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Diffstat (limited to 'Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter14.ipynb')
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diff --git a/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter14.ipynb b/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter14.ipynb new file mode 100755 index 00000000..daf732e9 --- /dev/null +++ b/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter14.ipynb @@ -0,0 +1,513 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:1671a89ef38b6b7afbc72d0d6b374367e1ac4b1abd5ab2d480c98bd2b6a92ca8"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14: Ensemble and Molecular Partition Function"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.1, Page Number 332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "l = 0.01 #Box length, m \n",
+ "n1,n2 = 2,1 #Energy levels states\n",
+ "m = 5.31e-26 #mass of oxygen molecule, kg\n",
+ "\n",
+ "#Calculations \n",
+ "dE = (n1+n2)*h**2/(8*m*l**2)\n",
+ "dEcm = dE/(h*c*1e2)\n",
+ "#Results\n",
+ "print 'Difference in energy levels is %3.2e J or %3.2e 1/cm'%(dE,dEcm)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Difference in energy levels is 3.10e-38 J or 1.56e-15\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.2, Page Number 333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import pi, sqrt\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "v = 1.0 #Volume, L\n",
+ "T = 298.0 #Temeprature of Ar, K\n",
+ "m = 6.63e-26 #Mass of Argon molecule, kg \n",
+ "\n",
+ "#Calculations \n",
+ "GAMA = h/sqrt(2*pi*m*k*T)\n",
+ "v = v*1e-3\n",
+ "qT3D = v/GAMA**3\n",
+ "\n",
+ "#Results\n",
+ "print 'Thermal wave length is %3.2e m and\\nTranslational partition function is %3.2e'%(GAMA,qT3D)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thermal wave length is 1.60e-11 m and\n",
+ "Translational partition function is 2.44e+29\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.4, Page Number 338"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import pi, sqrt\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "J = 4 #Rotational energy level\n",
+ "B = 8.46 #Spectrum, 1/cm\n",
+ "\n",
+ "#Calculations \n",
+ "T = (2*J+1)**2*h*c*100*B/(2*k)\n",
+ "#Results\n",
+ "print 'Spectrum will be observed at %4.0f K'%(T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Spectrum will be observed at 494 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.5, Page Number 340"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import exp\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "B = 60.589 #Spectrum for H2, 1/cm\n",
+ "T = 1000 #Temperture of Hydrogen, K\n",
+ "#Calculations \n",
+ "qR = k*T/(2*h*c*100*B)\n",
+ "qRs = 0.0\n",
+ "#for J in range(101):\n",
+ "# print J\n",
+ "# if (J%2 == 0):\n",
+ "# qRs = qRs + (2*J+1)*exp(-h*c*100*B*J*(J+1)/(k*T)\n",
+ "# else:\n",
+ "# qRs = qRs + 3*(2*J+1)*exp(-h*c*100*B*J*(J+1)/(k*T))\n",
+ "#print qRs/4\n",
+ "\n",
+ "#Results\n",
+ "print 'Rotation partition function of H2 at %4.0f is %4.3f'%(T,qR)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Rotation partition function of H2 at 1000 is 5.729\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.6, Page Number 341"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "B = 0.0374 #Spectrum for H2, 1/cm\n",
+ "T = 100.0 #Temperture of Hydrogen, K\n",
+ "sigma = 2.\n",
+ "#Calculations\n",
+ "ThetaR = h*c*100*B/k\n",
+ "qR = T/(sigma*ThetaR)\n",
+ "\n",
+ "#Results\n",
+ "print 'Rotation partition function of H2 at %4.0f K is %4.3f'%(T,qR)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Rotation partition function of H2 at 100 K is 928.121\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.7, Page Number 342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import pi, sqrt\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "Ba = 1.48 #Spectrum for OCS, 1/cm\n",
+ "Bb = [2.84,0.191,0.179] #Spectrum for ONCI, 1/cm\n",
+ "Bc = [9.40,1.29,1.13] #Spectrum for CH2O, 1/cm\n",
+ "T = 298.0 #Temperture of Hydrogen, K\n",
+ "sigmab = 1\n",
+ "sigmac = 2\n",
+ "\n",
+ "#Calculations\n",
+ "qRa = k*T/(h*c*100*Ba)\n",
+ "qRb = (sqrt(pi)/sigmab)*(k*T/(h*c*100))**(3./2)*sqrt(1/Bb[0])*sqrt(1/Bb[1])*sqrt(1/Bb[2])\n",
+ "qRc = (sqrt(pi)/sigmac)*(k*T/(h*c*100))**(3./2)*sqrt(1/Bc[0])*sqrt(1/Bc[1])*sqrt(1/Bc[2])\n",
+ "\n",
