Kinetic Theory of Temperature and Pressure

Kinetic theory ties two macroscopic readings to particle motion. Temperature is the average translational kinetic energy of a single particle, $K_{\text{avg}} = \tfrac{3}{2}k_BT$, so it says nothing about how many particles there are. Pressure is the perpendicular force per area that those particles deliver by colliding, $P = F_\perp/A$, and it is defined on any surface you care to imagine inside the gas rather than only on the container. Inverting the energy relation gives $v_{\text{rms}} = \sqrt{3k_BT/m}$, which puts speed a square root away from temperature and makes the heavier species in a mixture the slower one.

Four errors dominate. Ranking total thermal energy by temperature, which sends a spark's energy past a bathtub's. Treating pressure as a coating on the container, so a point in the middle of the gas is reported at zero. Scaling speed linearly with temperature instead of with its square root, or matching the speeds of two gases because their temperatures match. And reading $v_{\text{rms}}$ as the speed every particle has, which turns the Maxwell-Boltzmann curve into a single spike and makes heating look like it lifts the entire distribution.