PHYSICAL CHEMISTRY IN BRIEF

CHAP. 10: TRANSPORT PROCESSES [CONTENTS] 345

10.5.4 Transport quantities for the hard spheres model

For viscosity at low pressures we may derive the following relation from the hard spheres model

η=

5

16 NAσ^2

√

MRT

π

, (10.21)

whereσis the collision diameter of the molecule andMis its molar mass. The formula clearly
shows that the viscosity of a diluted gas increases linearly with the second root of temperature,
and that it does not depend on pressure.
For thermal conductivity we may derive the following relation from the hard spheres model

λ=

5

2

η

M

CVm, (10.22)

whereCVmis the molar isochoric heat capacity. The viscosityηis given by relation (10.21).
From this relation it follows that the thermal conductivity of a dilute gas does not depend on
pressure but only on temperature, throughηandCVm.
For the diffusion coefficient of a binary mixture we have

D 12 =

3 RT

16 σ 122 NAp

√

2 RT(M 1 +M 2 )

π M 1 M 2

, (10.23)

whereσ 12 =

σ 1 +σ 2

2

.

For the self-diffusion coefficient we have

D=

3 RT

8 σ^2 NAp

√

RT

π M

. (10.24)

It follows from relations (10.23) and (10.24) that the diffusion and self-diffusion coefficients
of a gas at low densities increase with temperature and decrease with increasing pressure; the
diffusion coefficient does not depend on composition.

Note: The hard spheres model is a good approximation for the description of viscosity

and diffusion of gases. In the case of thermal conductivity, however, it provides results

which are correct only within orders of magnitude.