Revision summary

Name the particles, use absolute pressure and temperature, and distinguish an individual collision from a time or particle average.

Temperature, amount and counting

The thermodynamic scale is independent of the property of a particular substance. Use T/K = θ/°C + 273.15. Temperature differences have equal numerical size in K and °C; ratios in gas and particle-energy equations require kelvin.

N counts the specified particles. For 0.500 mol of O₂, it is 3.01 × 10²³ molecules, not the twice-as-large atom count. Relative atomic and molecular masses are dimensionless comparisons with one twelfth of a carbon-12 atom's mass; molar mass M has unit kg/mol.

Gas states and controlled changes

Use Pa, m³ and K. Add ambient pressure to gauge pressure. Recall 1 atm = 101325 Pa, 1 litre = 10^-3 m³ and 1 cm³ = 10^-6 m³. The actual atmosphere may differ from the standard unit.

• Fixed N and T: p ∝ 1/V; a reciprocal pressure-volume curve.
• Fixed N and V: p ∝ T; a straight pressure-kelvin line.
• Fixed N and p: V ∝ T; a straight volume-kelvin line.

The 0.500 mol, 12.0 litre, 300 K model gives p ≈ 1.04 × 10⁵ Pa and N/V ≈ 2.51 × 10²⁵ m^-3. Keep it separate from the generated graph sample whose 300 K pressure is 100.000 kPa.

For a fixed-volume investigation, control leaks and total gas volume, wait for a common settled gas temperature, and use absolute pressure. A graph's gradient has meaning only with the correct axes and units. A pressure-temperature area is not energy transferred, and extrapolation is not evidence that a real gas remains ideal.

Rebuild the pressure derivation

The model assumes many Newtonian particles in random isotropic motion, negligible particle volume, negligible forces between collisions, and brief elastic collisions. For N particles of the same mass m, use a positive incoming normal speed c_x:

The round-trip interval is not collision duration. Mean-square isotropy is an ensemble statement, not equal components for every particle. Zero mean velocity does not imply zero mean-square speed or zero pressure. Revisit the wall impulse and averaging steps if the factor of one third is unclear.

Connect temperature to an average energy

Equal T gives equal mean translational energy per particle. Four times the particle mass gives half the rms speed at that T. Doubling T gives twice the mean energy and √2 times the rms speed for the same gas. Mean speed, rms speed and mean velocity are different averages.

Quantities and units

The same letter can denote different quantities in different models: c here is microscopic speed, whereas c can mean specific heat capacity in thermal calculations. Use the definition and units to identify the quantity.