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tree9806b0d68a708d2cfc4efc8ae3751423c56b7721 /Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter17.ipynb
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-{
- "metadata": {
- "name": "",
- "signature": "sha256:28b1b127871a242526fc780b7f95bfe7e107178dbbf2ff194eb0ee46817a771a"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 17: Transport Phenomena"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.1, Page Number 417"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from scipy import constants\n",
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "M = 0.040 #Molecualar wt of Argon, kh/mol\n",
- "P, T = 101325.0, 298.0 #Pressure and Temperature, Pa, K\n",
- "sigm = 3.6e-19 #\n",
- "R = 8.314 #Molar Gas constant, mol^-1 K^-1\n",
- "N_A = 6.02214129e+23 #mol^-1\n",
- "#Calculations\n",
- "DAr = (1./3)*sqrt(8*R*T/(pi*M))*(R*T/(P*N_A*sqrt(2)*sigm))\n",
- "\n",
- "#Results\n",
- "print 'Diffusion coefficient of Argon %3.1e m2/s'%DAr"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Diffusion coefficient of Argon 1.1e-05 m2/s\n"
- ]
- }
- ],
- "prompt_number": 17
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.2, Page Number 418"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from scipy import constants\n",
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "DHebyAr = 4.0 \n",
- "MAr, MHe = 39.9, 4.0 #Molecualar wt of Argon and Neon, kg/mol\n",
- "P, T = 101325.0, 298.0 #Pressure and Temperature, Pa, K\n",
- "sigm = 3.6e-19 #\n",
- "R = 8.314 #Molar Gas constant, mol^-1 K^-1\n",
- "N_A = 6.02214129e+23 #mol^-1\n",
- "#Calculations\n",
- "sigHebyAr = (1./DHebyAr)*sqrt(MAr/MHe)\n",
- "\n",
- "#Results\n",
- "print 'Ratio of collision cross sections of Helium to Argon %4.3f'%sigHebyAr"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Ratio of collision cross sections of Helium to Argon 0.790\n"
- ]
- }
- ],
- "prompt_number": 20
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.3, Page Number 420"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "D = 1.0e-5 #Diffusion coefficient, m2/s \n",
- "t1 = 1000 #Time, s\n",
- "t10 = 10000 #Time, s\n",
- "\n",
- "#Calculations\n",
- "xrms1 = sqrt(2*D*t1)\n",
- "xrms10 = sqrt(2*D*t10)\n",
- "\n",
- "#Results\n",
- "print 'rms displacement at %4d and %4d is %4.3f and %4.3f m respectively'%(t1,t10,xrms1,xrms10)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "rms displacement at 1000 and 10000 is 0.141 and 0.447 m respectively\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.4, Page Number 421"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "D = 2.2e-5 #Diffusion coefficient of benzene, cm2/s \n",
- "x0 = 0.3 #molecular diameter of benzene, nm\n",
- "\n",
- "#Calculations\n",
- "t = (x0*1e-9)**2/(2*D*1e-4)\n",
- "\n",
- "#Results\n",
- "print 'Time per random walk is %4.3e s or %4.2f ps'%(t,t/1e-12)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Time per random walk is 2.045e-11 s or 20.45 ps\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.5, Page Number 424"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "P = 101325 #Pressure, Pa\n",
- "kt = 0.0177 #Thermal conductivity, J/(K.m.s)\n",
- "T = 300.0 #Temperature, K\n",
- "k = 1.3806488e-23 #Boltzmanconstant,J K^-1\n",
- "sigm = 3.6e-19 #\n",
- "R = 8.314 #Molar Gas constant, mol^-1 K^-1\n",
- "NA = 6.02214129e+23 #mol^-1\n",
- "M = 39.9 #Molecualar wt of Argon and Neon, kg/mol\n",
- "#Calculations\n",
- "CvmbyNA = 3.*k/2\n",
- "nuavg = sqrt(8*R*T/(pi*M*1e-3))\n",
- "N = NA*P/(R*T)\n",
- "labda = 3*kt/(CvmbyNA*nuavg*N)\n",
- "sigm = 1/(sqrt(2)*N*labda)\n",
- "\n",
- "#Results\n",
- "print 'Mean free path %4.3e m and collisional cross section %4.2e m2'%(labda, sigm)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Mean free path 2.627e-07 m and collisional cross section 1.10e-19 m2\n"
- ]
- }
- ],
- "prompt_number": 34
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.6, Page Number 427"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "eta = 227. #Viscosity of Ar, muP\n",
- "P = 101325 #Pressure, Pa\n",
- "kt = 0.0177 #Thermal conductivity, J/(K.m.s)\n",
- "T = 300.0 #Temperature, K\n",
- "k = 1.3806488e-23 #Boltzmanconstant,J K^-1\n",
- "R = 8.314 #Molar Gas constant, mol^-1 K^-1\n",
- "NA = 6.02214129e+23 #mol^-1\n",
- "M = 39.9 #Molecualar wt of Argon and Neon, kg/mol\n",
- "\n",
- "#Calculations\n",
- "nuavg = sqrt(8*R*T/(pi*M*1e-3))\n",
- "N = NA*P/(R*T)\n",
- "m = M*1e-3/NA\n",
- "labda = 3.*eta*1e-7/(nuavg*N*m) #viscosity in kg m s units\n",
- "sigm = 1./(sqrt(2)*N*labda)\n",
- "\n",
- "#Results\n",
- "print 'Collisional cross section %4.2e m2'%(sigm)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Collisional cross section 2.74e-19 m2\n"
