|Although the pressure law is an empirical law, we can make sense of it by relating it to the average KE of particles. |
If we double the speed of particles, then their KE quadruples (KE=1/2mv2)
Therefore, the temperature is 4 times bigger (T µ KE)
However, if we double the speed there will be twice as many collisions every second.
Also, each collision has twice the impulse.
So, with twice as many, doubly hard, collisions the pressure is 4 times bigger as well.
Both the temperature and the pressure are 4 times bigger, i.e. they have gone up in proportion.