You open an energy lesson and run into ΔT, Δm and ΔᵣH°. It looks as if someone fell on the keyboard. Not so: they’re three simple ideas, and secondary-school maths is more than enough to follow them.

Δ Delta: what changed

Say it
“delta” or “change in”. ΔT is read “change in temperature”.
It means
Δ in front of something is how much it changed: the final value minus the starting value.

Δ is the capital D of the Greek alphabet, the D of “difference”. If water goes from 18 °C to 25 °C, ΔT = 25 − 18 = 7 °C. If it cools from 25 °C to 18 °C, ΔT = 18 − 25 = −7 °C. The sign tells you which way the change went: positive if it rose, negative if it fell.

Real example · in the lesson Joules, watts or calories? Energy and power without fear

ΔT = Q / (m · c): how much the temperature rises for the heat Q you put in.

Real example · in the lesson Can you make something from nothing? Conservation, no fear

Δm = E / c²: the mass that disappears when an energy E is released.

Eₐ Subscripts: the label underneath

Say it
Eₐ is read “E sub a” or, better, by its name: “activation energy”.
It means
The small letter or number at the bottom right is a label: it says what that quantity is. It doesn't multiply or raise anything.

Science has lots of energies, lots of masses and lots of temperatures. To keep them apart, they get a label underneath: Eₐ is the activation energy, mₑ the mass of the electron, T₁ and T₂ are two different temperatures. When the label doesn’t fit as a small letter, it’s written with an underscore: N_A is Avogadro’s number, the N with the label A.

Chemistry has one special case: in a formula like H₂O, the small number counts atoms. There are two hydrogens and one oxygen.

Real example · in the lesson What is a wall made of? Atoms and elements without fear

N_A = 6.022 140 76×10²³ mol⁻¹: Avogadro’s number, with its label A.

H° The ° for standard, which isn't degrees

Say it
ΔfH° is read “standard enthalpy of formation”.
It means
A little circle stuck to the top right of a quantity means “measured under standard conditions”, which have a reference pressure of 1 bar.

In chemistry, what a reaction gives depends on the pressure and on how concentrated everything is. To compare reactions fairly, values are given under reference conditions, the standard ones, and marked with °. IUPAC sets the standard pressure at 1 bar. Temperature isn’t part of the definition, but tables are usually given at 25 °C (298.15 K).

Real example · in the lesson Why doesn't diamond turn into graphite?

ΔᵣH° = Σν ΔfH°(products) − Σν ΔfH°(reactants): the heat of a reaction, under standard conditions.

Try it

Move both temperatures. Watch what happens to the sign of Δ when the final one ends up below the starting one.

Δ of the temperatureA temperature line from −10 to 40 °C with two marks, start and end, and an arrow between them that measures Δ. At the start, from 18 °C to 25 °C: Δ = +7 °C.−10010203040Δ = +7
18 °C
25 °C

ΔT = 25 − 18 = +7 °C. It went up: Δ is positive.

Challenge

Water goes from 80 °C to 20 °C. What is ΔT?
In a list of numbers, what is x₂?
In ΔᵣH°, what does the little circle ° mean?

Sources

  • Δ as a finite increment, subscripts and general notation: ISO 80000-2:2019, Quantities and units — Part 2: Mathematics (iso.org).
  • Standard conditions (1 bar pressure), ΔᵣH and chemistry notation: IUPAC, Quantities, Units and Symbols in Physical Chemistry (“Green Book”), 3rd ed., 2007 (iupac.org).

How this cheat sheet was made: written with Claude’s help from the sources above and translated from the Spanish original. The examples are copied from the site’s lessons. The drawings are original.