EXTENSIVE (scales with amount)
INTENSIVE (doesn't)
TEA
CHAPATI
POOL/TUB
IRON
ROOM
THE RULE
Pour two cups together
Two identical cups of tea, both at 80 °C. Tap to pour them together and watch both readouts.
POUR TOGETHER
POUR APART AGAIN
Two separate cups, same temperature, each with its own share of energy.
Cut a chapati in half
Same chapati, same oven. Tap to cut it.
CUT IN HALF
PUT IT BACK
Mass halves the instant you cut it. Temperature has no idea a cut happened.
A swimming pool and a bathtub
Both at exactly the same temperature. Nothing else about them is close.
🏊
POOL · 400,000 L
30 °C
≈ 50.2 GJ stored
🛁
BATHTUB · 150 L
30 °C
≈ 18.8 MJ stored
Identical intensive reading. A 2,667× gap in the extensive one. The thermometer genuinely cannot tell you which one you're in.
Density survives cutting
Halve the block. Watch which number refuses to move.
CUT IN HALF
PUT IT BACK
Mass and volume are both about how much iron you have. Density is about what iron is — it doesn't care how much of it you're holding.
Pressure in a room
Tap to draw a line down the middle of a sealed room.
1.00 bar
30 m³
1.00 bar
15 m³
DRAW A LINE DOWN THE MIDDLE
REMOVE THE LINE
One room, one pressure reading, one total volume.
The sorting rule
Tap each one. Watch which column it lands in.
Mass
Volume
Energy
Temperature
Pressure
Density
If it depends on how much you have — extensive. If it doesn't — intensive. That's the entire rule.
Puzzle · Two Tanks Merge
Predict both numbers
Two water tanks, valve between them opens. They mix completely. One of your two predictions below is a trick.
Drag to predict: final temperature
0 °C100 °C
Drag to predict: total energy content (relative to 0 °C)
0 kJ6,500 kJ
OPEN THE VALVE →