Kinetic theory of temperature and pressure

At the microscopic level, a gas consists of atoms in constant, random motion. These atoms collide with each other and with the container walls, and each collision involves forces governed by Newton's laws and the conservation of momentum.

Pressure

• The macroscopic quantity we call pressure arises from the enormous number of these collisions.
• It equals the total perpendicular force exerted on a surface divided by that surface's area.
• Pressure is not confined to the walls — it exists throughout the volume of the gas, because atoms bombard any surface, real or imaginary, from all sides.

P = $F_{\mathrm{perp}}$/A

Temperature

Key Definition Temperature is a measure of the average translational kinetic energy of the gas atoms.

Temperature therefore has a direct microscopic interpretation. The following relationship links the temperature on the kelvin scale to the energy of atomic motion:

Kₐvg = 3/2k_BT

At the same temperature, lighter atoms move faster than heavier atoms, because both must have the same average translational kinetic energy.

Maxwell–Boltzmann distribution

• The Maxwell–Boltzmann distribution captures the full picture — not all atoms move at one speed; rather, their speeds are spread over a range.
• Higher temperatures broaden this distribution and shift its peak toward higher speeds, which directly explains why hotter gases exert more pressure on their containers.