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Is it possible to directly relate a fuel/oxidizer selection to specific impulse at vacuum? I have tried a few different methods, but cannot seem to directly relate the two.

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The specific impulse will vary with the exact design of the engine (engine cycle, mixture ratio, chamber pressure, nozzle size, and other thermodynamic features), but there's a table on the Wikipedia liquid rocket propellant page giving typical specific impulse (expressed as exhaust velocity in m/s) for various propellant combinations.

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The chemistry side of things is usually like this:

  1. Make a qualified guess for what exhaust products are formed by the reaction.
  2. Calculate the energy freed from that reaction (by the help of delta-h tables).
  3. Use the energy freed to find the chamber conditions (temperature/pressure)
  4. Look up chemical equilibriums for those chamber conditions to make a better guess for 1) (more table values)
  5. Repeat these steps until you have a somewhat clear picture of how the reaction proceeds.
  6. Use simple thermophysics to calculate the exhaust velocity given the exhaust's composition, temperature and pressure.

Actual specific impulse will vary between different engine designs.

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There is only one unknown that you can't easily calculate in this, and that is the composition of the exhaust gasses. If you guess some distribution by high school chemistry, you can get a first order estimate of the temperature change and the molecular weight.

While the influence of pressure on vacuum ISP is low, the chamber pressure shifts the combustion's chemical equilibrium, which can cause larger molecules to form at higher pressures, thus reducing ISP.

Try plugging in some numbers and substances to this handy tool:

https://cearun.grc.nasa.gov/

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As a very general rule, Isp is proportional to the square root of the ratio of chamber temperature to propellant molecular mass, so lighter fuels (like hydrogen) tend to provide higher Isp.

As the other folks have mentioned, Isp is a function of both the combustion and the nozzle design, even at vacuum. If you're interested in propellant's/combustion's contribution to Isp, check out Characteristic Velocity.

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