, (m) = molar mass, and (deltaT) equals the change in temperature, when rearranged as c = Q / (m * deltaT), requires a value for (Q) that I do not know, and asks for a change in temperature that I ASSUME means a change of 1deg (in keeping with the definition of specific heat which states that it is the amount of energy required to raise 1 unit mass of a substance 1 unit degree in temperature). But it also does not take into account the average temperature and pressure of the mix (which definitely affects the value for specific heat capacity) and does not specify whether (c) is measured with respect to constant pressure or constant volume.

I am not looking so much for a solution to the problem above as I am looking for a good reference (or explanation)that explains specific heat capacity in more detail (my college text book offers no help to the degree I need).

Many thanks!

 

[Latexman]

Most oxidation reactions are carried to CO₂. Did you omit the 2 or you have a reason to stop at carbon monoxide?

A good reference is Sherwood, Reid and Prausnitz or Poling, Prausnitz, and O'Connell depending on what Edition you get. The title is The Properties of Gases and Liquids.

There is also a good website that may have the information you want:

http://webbook.nist.gov/

Good luck,
Latexman

 

[CJKruger]

treddie, I assume you require the heat capacity of the feeds or products (and not some pseudo heat capacity for the heat of reaction).

In this case two methods are commonly used:

Method 1) Get the heat capacity for each component from say API Tech Handbook or those mentioned by Latexman.

They are polynomials in terms of temperature. Calculate the average heat capacity by the mass/molar average of the components.

The effect of pressure is usually ignored in this method.

Method 2) Perform a flash calculation using an equation of state (SRK, PR, etc). This requires only the composition and two other properties (T and P in your case).

But for this you need the software that does these flash calcs.

Cilliers

http://www.korf.co.uk

 

[treddie]

Thanks for your reply, Latexman.

You know, it's curious; the reaction for C12H24 was published as:
C12H24 + O2 --> CO2 + H2O

But for C12H26, the source indicated CO as the end result:
C12H26 + O2 --> CO + H2O,

Empirically, that comes out to:
2C12H26 + 25(O2) --> 24CO +26H2O

As always with the internet, it is so hard to tell whether someone has made a typo or something, and this particular reaction is hard to find info on to check against. I noticed that difference too, early on, but just had to assume it was correct for the time being.

I will check the references you have listed.

Thanks again!

 

[treddie]

CJKruger,

Yes, the specific heat of the feeds, but I would imagine that there would be a different specific heat for a swirling, turbulent and completely mixed combination of the two as if that mix was a new compound in and of itself. Is this assumption correct? So if I understand you correctly, that specific heat would be the average of the component specific heats.

But in the equation Q = c*m*deltaT, is (c) the specific heat at constant pressure (cp) or constant volume(cv)?

 

[Latexman]

I know no reason why changing the fuel from C12H24 to C12H26 would change the products of the oxidation. If you find something out, please let us know.

Good luck,
Latexman

 

[treddie]

Latexman > I would imagine you are correct about it needing to be CO2 instead of CO. I will check further.

 

[CJKruger]

treddie, regarding your questions:

1) Yes, for hand calcs you use the average Cp as a mol/mass average of the components.

2) With Q=C.m.dT you can have C as Cv or Cp, depending on whether you add the duty at constant volume or constant pressure. In engineering almost all processes are at constant pressure.

Cilliers

http://www.korf.co.uk

 

[treddie]

OK, then. I will hit the books, and get back in awhile.

By the way, the API Tech Data Book looks like an indispensable resource. I downloaded it and on my initial run of it, I love the way they turned it into a program and a search-able document. Thanks for the lead!

Also located "The Properties of Gases and Liquids" and have much to read for now.

 

[Latexman]

Also located "The Properties of Gases and Liquids" and have much to read for now.

Check out the appendix. It probably has Cp in polynomial form for the components you are interested in.

Good luck,
Latexman

 

[treddie]

Bummer. This e-copy of "Properties of..." doesn't have the appendices, nor contents or index. Just a collection of papers organized as chapters. I will have to search further to find a complete copy.

 

[25362]

Heat capacities of the relevant gases are usually tabulated according to temperature. Heat capacities are not strongly pressure-dependent and the tabulated values may be used over quite a wide range of pressures.

 

[treddie]

I'm glad about C's lack of sensitivity to pressure then...simplifies things I suppose...one less thing to worry about.

 

[treddie]

Oh...and found the 4th edition with contents, appendices and index. Getting there, slowly but surely.

 

[treddie]

Well, I tried the polynomial approach and came up with confusing results:

For instance, dodecane (C12H26) (molar mass 170.3374g) has a published specific heat capacity of:
.45 BTU/lb-degF (@ 20 degC).
= 1.88 J/g-degC

which, when multiplied by the molar mass of dodecane:
= 320.93 J/K-mol.

...if I did my conversions correctly.

Going with that, and applying the polynomial at the back of the book "Properties of gases and Liquids":
cp = a + bT + cT^2 + dT^3 (with results in J/K-mol)

with the coefficients for dodecane:
a = -9.328
b = 1.149
c = -6.347 x 10^-4
d = 1.359 x 10^-7

I get (with trial and error values for T (deg K):
cp = 320.928 J / K-mol @ T = 350.04 K.

But this is odd because T = 350.04 K (76.89 degC) is not the standard temperature of 20 degC that the published value for cp was referenced to. If I go ahead and input 20 degC (293.15 K), I get
cp = 276.381 J / k-mol

Which is a big difference. Does this mean that the polynomial is only meant to be a gross approximation?

 

[25362]

Take the values from:

http://webbook.nist.gov/cgi/fluid.cgi?ID=C112403&Action=Page

 

[Latexman]

.45 BTU/lb-degF (@ 20 degC) sounds like a liquid organic Cp to me. Is the equation in "Properties of gases and Liquids" for a gas or liquid?


Good luck,
Latexman

 

[25362]

Using NIST data one gets for the liquid at atmospheric pressure:

for 20^oC : 374.03 J mol^-1 K^-1
for 350.04 K: 408.31 J mol^-1 K^-1

 

[treddie]

Latexman > Ahhh, yes darnit, the equation is for a gas. So I need to read the fine print more often (or get my eyes checked!).

I am testing my data against what I know for the F-1 rocket engine. I knew that the fuel was a liquid before it got to the turbopump and was still only 292.6K when it left, but it still had a long way to go (its used as a cooling fluid in the combustion chamber walls), so I was hoping it had gotten past its boiling point of 489.3 K by the time the fuel reached the injector. I do not have data for what that is. But just yesterday evening, I located a technical article on what actually happens to a flame "droplet" in a generic thrust chamber, so right there it SOUNDS like the fuel is still a liquid by the time it enters the injector of the F-1. So whatever its temperature is, it has to be below 489.3K (the combustion chamber temp is 3025K). But of course, we're no longer at STP then, either, so making any comparison to dodecane at STP is useless, regardless of whether it's a gas or a liquid.

25362 > Thanks for the lead to that calculator. Now I wish I knew what the underlying code was!