Consider Argon (Ar) gas at a pressure of 1 bar and temperature of 300 K. The equivalent hard sphere radius (known as the Van Der Waal radius) of an Argon molecule is 188 picometers (pm) and its atomic mass is 39.948u. Note that 1u = 1.6605 x 10-27kg. a)How many molecules are contained in a cube 1 cm by 1 cm by 1 cm? b)Estimate the mean free path. At scales much larger than this, a continuum description holds. c)What is the density of the gas? d)Estimate the "root mean squared" molecular speed, i.e. SQRT( (V^2) )

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Chapter5: Gases
Section: Chapter Questions
Problem 46E
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Consider Argon (Ar) gas at a pressure of 1 bar and temperature of 300 K. The equivalent hard
sphere radius (known as the Van Der Waal radius) of an Argon molecule is 188 picometers (pm)
and its atomic mass is 39.948u. Note that 1u = 1.6605 x 10-27kg.

a)How many molecules are contained in a cube 1 cm by 1 cm by 1 cm?

b)Estimate the mean free path. At scales much larger than this, a continuum description holds.

c)What is the density of the gas?

d)Estimate the "root mean squared" molecular speed, i.e. SQRT( (V^2) )

e)Estimate the dynamic and kinematic viscosities. Compare these with literature values, for
example from webbook.nist.edu.

f) Plot the variation of dynamic viscosity with temperature in the range between 300K and
3000K at a fixed pressure of 1 bar. Use Matlab, Python, Mathematica, or any other software
you may choose.

 

Question 1:
Consider Argon (Ar) gas at a pressure of 1 bar and temperature of 300 K. The equivalent hard
sphere radius (known as the Van Der Waal radius) of an Argon molecule is 188 picometers (pm)
and its atomic mass is 39.948u. Note that lu = 1.6605 × 10-27kg.
1. How many molecules are contained in a cube 1 cm by 1 cm by 1 cm?
2. Estimate the mean free path. At scales much larger than this, a continuum description holds.
3. What is the density of the gas?
4. Estimate the "root mean squared" molecular speed, i.e., V(V*).
5. Estimate the dynamic and kinematic viscosities. Compare these with literature values, for
example from webbook.nist.edu.
6. Plot the variation of dynamic viscosity with temperature in the range between 300K and
3000K at a fixed pressure of 1 bar. Use Matlab, Python, Mathematica or any other software
you may choose.
Transcribed Image Text:Question 1: Consider Argon (Ar) gas at a pressure of 1 bar and temperature of 300 K. The equivalent hard sphere radius (known as the Van Der Waal radius) of an Argon molecule is 188 picometers (pm) and its atomic mass is 39.948u. Note that lu = 1.6605 × 10-27kg. 1. How many molecules are contained in a cube 1 cm by 1 cm by 1 cm? 2. Estimate the mean free path. At scales much larger than this, a continuum description holds. 3. What is the density of the gas? 4. Estimate the "root mean squared" molecular speed, i.e., V(V*). 5. Estimate the dynamic and kinematic viscosities. Compare these with literature values, for example from webbook.nist.edu. 6. Plot the variation of dynamic viscosity with temperature in the range between 300K and 3000K at a fixed pressure of 1 bar. Use Matlab, Python, Mathematica or any other software you may choose.
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