EASA/GCAA Part-66 · Module 2 — Physics · Thermodynamics

Gas Laws — PV = nRT

Objective: the pressure, volume, temperature and amount of an ideal gas are tied together by PV = nRT. Move the piston and heat the gas, and watch the molecules speed up and hit the walls harder. Pick a process to hold one quantity fixed.

Piston & cylinder — kinetic theory

P–V diagram

Volume V 25 L

Temperature T 300 K

Amount n 1.0 mol

Pressure P

0kPa

Volume V

Temperature T

Amount n

0mol

PV = nRT · R = 8.314 J·mol⁻¹·K⁻¹

Temperature is a measure of the average kinetic energy of the molecules — heat the gas and they move faster (speed ∝ √T). Pressure comes from those molecules hitting the walls: more molecules, higher speed, or a smaller volume all raise the collision rate and so the pressure. The three classic gas laws are just PV = nRT with one quantity held constant: Boyle (T fixed → P ∝ 1/V), Charles (P fixed → V ∝ T) and Gay-Lussac (V fixed → P ∝ T).

Try this: Pick Isothermal and squeeze the volume — pressure rises as 1/V (Boyle's law).
Try this: Pick Isobaric and heat the gas — the piston rises so V ∝ T (Charles's law).
Try this: Pick Isochoric and heat the gas — pressure climbs as P ∝ T (Gay-Lussac).
Try this: Add more gas (n) — more molecules, more wall hits, higher pressure.