Foundations — Combustion thermodynamics — stoichiometry, adiabatic flame temperature

Before you can read the parent note on combustion thermodynamics, you must own every symbol it throws at you. This page builds them one at a time, from nothing, each anchored to a picture. Never skip forward — each block earns the next.

0. The very first picture: reactants → products

Look at the figure: the same beads (2 red hydrogen atoms, 1 blue oxygen atom of each type) are present on both sides. Nothing is created or destroyed — this single fact is the seed of everything below.

1. Counting molecules — the coefficient (the number in front)

When we write $2{\mathrm{H}}_2$, the small 2 in front is a coefficient: it means "two whole copies of this molecule". It is multiplication over the entire molecule.

2. The mole — a "counting bag" for atoms

We can't weigh single atoms, so chemists count them in huge fixed batches called moles.

Why the topic needs it: engineers store propellant by the kilogram, but reactions balance by the molecule. The mole is the bridge — it lets us jump from "how many molecules" to "how many grams".

3. Molar mass $M$ — grams per bag

$M$ turns the mole ratio of a balanced reaction into the mass ratio engineers actually load into tanks. That conversion is the $O/F$ ratio in the parent note. See more in Propellant Selection.

4. Enthalpy $H$ — the "energy content" of a chemical

Here is the trickiest symbol, so we build it very slowly with a picture.

The Greek capital delta $\Delta$ (a triangle) always means "change in": final minus initial. $\Delta H=H_{\text{final}}-H_{\text{initial}}$

This machinery is Hess's Law and Enthalpy of Formation; the energy-accounting rule behind it is the First Law of Thermodynamics.

5. Sigma $\sum$ — "add up over all of them"

Why the topic needs it: reactions can have many products. Instead of writing a long chain of plus signs, $\sum$ packs "loop over every species and total it up" into one symbol. That is exactly what Hess's law does to get $\Delta H_{rxn}$.

6. Heat capacity $c_p$ — how much heat to warm one mole by one degree

Read the figure as a staircase of heat: pour energy in on the left, the temperature climbs on the right, and the slope of that climb is set by $c_p$. Steeper (small $c_p$) = same heat gives a bigger temperature jump.

7. The integral $\int$ — adding heat over a changing $c_p$

Because $c_p$ changes as the gas heats, we can't just multiply once. We must add tiny slices of heat, degree by degree.

Why the topic needs it: the exact governing equation for $T_{ad}$ balances "heat released" against ${\sum }_i{n}_i\int c_{p,i}dT$ — the total heat the products can swallow while heating up. The integral is how we handle a heat sponge whose thirst grows with temperature.

8. Temperature symbols and $\varphi$ — the final labels

How these foundations feed the topic

Every arrow is a symbol you now own. The parent note simply chains them: balance → mass ratio → heat released → temperature reached → performance.

Equipment checklist

Cover the right side and test yourself before reading the parent note.