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?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

A) Estimate the lifetime of a 40µm diameter carbon particle assuming diffusionally-controlled combustion at the conditions given below : 1) Carbon density =1900 kg/m^3 2) Gas phase density = 0.2 kg/m^3 3) Mass diffusivity (D) = 1.57*10^-4 m^2/s 4) YO2, ∞ = 0.233 5) YCO2, s = 0 B) Consider a 0.8 mm diameter nozzle hole with ΔP=34.3 MPa. The diesel fuel sprays into compressed air at 25 kg/m^3 density and 6.2 MPa pressure. Prior to compression, the air was at 1 atm and 25deg C. Calculate the total cone angle (θ) of the spray
a) The number of kilocalories in food is determined by calorimetry techniques in which the food is burned and the amount of heat transfer is measured. How many kilocalories per gram are there in a 5.00-g peanut if the energy from burning it is transferred to 0.500 kg of water held in a 0.100-kg aluminum cup, causing a 54.9C temperature increase? (b) Compare your answer to labeling information found on a package of peanuts and comment on whether the values are consistent.
1. The pipe size of a pneumatic conveyer to convey plastic pellets with bulk density of 30 lb/ft2 using a blower with a capacity of 600 ft2 is approximately inches. A. 2 B. 6 C. 4 D. 8 2. A solution of 28% Na2SO4 is to be crystallized to yield Glauber salt (amount of crystalline crop (C) produced in lb/hr A. 285.3 B. 214.65 C. 249.3 D. 255.65
4. (Kittel 7.14) Two orbital boson system. Consider a system of N bosons of spin zero, with orbitals at the single particle energies 0 and e. The chemical potential is u and the temperature is 7. Find 7 such that the thermal average population of the lowest orbital is twice the population of the orbital at E. Assume N>>1 and make what approximations are reasonable.
5. a. Determine the diffusion coefficient for zinc diffusing into copper at 200°C. b. Create a plot showing diffusion coefficient vs. temperature for zinc diffusing into copper over the range of 0°C to 600°C. Include a minimum of six data points (you may use Excel for the repetitive calculations). What does the shape of the curve tell you about the dependence of diffusion rate on temperature? c. Determine the diffusion coefficient for nickel diffusing into copper at 200°C. Explain why the value differs from that found in Part a.
5. The sketch shows a cylindrical hollow fiber with membrane walls. Species 'A' is undergoing steady-state diffusion through the membrane wall where its concentrations at the inner and outer membrane walls are CAI, and CA2, respectively. It can be assumed that the membrane wall eliminates any bulk diffusion effects and that the diffusion flux follows Fick's Law with a membrane diffusion coefficient, DAM- (a) Solve for the concentration profile of 'A' in the membrane wall in terms of the dimensions of the fiber and concentrations at R₁ and R₂. (b) Solve for the molar flux of 'A' leaving the outer wall of the membrane. XA2 XB2 FIBER WALL *****
S-curve model of diffusion: (true/false) and reasoning a. k = 0, the rate of diffusion is instantaneous? b. fixed k ≥ 0, the carrying capacity is determined only by the ratio of a and b? c. fixed k ≥ 0, the rate of diffusion is determined only by the ratio of a and b?
COMBUSTION ENGINEERING PROBLEM: 20.6 kmols Oxygen 794 kmol nitrogen If gasoline fuel is approximated by the formula CaH18 , in an atmosphere of : Calculate the following: (c) Determine the theoretical Air/Fuel Ratio by Volume (m²air/m³ fuel) with both reactants having the same Temperatures. (d) Solve for the Air/fuel Ratio by mass, in kg air
12. Cylindrical metallic parabolic solar thermal concentrator A. Does not rotate. B. It rotates around one axis only. C. It rotates around two axes only. D. The concentration ratio achieved is: 500-1000. E. The concentration ratio achieved is: 50-100. F. The concentration ratio achieved is: 10-50. * A + D only. B +E only. B + F only. O C + E only
17.30 The following table gives weight gain-time + data for the oxidation of nickel at an elevated temperature. W (mg/cm?) Time (min) 0.527 10 0.857 30 1.526 100 (a) Determine whether the oxidation kinetics obey a linear, parabolic, or logarithmic rate expression. (b) Now compute W after a time of 600 min.
If you are Good at heat transfer then Please Solve This Problem. Otherwise Skip. [rating will be Given after verification ]
Show that; Pd: %3D th Imt 2m