This problem is (16.23) from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell" 16.23. A gas is in equilibrium with a solid surface onto which its molecules can adsorb.The surface exposes M adsorption sites, each of which can be either free oroccupied by a single gas molecule. Adsorbed molecules do not interact with eachother, but there is a favorable energetic decrease of amount -e each time a site isoccupied.(a) Find the canonical partition function for N molecules adsorbed on M sites at atemperature T.(b) Find an expression for the chemical potential of an adsorbed molecule, lads.(c) At equilibrium at constant T, show that the dependence of the fractionof occupied sites, x =isotherm,N/M, is given by the so-called Langmuir adsorptioncP1+ cPwhere c is a constant. How does c vary with temperature?

Adsorption is different than the absorption. Adsorption occur in many system such as biological,…

16.23. A gas is in equilibrium with a solid surface onto which its molecules can adsorb. The surface exposes M adsorption sites, each of which can be either free or occupied by a single gas molecule. Adsorbed molecules do not interact with each other, but there is a favorable energetic decrease of amount -e each time a site is осcupied. (a) Find the canonical partition function for N molecules adsorbed on M sites at a temperature T. (b) Find an expression for the chemical potential of an adsorbed molecule, µads- (c) At equilibrium at constant T, show that the dependence of the fraction of occupied sites, x = N/M, is given by the so-called Langmuir adsorption %3D isotherm, cP X = 1+ cP where c is a constant. How does c vary with temperature?

16.23. A gas is in equilibrium with a solid surface onto which its molecules can adsorb. The surface exposes M adsorption sites, each of which can be either free or occupied by a single gas molecule. Adsorbed molecules do not interact with each other, but there is a favorable energetic decrease of amount -e each time a site is осcupied. (a) Find the canonical partition function for N molecules adsorbed on M sites at a temperature T. (b) Find an expression for the chemical potential of an adsorbed molecule, µads- (c) At equilibrium at constant T, show that the dependence of the fraction of occupied sites, x = N/M, is given by the so-called Langmuir adsorption %3D isotherm, cP X = 1+ cP where c is a constant. How does c vary with temperature?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter6: Forced Convection Over Exterior Surfaces

Section: Chapter Questions

Problem 6.52P

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