15.2 Equation of state

At fixed amount and volume, an ideal gas obeys p∝T, so p/T is constant when T is measured in kelvin.

Use absolute temperature and keep volume and amount fixed. A pressure change can be compared through p₁/T₁=p₂/T₂.

Heating a sealed rigid container from 300 K to 450 K raises ideal-gas pressure by a factor of 1.5.

The proportionality fails if volume or amount changes, and Celsius temperature cannot be used in the ratio.

For an ideal gas, pressure p, volume V, amount n and thermodynamic temperature T satisfy pV=nRT.

Use pascals, cubic metres, moles and kelvin with R=8.31 J mol⁻¹ K⁻¹. Check whether the gas is dilute enough for the ideal model.

One mole at 300 K in 0.0249 m³ has pressure about 1.00×10⁵ Pa.

pV=nRT is not a universal exact law for real gases under all conditions.

Boltzmann constant k=R/N_A, so kT is the thermal energy scale per particle while RT is the corresponding molar scale.

Use k when counting individual particles and R when working with moles; the two forms describe the same thermal physics at different scales.

The average translational energy scale of one molecule uses kT, whereas one mole uses RT.

k and R are not interchangeable numbers; their units and particle-count basis differ.