what are pressure and temperature
The gas in a tank looks still, but in fact countless molecules are flying without a pause. Put more molecules in the tank and they strike the wall more often and the drumming on the wall grows stronger, and what we call pressure is exactly the force of all those collisions pushing the wall. Heat the molecules and the same molecules fly faster, and the average of that speed is the temperature. Both pressure and temperature summarize the motion of molecules we cannot see as one number of the large-scale world. With this view it is plain why heating raises the pressure and why two bodies grow lukewarm when they touch.
Start with where pressure comes from. The molecules in the tank strike the wall without stopping, and one collision is a tiny tap, but when an enormous number gather in one second they become a steady force pushing the wall. Raise the number of molecules with the slider and more molecules mean more frequent hits on the wall and the pressure bar fills, so pressure is the sum of the collisions a unit area of wall receives. A balloon is taut and a tire is firm because molecules inside keep drumming on the wall. The air around us drums on every wall like this and presses with a force near 10 tonnes on each 1 square meter, yet we do not feel that weight because the push is the same from inside and outside.
Now the temperature. Heat the tank and each molecule flies faster, and raising the temperature with the slider makes the molecules bounce farther and harder and the color grows hot. Temperature is the average of the motion these molecules have, and more precisely it says how much kinetic energy one molecule has on average. So hot means the molecules move fast and cold means they move slowly. One caution is that temperature is not the speed of one molecule but the average of a great many, so whether there are many molecules or few the temperature is the same if only the average is the same. The molecules are not all equally fast, and they spread from fast to slow, and the fastest ones at the surface flying off is evaporation, so a puddle dries a little even far from the boiling point.
Now put a hot body against a cold one. Let time pass with the slider and the fast molecules on the hot side strike the molecules on the cold side at the boundary and share their motion, the hot side cools and the cold side warms. When the two temperatures become equal, heat no longer flows one way, and this state is called thermal equilibrium. What matters is that they stop at the same temperature, and equal temperature means the averages of molecular motion have become equal so there is nothing left to exchange. We can compare the temperatures of two bodies because of this equilibrium. Things left long in one room have already reached it, so a metal handle and a wooden door are in fact the same temperature, and the metal feels colder only because it carries heat away from the hand faster.
Lower the temperature step by step and the motion of the molecules slows step by step. On the graph of how the tank pressure changes with temperature, lowering the temperature weakens and rarefies the collisions and the pressure falls in a straight line. Extend that line and it reaches a point where the pressure is 0, about 273 degrees below zero Celsius, the floor where molecular motion can shrink no further and nothing can be colder. Scientists made a new scale with this point as 0, absolute temperature in kelvin, and adding 273 to Celsius gives kelvin. Every formula of thermodynamics uses kelvin rather than Celsius because the true amount of molecular motion has to be counted from the floor. The floor can be approached but not quite touched, and even the coldest laboratory has gone only to 1 degree above absolute zero by a part in 10 to the ninth, and even that is far colder than empty space.
Finally there is one simple and deep agreement. Measure a cup of water with one thermometer and get some temperature, and measure an iron bar with the same thermometer and get the same temperature again, and you can press the button to put the thermometer against each in turn. If both match the thermometer, the water and the iron bar are the same temperature even without touching each other. It looks too obvious, but that obviousness is the foundation on which the idea of temperature stands, and it is called the 0th law of thermodynamics. If A is in equilibrium with C and B is in equilibrium with C, then A and B are in equilibrium too, and because of this law one reference called a thermometer can line up and compare the temperature of everything. This law is called the 0th law because it is more foundational than the 1st law and the 2nd law, yet it was set down only after those two already had names, so it had to be inserted in the place numbered 1 in front.