amount of substance in moles; Avogadro constant N_A equals 6.02 × 10²³ mol^–1

model of kinetic theory of gases

Assumptions for the model:
- large number of molecules in random, rapid motion
- particles (atoms or molecules) occupy negligible volume compared to the volume of gas
- all collisions are perfectly elastic and the time of the collisions is negligible compared to the time between collisions
- negligible forces between particles except during collision

pressure in terms of this model

(i) the equation of state of an ideal gas \(pV = nRT\), where n is the number of moles

(ii) techniques and procedures used to investigate \(PV = \text{constant} \) (Boyle’s law)
and \(\dfrac{P}{T} = \text{constant} \)

PAG8

(iii) an estimation of absolute zero using variation of gas temperature with pressure

PAG8

the equation \(pV = \dfrac{1}{3} Nm\bar{c}^2 \),

where N is the number of particles (atoms or molecules) and \(\bar{c}^2\) is the mean square speed

Derivation of this equation is not required.

root mean square (r.m.s.) speed; mean square speed

Learners should know about the general characteristics of the Maxwell-Boltzmann distribution.

the Boltzmann constant; \(k = \dfrac{R}{N_A} \)

\(pV = NkT \);
\(\dfrac{1}{2}m\bar{c}^2= \dfrac{3}{2}kT \)

Learners will also be expected to know the derivation of the equation \(\dfrac{1}{2}m\bar{c}^2= \dfrac{3}{2}kT \) from \(pV = \dfrac{1}{3} Nm\bar{c}^2 \) and \(pV = NkT \)

internal energy of an ideal gas.