# Difference in collision cross-section obtained by measurement method

I have a simple question of Physical Chemistry, but I don't know the answer.

We can find collision cross-section(σ) through experiments in three ways. first, diffusion flux experiment. diffusion coefficient D = (1/3)x(vλ) = (1/3)x(8RT/πM)x(RT/PNσ). So, σ can be found by measuring the diffusion flux.

Second, Thermal conduction experiment. κ = (1/3)x(C/N)x(8RT/πM)x(RT/PNσ). So, σ can be found by measuring the thermal conductivity.

Third, viscosity experiment. μ = (1/3)x(m)x(8RT/πM)x(RT/PNσ). So, σ can be found by measuring the viscosity.

This is the question. I do not know why the sigma obtained through each experiment is different. The sigma obtained by measuring the diffusion flux is different from the sigma obtained by measuring the viscosity. The same is true of thermal conductivity. Why is this happening?

• For eventual writing and formatting of chemical/mathematical formulas or equations, see MathJax usage guide It is not mandatory, but highly recommended and it gives huge advantage for writers and readers. Dec 15 '20 at 20:03
• Before starting to think about this question, why do you write RT/PN and not V = Volume of one molecule ? And can you simply give us your calculated value for sigma with these three approaches ? Are they different by a factory greater than 1000 ? Dec 15 '20 at 20:05
• In which sense they differ? Because each methods can have errors and especially under or overestimate a quantity. This can be dramatic if any approximation is required to theoretically attain the formulae you've list (which I think is the case, by feeling). Dec 17 '20 at 13:09