Specific Heat Ratio - Rocketry

  1. mrjeffy321

    mrjeffy321 882
    Science Advisor

    I know that the Specific Heat Ratio when refering to the gass(es) comming out the back of a rocket engine is the ratio of the specific heats at a constant pressure/volume and then what I am trying to do is use that to help me solve for what the theoretical force I can expect from the rocket using a rather long equation.

    Here is my question,
    I dont know which specific heat ratios to use and for which gasses?
    I have found many tables that list common gasses specific heat rations, the most meaningful being Oxygen gas, Carbon Dioxide, "Air", and Water Vapor/Steam, all of which are involved with a combustion reaction that is taking place inside my solid fueled rocket (propelent is Potassium Chlorate + Sucrose),
    the reaction is a combination os two reactions actually,
    first the chlorate decomposes: 2KClO3 --> KCl + 3O2
    second, the oxygen made during the first reaction is used to combust the sucrose: 12O2 + C12H22O11 + 11H2O

    which is then combined to this reaction:
    8KClO3 + C12H22O11 --> 12CO2(g) + 11H20(g)

    so I know the ratio of gasses to eachother, their molar wieghts, each individuals specific heat ratios, but how do I combine them all to find the overall specific heat ratio of the whole reaction?
    is it just the average so to speak of carbon dioxide and water vapor? would I just find out the ratio of carbon dioxide's weight to water vapor's weight and then use that to determine the average specific heat ratio?
  2. jcsd
  3. Clausius2

    Clausius2 1,479
    Science Advisor
    Gold Member

    If I were you I'd do:

    [tex] \gamma_{average}=\frac{\sum X_i C_{pi}}{\sum X_i C{vi}}[/tex]

    where Xi is the molar fraction of the i-th chemical product.
  4. mrjeffy321

    mrjeffy321 882
    Science Advisor

    So I was correct in thinking that I needed to take the average of the gasses in the product,
    but it is the molar heat ratio, and not the weight ratio?
    are you sure? even though my specific heats are given in kJ/kg*degree kelvin, but then the units would cancel I suppose when you divided them.

    so for the above reaction,
    I would take the average ( i use italics because it really isnt a true average), specific heat ratios of carbon dioxide and water vapor, using the ratios 12/23 for carbon dioxide and 11/23 for oxygen, and we just disreguard the oxygen in the middle that is comming off the chlorate and going right back into another reaction,
    rather than doing the ratio of thier weights
  5. Clausius2

    Clausius2 1,479
    Science Advisor
    Gold Member

    Sorry, I forgot to say that Cp_i and Cv_i are the molar heat capacities. I think you will obtain the same number (or at least a very close number to that) if you calculate it by means of the mass fraction and the mass heat capacities. The fact is such coefficients are calculated assuming an equal energetic state of both the complete mixture and the sum of the components:

    [tex] U=N_{total}C_{Vaverage}T)_{average of the mixture}=\sum U_i[/tex]

    If you start from that point, using a mass weighted average or molar weighted average you will obtain an equivalent number for Cv (molar or mass based).
  6. mrjeffy321

    mrjeffy321 882
    Science Advisor

    OK, thanks, so I will go good to continue with my mass ratioed specific heat ratios, that makes my life slightly easier since I had already worked out the math and I wont have to look for a new table with the substances' molar spcific heat ratios (even though it should be the same in theory, since it is the ratio I want, not the actual specific heats).
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