Thermo_ISM_ch17

Thermo_ISM_ch17 - Chapter 17: Transport Phenomena Problem...

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17-1 Chapter 17: Transport Phenomena Problem numbers in italics indicate that the solution is included in the Student’s Solutions Manual. Questions on Concepts Q17.1) What is the general relationship between the spatial gradient in a system property and the flux of that property? The spatial gradient of a property is a continuous difference in a physical property such as pressure, temperature, or molecular distribution. The flux of the property is a change that occurs due to the spatial gradient, defined as the amount of a given property that passes through a specific area per unit time. Q17.2) What is the expression for the diffusion coefficient, D , in terms of gas kinetic theory parameters? How is D expected to vary with an increase in molecular mass or collisional cross section? The diffusion coefficient, D , is defined as 1 3 ave Dv λ = where v ave is the average speed and λ is the mean free path of a gas particle, both as defined by the kinetic gas theory. The v ave term is inversely proportional to the square root of the molar mass, therefore the diffusion coefficient will decrease as the molar mass increases. The mean free path is inversely proportional to the collisional cross section; therefore, the diffusion coefficient will decrease as the collisional cross section increases. Q17.3) Particles are confined to a plane and then allowed to diffuse. How does the number density vary with distance away from the initial plane? The number density of particles that diffuse from a fixed plane is given by the solution to Fick's Second Law of Diffusion, () 2 0 1/2 exp 4 2 N x N Dt AD t π = ± where N 0 is the number of particles initially confined to the plane, D is the diffusion coefficient, A is the area of the initial plane, and t is the time. The number density in the x-direction will decrease in accord with the exponential dependence on the square of distance away from the plane (so-called Gaussian dependence). Q17.4) How does the root-mean-square diffusion distance vary with the diffusion coefficient? How does this quantity vary with time?
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Chapter 17/Transport Phenomena 17-2 The root mean square diffusion distances depend on the square root of the both the time and the diffusion coefficient. Q17.5) What is the expression for thermal conductivity in terms of particle parameters derived from gas kinetic theory? The thermal conductivity, κ , is defined as , 1 3 vm ave A C vN N κ λ = ± where C v,m is the molar volume independent heat capacity, and v ave and λ are the average speed and the mean free path, respectively. Q17.6) Why is the thermal conductivity for an ideal gas expected to be independent of pressure? Why does the thermal conductivity for an ideal gas increase as T 1/2 ? With reference to the equation provided in Question Q17.5 above, we see that the thermal conductivity depends on the product of the number density and the mean free path. For an ideal gas, the mean free path is dependent on the inverse of the pressure, while the number density is directly dependent on the pressure. As
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This note was uploaded on 06/10/2010 for the course CHEM 127 taught by Professor Nefzi during the Spring '03 term at UCSD.

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Thermo_ISM_ch17 - Chapter 17: Transport Phenomena Problem...

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