Kinetic Theory & Ideal Gases

the universal gas constant

The fixed number R in P V = n R T that makes the units balance. It is the same for every ideal gas, which is why it is called universal: hydrogen, helium, air, and carbon dioxide all share the very same R.

Precisely, R = 8.314 J/(mol·K). It is the proportionality constant relating PV to nT, and it equals Avogadro's number times the Boltzmann constant, R = N_A k_B. In other units it is 0.08206 L·atm/(mol·K), handy when volumes are in litres and pressures in atmospheres.

It turns up everywhere in thermal physics: RT is the energy scale for one mole of gas, and the equipartition theorem and molar heat capacities (such as C_V = (3/2)R for a monatomic gas) are all written in terms of R.

At standard conditions, working out the volume per mole (about 22.4 litres) from P V = n R T relies on R = 8.314 J/(mol·K).

The proportionality constant R shared by every ideal gas.

R and the Boltzmann constant k_B express the same physical fact, differing only in whether you count per mole (R) or per molecule (k_B).

Also called
molar gas constantR通用氣體常數