Foundations — System vs surroundings; open, closed, isolated

Before you can read "$\Delta U=q+w$" and know what it means, you need to know what each squiggle stands for and — more importantly — what picture it draws in your head. This page builds every one of them from nothing. Read it top to bottom; each block uses only symbols defined above it.

The parent note is System vs surroundings; open, closed, isolated. Everything below is the toolkit it silently assumes you own.

0. The very first picture: a line around "stuff"

Everything in thermodynamics starts with one drawn line.

Why the topic needs this: you cannot say "energy went in" until you have defined an in. The line creates the words "inside" and "outside." No line, no bookkeeping.

1. Matter and energy: the two things that can cross

The parent talks about matter crossing and energy crossing. Let's earn both words.

Why we separate them: the three system types (open / closed / isolated) are defined entirely by which of these two — matter, energy — is allowed across. Keeping them separate is the whole game.

2. Heat ($q$) and work ($w$): the two disguises of energy

Energy never crosses as "energy." It always crosses as heat or as work.

Why two symbols, not one? Because later laws treat them differently — work depends on how you push (the path), heat makes up the difference. We keep $q$ and $w$ apart so we can add them cleanly. That addition is the First Law.

3. The Greek letter delta: $\Delta$ means "change in"

The parent writes $\Delta U$, $\Delta V$, $\Delta T$, $\Delta m$, $\Delta S$. All of these use one symbol.

Why the topic needs $\Delta$: thermodynamics almost never cares about the value of energy, only how much it changed. $\Delta$ is the tool that says "I only want the difference."

4. Internal energy, symbol $U$

Why the topic needs $U$: it is the quantity being accounted for. Heat $q$ and work $w$ are the deposits and withdrawals; $U$ is the account.

5. The First Law glued together: $\Delta U=q+w$

Now every symbol in the headline equation is defined, so we can read it.

This is the payoff: the line, matter/energy, $q$, $w$, $\Delta$, $U$ — all six ideas combine into one bookkeeping equation. Deeper study is First Law of Thermodynamics.

6. Boundary properties: the six adjectives

The parent lists six adjectives for boundaries. They come in three independent pairs. Independent means you can mix and match freely.

Why three pairs, not one: because matter, heat, and work are three separate things that cross. Each needs its own gatekeeper. This is exactly why the parent warns "rigid ≠ impermeable."

7. Reading the three system types as switch-settings

Now the three types are just choices of the switches.

That last line — $\Delta U=0$ for an isolated system — falls straight out of the First Law once heat and work are both zero. Everything on the parent page is now readable.

8. Two symbols you'll meet immediately after: $C_V$ and $P_{\text{ext}}\Delta V$

The worked examples use these, so let's define them here.

9. Entropy ($S$) — just a name for now

The parent mentions $\Delta S_{\text{isolated}}\ge 0$. You don't need to master entropy here — only recognise the symbol.

Prerequisite map

Equipment checklist

Cover the right side and see if you can answer each before revealing.