Video narration
If cup A matches cup B, and cup B matches cup C, can you trust that A matches C-even without comparing them directly? Imagine three cups of water. A and B are in thermal equilibrium: at balance, no net heat flows between them. Then B reaches that balance with C. The surprising step: A must also be in thermal equilibrium with C. That is the zeroth law of thermodynamics. This relationship carries through, making temperature a consistent property. It is why a thermometer works. The thermometer becomes the middle system, reaching thermal equilibrium with cup A so its temperature can be compared consistently with C. It does not read instantly; it must reach that balance. So yes: if A matches B and B matches C, A matches C. That is why temperatures in all three cups-and readings from one shared thermometer-can be compared reliably.