Employing rigorous transport theory, determine the following transport properties for gaseous argon:
(a) its dynamic viscosity at 300 K;
(b) its thermal conductivity at 300 K;
(c) its self-diffusion coefficient at 300 K and 1 atm.

Question

Accepted Answer

(a) From Appendix O, ε/k = 124 K and σ = 3.42 Å for argon. Hence, from Eq. (16.48), the reduced temperature is

[latex]T^{\ast} =\frac{kT}{\varepsilon} = \frac{300}{124} = 2.42[/latex].

Consequently, from Appendix P, the normalized collision integral is [latex]Ω^{(2,2)∗}[/latex] = 1.104. On this basis, from Eq. (16.50), the dynamic viscosity becomes

[latex]\eta=2.6696 imes 10^{-6} \frac{\sqrt{M T}}{\sigma^{2} \Omega^{(2,2) *}}[/latex] N · s/m², (16.50)

[latex]=2.6696 imes 10^{-6} \frac{\sqrt{(39.948)(300)}}{(3.42)^{2}(1.104)}[/latex]

= 2.263 × [latex]10^{−5}[/latex] N · s/m.

(b) For any atomic species, the specific heat ratio is γ = 5/3. Moreover, the gravimetric specific heat at constant volume for argon is

[latex] ilde{c}_{v}=\frac{3}{2}\left(\frac{R}{M} ight)=\frac{3}{2}\left(\frac{8.3145 kJ / kmol \cdot K }{39.948 kg / kmol } ight)[/latex] = 0.3122 kJ/kg · K.

Hence, from Eq. (16.51), the thermal conductivity for argon at 300 K is

λ = 250(9γ − 5)[latex] ilde{c}_{v}\eta [/latex] W/m · K , (16.51)

= 2500(0.3122)(2.263 × [latex]10^{−5}[/latex]) = 1.766 × [latex]10^{−2}[/latex] W/m · K.

(c) From the reduced temperature of part (a) and Appendix P, the normalized collision integral [latex]\Omega^{(1,1) *}[/latex] = 1.010. Therefore, from Eq.(16.52), the self-diffusion coefficient for argon at 300 K and P = 1 atm becomes

[latex]D=2.6295 imes 10^{-7} \frac{T^{3 / 2}}{\sqrt{M} P \sigma^{2} \Omega^{(1,1) *}}[/latex] m²/s, (16.52)

[latex]=2.6295 imes 10^{-7} \frac{(300)^{3 / 2}}{\sqrt{39.948}(3.42)^{2}(1.010)}[/latex]

= 1.830 × [latex]10^{−5}[/latex] m²/s.

While the dynamic viscosity evaluated when using the L–J potential is only 33% higher than that obtained in Example 16.3 when using the rigid-sphere model, the thermal conductivity is a whopping 232% greater and the self-diffusion coefficient is 76% greater than the associated rigid-sphere calculations.

Question 16.4: Employing rigorous transport theory, determine the following...

Related Answered Questions

Employing basic transport theory, determine the following transport properties for gaseous argon: (a) its dynamic viscosity at 300 K, (b) its thermal conductivity at 300 K, and (c) its self-diffusion coefficient at 300 K and 1 atm. ...

Verified Answer:

A vessel contains gaseous argon at 300 K and 1 atm. (a) Calculate the collision rate (collisions/s) for a typical argon atom within the vessel. (b) Determine the mean free path for argon in this vessel. ...

Verified Answer:

vessel containing gaseous argon is maintained at 300 K and 1 atm. Presuming a hard-sphere diameter of 3.42 Å, calculate the volumetric collision rate between argon atoms within the vessel. Discuss the implications of your result. ...

Verified Answer: