Question: what is the relationship between kinetic energy and pressure?
Answer: Pressure, a macroscopic property, can be related to the average (translational) kinetic energy per molecule which is a microscopic property by P=nm¯¯¯¯¯v23 P = nm v 2 ¯ 3 . Since the assumption is that the particles move in random directions, the average value of velocity squared along each direction must be same.