Question

Predict the viscosities of molecular oxygen, nitrogen, and methane at 20°C and atmospheric pressure, and express the results in mPa·s. Compare the results with experimental data given in Chapter 1.

Answer 1

Given: Temperature, T=20⁰C=293.15 K

The viscosity of monoatomic gas can be expressed in terms of Lennard Jones parameters as,

where is the viscosity (in g/cm s)

M is the Molecular weight

T is the Temperature (in K)

is Lennard-Jones Parameter (in Angstrom)

is a slowly varying function of dimensionless temperature

For Oxygen:

Molecular weight, M=32.

Refer the Lennard-Jones Potential Parameters and Critical Properties Table.

Lennard Jones Parameters, =3.433 and

At 20⁰C

Refer Collision Integrals for Use with the Lennard-Jones Potential for the Prediction of Transport Properties of Gases at Low Densities Table.

For kT/=2.59 or 2.60, the corresponding value of is

Substituting these values in the above equation, we get

(For experimental viscosity value refer Viscosities of Some Gases and Liquids at Atmospheric Pressure table)

The calculated viscosity is 2.03*10^-2 mPa s and experimental viscosity value is 2.04*10^-2 mPa s

For Nitrogen:

Molecular weight, M=28.01

Refer the Lennard-Jones Potential Parameters and Critical Properties Table.

Lennard Jones Parameters, =3.667 and

At 20⁰C,

Refer Collision Integrals for Use with the Lennard-Jones Potential for the Prediction of Transport Properties of Gases at Low Densities Table.

For kT/=2.9, =1.0482 and for kT/=3.0, =1.0388. Interpolate the values.

For kT/=2.94,  

Substituting these values in the above equation, we get

The calculated viscosity is 1.723*10^-2 mPa s and experimental viscosity value is 1.75*10^-2 mPa s.

For Methane:

Molecular weight, M=16.04

Refer the Lennard-Jones Potential Parameters and Critical Properties Table.

Lennard Jones Parameters, =3.780 and

At 20⁰C,

Refer Collision Integrals for Use with the Lennard-Jones Potential for the Prediction of Transport Properties of Gases at Low Densities Table.

For kT/=1.9, =1.198 and for kT/=1.95, =1.186. Interpolate the values.

For kT/=1.904,

Substituting these values in the above equation, we get

The calculated viscosity is 1.07*10^-2 mPa s and experimental viscosity value is 1.09*10^-2 mPa s.