Pressure is the result of countless molecules striking the walls. Kinetic theory links the large-scale quantities to the microscopic motion: pV = ⅓Nm⟨c²⟩, and the mean translational kinetic energy of a molecule is ₃⁄₂ kT. Raise the temperature and watch the molecules speed up.
MissionPredict what happens to a molecule's mean translational kinetic energy when T is doubled.Streak 0Best 0
Doubling the thermodynamic temperature changes a molecule's mean translational KE to:
temperature T300 K
mean translational KE = ₃⁄₂ kT6.2 × 10⁻²¹ J
r.m.s. speed of a nitrogen molecule517 m s⁻¹
k = 1.38 × 10⁻²³ J K⁻¹. KE ∝ T, while c_rms = √(3kT/m) ∝ √T. More molecules or higher speeds mean more wall collisions and higher pressure.