Temperature and particle speed

1. The temperature of a gas is a measure of the average kinetic energy of its particles.
2. Heating a gas increases that average kinetic energy, and since the mass of each particle cannot change, the average speed of the particles increases.
3. The particles never all move at the same speed, so temperature describes the average of a wide spread of speeds.
4. Raising the temperature shifts that whole spread of speeds upwards, so a larger share of the particles are moving quickly.
5. Cooling a gas reduces the average kinetic energy, so the average speed of the particles falls.
6. The direction of each particle stays random at every temperature, so warming a gas makes the motion faster rather than more organised.

Heating a gas at constant volume

1. A fixed mass of gas in a sealed rigid container has the same number of particles and the same volume throughout, so nothing but the temperature is changing.
2. Raising the temperature increases the average speed of the particles.
3. Faster particles cross the container in less time, so they reach the walls more often and the number of collisions each second increases.
4. Faster particles also rebound more forcefully, so each individual collision exerts a larger force on the wall.
5. Both effects push in the same direction, so the total force on the walls increases.
6. The area of the walls has not changed, so a greater total force on the same area means a greater pressure.
7. The pressure keeps climbing for as long as the temperature keeps rising, and the container can eventually fail if the pressure grows too large.

Cooling a gas at constant volume

1. Lowering the temperature of the same sealed container reduces the average speed of the particles.
2. Slower particles take longer to cross the container, so they collide with the walls less often.
3. Each collision also exerts a smaller force, because the particles arrive at the wall more slowly.
4. The total force on the walls therefore falls, and with the area unchanged the pressure falls too.
5. The relationship works both ways, so a measurement of pressure in a sealed rigid container can be used to tell you the temperature of the gas inside it.

Everyday situations

1. An aerosol can carries a warning against heating it, because the metal cannot expand, so heating the gas raises the pressure until the can bursts.
2. A pressure cooker traps steam in a fixed volume, so heating raises the pressure inside and the water boils at a temperature above $100{}^{\circ }C$.
3. Car tyres read a higher pressure at the end of a long motorway journey, because friction and flexing have warmed the air inside them.
4. The same tyres read a lower pressure on a cold winter morning, which is why they should be checked when they are cold.
5. A sealed glass jar taken straight from a hot dishwasher becomes hard to open once it cools, because the pressure of the trapped air inside has dropped below atmospheric pressure.