path: root/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter14.ipynb

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  {
   "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": {}
  }
 ]
}