Explanation Given: The diameter of tube is D = 10 μm . The temperature of gases is T = 23 o C . Formula used: The expression for transition density is given as, ρ c = 100 k B M 2 π d 2 R D Here, k B is the Boltzmann constant, d is the molecular diameter, ρ c is the density, R is the ideal gas constant, and M is the molecular mass. Calculation: The expression for mean free path is given as, λ m f p = k B T 2 π d 2 p ...... ( 1 ) The expression for pressure from ideal gas equation is given as, p = ρ R T M ...... ( 2 ) The effect of micro scale comes to action when, λ m f p D ≈ 0.01...... ( 3 ) On combining the above three equation, transition density can be obtained. λ m f p D = 0.01 0.01 = k B M 2 π d 2 ρ c R D ρ c = 100 k B M 2 π d 2 R D Refer table A.4 “Thermo physical properties of gases at atmospheric pressure”. Molecular density of air ρ = 1.161 kg / m 3 . Molecular density of hydrogen ρ = 0.0808 kg / m 3 . Molecular density of air ρ = 1.773 kg / m 3 . Refer figure 2.8 for the molecular weight of substances. Molecular mass of air is M = 28.97 kmol / kg . Molecular mass of hydrogen is M = 2.016 kmol / kg . Molecular weight of carbon dioxide is M = 44.01 kmol / kg . Refer Figure 2.8 “The temperature dependence of the thermal conductivity of selected gases at normal pressures” The molecular diameter forair is d = 0.327 nm . The molecular diameter for hydrogen is d = 0.274 nm . The molecular diameter for carbon dioxide is d = 0.464 nm . The transition density of air can be calculated as, ρ c , a i r = 100 k B M 2 π d 2 R D = 100 ( 1.381 × 10 − 23 J / K ) ( 28.97 kmol / kg ) 2 π ( 0.327 nm ( 1 m 10 9 nm ) ) 2 ( 8315 J / kmol ⋅ K ) ( [ 10 μm ( 1 m 10 6 μm ) ] ) = 1.0127 kg / m 3 The transition density of hydrogen can be calculated as, ρ c , a i r = 100 k B M 2 π d 2 R D = 100 ( 1.381 × 10 − 23 J / K ) ( 2

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ISBN: 9780470501979

Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

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Chapter 8, Problem 8.108P

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The transition density for hydrogen

The transition density for air.

The transition density carbon dioxide.

The comparison of calculated transition density to the gas density at T=23oC .

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Chapter 8, Problem 8.107P

Chapter 8, Problem 8.109P

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The transition density for hydrogen The transition density for air. The transition density carbon dioxide. The comparison of calculated transition density to the gas density at T = 23 o C .

Solution Summary: The author compares the transition density for hydrogen and carbon dioxide to the gas density at T=23oC.

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The transition density for hydrogen

The transition density for air.

The transition density carbon dioxide.

The comparison of calculated transition density to the gas density at T=23oC .

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Chapter 8 Solutions

The transition density for hydrogen The transition density for air. The transition density carbon dioxide. The comparison of calculated transition density to the gas density at T = 23 o C .

Solution Summary: The author compares the transition density for hydrogen and carbon dioxide to the gas density at T=23oC.

Concept explainers

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The transition density for hydrogen The transition density for air. The transition density carbon dioxide. The comparison of calculated transition density to the gas density at T=23oC .

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Chapter 8 Solutions

The transition density for hydrogen

The transition density for air.

The transition density carbon dioxide.

The comparison of calculated transition density to the gas density at T=23oC .