Physics 4 — Thermo & Fluids

The ideal gas law

ELI5: P·V = n·R·T ties a gas's pressure, volume, amount, and temperature into a single rule — squeeze one and the others must respond. (One trap: temperature must be in kelvin, measured from absolute zero, never °C.) A scuba tank, 12 L at 230 atmospheres, holds how many moles?

R_{gas} = 8.314

gas constant (J/mol·K)

P_{tank} = 230 \cdot 101325

2.3305 \times 10^{7}

pressure (Pa)

V_{tank} = 0.012

volume (m³)

T_{tank} = 293

room temperature (K) — gas laws need KELVIN

n_{mol} = \frac{P_{tank} \cdot V_{tank}}{R_{gas} \cdot T_{tank}}

114.8016

about 115 mol — over 3 kg of air

Real-world hook: PV = nRT inflates car tyres (warmer = higher pressure), lifts hot-air balloons, and is why a spray can gets cold as it empties.