+ "#Results\n",
+ "print 'Rotation partition function for OCS, ONCI, CH2O at %4.0f K are %4.0f, %4.0f, and %4.0f respectively'%(T,qRa,qRb,qRc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Rotation partition function for OCS, ONCI, CH2O at 298 K are 140, 16926, and 712 respectively\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.8, Page Number 344"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import pi, exp\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "Ba = 1.48 #Frequency for OCS, 1/cm\n",
+ "Bb = [2.84,0.191,0.179] #Frequency for ONCI, 1/cm\n",
+ "Bc = [9.40,1.29,1.13] #Frequency for CH2O, 1/cm\n",
+ "T298 = 298.0 #Temperture of Hydrogen, K\n",
+ "T1000 = 1000 #Temperture of Hydrogen, K\n",
+ "nubar = 208\n",
+ "\n",
+ "#Calculations\n",
+ "qv298 = 1./(1.-exp(-h*c*100*nubar/(k*T298)))\n",
+ "qv1000 = 1./(1.-exp(-h*c*100*nubar/(k*T1000)))\n",
+ "\n",
+ "#Results\n",
+ "print 'Vibrational partition function for I2 at %4d and %4d are %4.2f K and %4.2f respectively'%(T298, T1000,qv298, qv1000)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Vibrational partition function for I2 at 298 and 1000 are 1.58 K and 3.86 respectively\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.9, Page Number 346"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import exp\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "T = 298 #Temeprature, K\n",
+ "nubar = [450, 945, 1100] #Vibrational mode frequencies for OClO, 1/cm\n",
+ "\n",
+ "#Calculations\n",
+ "Qv = 1.\n",
+ "for i in nubar:\n",
+ " qv = 1./(1.-exp(-h*c*100*i/(k*T)))\n",
+ " print 'At %4.0f 1/cm the q = %4.3f'%(i,qv)\n",
+ " Qv = Qv*qv\n",
+ "#Results\n",
+ "print 'Total Vibrational partition function for OClO at %4.1f K is %4.3f'%(T, Qv)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "At 450 1/cm the q = 1.128\n",
+ "At 945 1/cm the q = 1.010\n",
+ "At 1100 1/cm the q = 1.005\n",
+ "Total Vibrational partition function for OClO at 298.0 K is 1.146 respectively\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.10, Page Number 348"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import exp\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "T = 298 #Temeprature, K\n",
+ "nubar = 917 #Vibrational mode frequencies for F2, 1/cm\n",
+ "\n",
+ "#Calculations\n",
+ "ThetaV = h*c*100*nubar/k\n",
+ "Th = 10*ThetaV\n",
+ "qv = 1/(1.-exp(-ThetaV/Th))\n",
+ "\n",
+ "#Results\n",
+ "print 'Vibrational partition function for F2 at %4.1f K is %4.3f'%(T, qv)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Vibrational partition function for F2 at 298.0 K is 10.508\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.11, Page Number 348"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import exp\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "T = 1000 #Temeprature, K\n",
+ "nubar = [1388, 667.4,667.4,2349] #Vibrational mode frequencies for CO2, 1/cm\n",
+ "\n",
+ "#Calculations\n",
+ "Qv = 1.\n",
+ "for i in nubar:\n",
+ " qv = 1./(1.-exp(-h*c*100*i/(k*T)))\n",
+ " print 'At %4.0f 1/cm the q = %4.3f'%(i,qv)\n",
+ " Qv = Qv*qv\n",
+ "#Results\n",
+ "print 'Total Vibrational partition function for OClO at %4.1f K is %4.3f'%(T, Qv)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "At 1388 1/cm the q = 1.157\n",
+ "At 667 1/cm the q = 1.619\n",
+ "At 667 1/cm the q = 1.619\n",
+ "At 2349 1/cm the q = 1.035\n",
+ "Total Vibrational partition function for OClO at 1000.0 K is 3.139\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 14.12, Page Number 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import exp\n",
+ "\n",
+ "#Variable Declarations\n",
+ "h = 6.626e-34 #Planks constant, J.s\n",
+ "k = 1.38e-23 #Boltzman constant, J/K\n",
+ "c = 3.0e8 #speed of light, m/s\n",
+ "\n",
+ "T = 298. #Temeprature, K\n",
+ "n = [0,1,2,3,4,5,6,7,8] #Energy levels\n",
+ "E0 = [0,137.38,323.46,552.96,2112.28,2153.21,2220.11,2311.36,2424.78] #Energies, 1/cm\n",
+ "g0 = [4,6,8,10,2,4,6,8,10]\n",
+ "\n",
+ "#Calculations\n",
+ "qE = 0.0\n",
+ "for i in range(9):\n",
+ " a =g0[i]*exp(-h*c*100*E0[i]/(k*T))\n",
+ " qE = qE + a\n",
+ "\n",
+ "#Results\n",
+ "print 'Electronic partition function for F2 at %4.1f K is %4.2f'%(T, qE)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Electronic partition function for F2 at 298.0 K is 9.45\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |