Pressure and Temperature Measure Molecular Motion
The gas in a box looks still, but countless molecules are flying around without rest. Pack more molecules into the box. They hit the walls more often, and the drumming on the walls grows stronger. What we call pressure is exactly this push of countless collisions on the walls. Now make the molecules hotter, and the same molecules fly faster. The average of that speed is what temperature is. Both pressure and temperature are a single number from the macroscopic world that sums up the motion of each invisible molecule. Once you hold this view, you can see at a glance why heating raises pressure and why two bodies that touch settle to something lukewarm.
Start with where pressure comes from. The molecules in the box keep slamming into the walls. One collision is a tiny tap, but trillions of them per second add up to a steady push on the wall. Use the slider to add more molecules. The more there are, the more often they hit the walls, and the pressure bar fills up. Pressure is, in the end, the sum of collisions a unit area of wall receives. A balloon is taut and a tire is firm for the same reason: inside, molecules drum on the walls without rest. The air around us drums on every surface this same way, pressing with nearly 10 tons on each square meter, yet we never feel that weight because it pushes equally from inside and out.
Now for temperature. Heat the box and each molecule flies faster. Use the slider to raise the temperature. The molecules bounce farther and harder, and the color turns hot. Temperature is the average of the motion these molecules carry. More precisely, it reflects how much kinetic energy a single molecule has on average. So hot means the molecules move fast, and cold means they move slowly. One thing to watch: temperature is not the speed of one molecule but the average over countless molecules. That is why, whether there are many molecules or few, the same average means the same temperature. In truth the molecules do not all move at one speed but spread over a wide range from fast to slow, and it is the fastest ones at the surface escaping that we call evaporation, which is why a puddle slowly dries even far below boiling.
Now bring a hot body and a cold body into contact. As you let time pass with the slider, the fast molecules on the hot side collide with the cold side's molecules at the boundary and share their motion. The hot side cools and the cold side warms. When their temperatures become equal, heat no longer flows one way. This state is thermal equilibrium. The key is that the two stop at the same temperature. Equal temperature means the average of molecular motion has become equal, so there is nothing left to exchange. It is exactly this equilibrium that lets us compare the temperatures of two bodies at all. So everything left in one room has already reached this equilibrium, meaning a metal doorknob and the wooden door are really at one temperature; the metal only feels colder because it carries heat away from your hand faster.
As you lower the temperature, the molecules' motion slows down too. On the graph, watch how the box's pressure changes with temperature. The colder it gets, the weaker and rarer the collisions, and the pressure falls in a straight line. Extend that line and you reach a point where the pressure would be zero, at about minus 273 degrees Celsius. It is the limit where molecular motion can shrink no further, a floor below which nothing can be colder. So scientists built a new scale that takes this very point as zero: the absolute temperature, the kelvin. Add 273 to a Celsius reading and you get kelvin. This is why every formula in thermodynamics uses kelvin, not Celsius: the true amount of molecular motion has to be counted up from the floor. This floor can be approached but never fully touched: even the coldest labs have come only within a billionth of a degree of absolute zero, and even that is far colder than empty outer space.
Finally, a simple but deep promise. Suppose a thermometer reads a cup of water and gives some temperature, and the same thermometer reads an iron bar and gives the same temperature. Use the buttons to touch the thermometer to each in turn. If both are at the same temperature as the thermometer, then the water and the iron bar are at the same temperature as each other, even without touching them together. It looks obvious, but this obviousness is the very foundation on which the concept of temperature stands. This is the zeroth law of thermodynamics: if A is in equilibrium with C and B is also in equilibrium with C, then A and B are in equilibrium too. Thanks to this law, a single reference, a thermometer, lets us line up and compare the temperature of everything in the world. The odd name, the zeroth law, comes from this: it is even more basic than the first and second laws, yet it was pinned down only after those had already been named, so it had to be slipped in ahead of number one.