- ]
- }
- ],
- "prompt_number": 48
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.7, Page Number 429"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "m = 22.7 #Mass of CO2, kg\n",
- "T = 293.0 #Temperature, K\n",
- "L = 1.0 #length of the tube, m\n",
- "d = 0.75 #Diameter of the tube, mm\n",
- "eta = 146 #Viscosity of CO2, muP\n",
- "p1 = 1.05 #Inlet pressure, atm\n",
- "p2 = 1.00 #Outlet pressure, atm\n",
- "atm2pa = 101325 #Conversion for pressure from atm to Pa \n",
- "M = 0.044 #Molecular wt of CO2, kg/mol\n",
- "R = 8.314 #Molar Gas constant, J mol^-1 K^-1\n",
- "\n",
- "#Calculations\n",
- "p1 = p1*atm2pa\n",
- "p2 = p2*atm2pa\n",
- "F = pi*(d*1e-3/2)**4*(p1**2-p2**2)/(16.*eta/1.e7*L*p2)\n",
- "nCO2 = m/M\n",
- "v = nCO2*R*T/((p1+p2)/2)\n",
- "t = v/F\n",
- "\n",
- "#Results\n",
- "print 'Flow rate is %4.3e m3/s'%(F)\n",
- "print 'Cylinder can be used for %4.3e s nearly %3.1f days'%(t, t/(24*3600))"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Flow rate is 2.762e-06 m3/s\n",
- "Cylinder can be used for 4.381e+06 s nearly 50.7 days\n"
- ]
- }
- ],
- "prompt_number": 80
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.8, Page Number 431"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "eta = 0.891 #Viscosity of hemoglobin in water, cP\n",
- "T = 298.0 #Temperature, K\n",
- "k = 1.3806488e-23 #Boltzmanconstant,J K^-1\n",
- "R = 8.314 #Molar Gas constant, mol^-1 K^-1\n",
- "D = 6.9e-11 #Diffusion coefficient, m2/s \n",
- "\n",
- "#Calculations\n",
- "r = k*T/(6*pi*eta*1e-3*D)\n",
- "\n",
- "#Results\n",
- "print 'Radius of protein is %4.3f nm'%(r/1e-9)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Radius of protein is 3.550 nm\n"
- ]
- }
- ],
- "prompt_number": 54
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.9, Page Number 432"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "s = 1.91e-13 #Sedimentation constant, s\n",
- "NA = 6.02214129e+23 #mol^-1\n",
- "M = 14100.0 #Molecualr wt of lysozyme, g/mol\n",
- "rho = 0.998 #Density of water, kg/m3\n",
- "eta = 1.002 #Viscosity lysozyme in water, cP\n",
- "T = 293.15 #Temperature, K\n",
- "vbar = 0.703 #Specific volume of cm3/g\n",
- "\n",
- "#Calculations\n",
- "m = M/NA\n",
- "f = m*(1.-vbar*rho)/s\n",
- "r = f/(6*pi*eta)\n",
- "\n",
- "#Results\n",
- "print 'Radius of Lysozyme particle is %4.3f nm'%(r/1e-9)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Radius of Lysozyme particle is 1.937 nm\n"
- ]
- }
- ],
- "prompt_number": 56
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.10, Page Number 433"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from numpy import arange,array,ones,linalg,log, exp\n",
- "from pylab import plot,show\n",
- "\n",
- "\n",
- "#Variable Declaration\n",
- "t = array([0.0,30.0,60.0,90.0,120.0,150.0]) #Time, min\n",
- "xb = array([6.00,6.07,6.14,6.21,6.28,6.35]) #Location of boundary layer, cm\n",
- "rpm = 55000. #RPM of centrifuge \n",
- "\n",
- "#Calculations\n",
- "nx = xb/xb[0]\n",
- "lnx = log(nx)\n",
- "A = array([ t, ones(size(t))])\n",
- "# linearly generated sequence\n",
- "[slope, intercept] = linalg.lstsq(A.T,lnx)[0] # obtaining the parameters\n",
- "# Use w[0] and w[1] for your calculations and give good structure to this ipython notebook\n",
- "# plotting the line\n",
- "line = slope*t+intercept # regression line\n",
- "#Results\n",
- "plot(t,line,'-',t,lnx,'o')\n",
- "xlabel('Time, min')\n",
- "ylabel('log(xb/xb0)')\n",
- "show()\n",
- "sbar = (slope/60)/(rpm*2*pi/60)**2\n",
- "print 'Slope is %6.2e 1/min or %4.3e 1/s '%(slope, slope/60)\n",
- "print 'Sedimentation factor is %4.3e s'%(sbar)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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- "text": [
- "<matplotlib.figure.Figure at 0x850c3d0>"
- ]
- },
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Slope is 3.78e-04 1/min or 6.299e-06 1/s \n",
- "Sedimentation factor is 1.899e-13 s\n"
- ]
- }
- ],
- "prompt_number": 67
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example Problem 17.11, Page Number 439"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import sqrt,pi\n",
- "\n",
- "#Variable Declaration\n",
- "LMg = 0.0106 #Ionic conductance for Mg, S.m2/mol\n",
- "LCl = 0.0076 #Ionic conductance for Cl, S.m2/mol\n",
- "nMg, nCl = 1, 2 #Coefficients of Mg and Cl \n",
- "\n",
- "\n",
- "#Calculations\n",
- "LMgCl2 = nMg*LMg + nCl*LCl\n",
- "\n",
- "#Results\n",
- "print 'Molar conductivity of MgCl2 on infinite dilution is %5.4f S.m2/mol'%(LMgCl2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Molar conductivity of MgCl2 on infinite dilution is 0.0258 S.m2/mol\n"
- ]
- }
- ],
- "prompt_number": 59
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file