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 "metadata": {
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  "signature": "sha256:a083e6230471b2aae4b74f2789d7281e7ea34670be129562c78e3830995cc56a"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# valid over 298-500\n",
      "\n",
      "Hf_liq = -285.830   # kJ/mol\n",
      "S_liq = 0.06995     # kJ/mol/K\n",
      "shomateL = [-203.6060,\n",
      "            1523.290,\n",
      "           -3196.413,\n",
      "            2474.455,\n",
      "               3.855326,\n",
      "            -256.5478,\n",
      "            -488.7163,\n",
      "            -285.8304]\n",
      "\n",
      "Hf_gas = -241.826  # kJ/mol\n",
      "S_gas = 0.188835   # kJ/mol/K\n",
      "\n",
      "shomateG = [30.09200,\n",
      "             6.832514,\n",
      "             6.793435,\n",
      "            -2.534480,\n",
      "             0.082139,\n",
      "          -250.8810,\n",
      "           223.3967,\n",
      "          -241.8264]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "T = np.linspace(0, 200) + 273.15\n",
      "t = T / 1000.0\n",
      "\n",
      "sTT = np.vstack([np.log(t),\n",
      "                 t,\n",
      "                 (t**2) / 2.0,\n",
      "                 (t**3) / 3.0,\n",
      "                 -1.0 / (2*t**2),\n",
      "                 0 * t,\n",
      "                 t**0,\n",
      "                 0 * t**0]).T / 1000.0\n",
      "\n",
      "hTT = np.vstack([t,\n",
      "                 (t**2)/2.0,\n",
      "                 (t**3)/3.0,\n",
      "                 (t**4)/4.0,\n",
      "                 -1.0 / t,\n",
      "                 1 * t**0,\n",
      "                 0 * t**0,\n",
      "                 -1 * t**0]).T\n",
      "\n",
      "Gliq = Hf_liq + np.dot(hTT, shomateL) - T*(np.dot(sTT, shomateL))\n",
      "Ggas = Hf_gas + np.dot(hTT, shomateG) - T*(np.dot(sTT, shomateG))\n",
      "\n",
      "from scipy.interpolate import interp1d\n",
      "from scipy.optimize import fsolve\n",
      "\n",
      "f = interp1d(T, Gliq - Ggas)\n",
      "bp, = fsolve(f, 373)\n",
      "print 'The boiling point is {0} K'.format(bp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The boiling point is 373.206081312 K\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "plt.figure(); plt.clf()\n",
      "plt.plot(T-273.15, Gliq, T-273.15, Ggas)\n",
      "plt.legend(['liquid water', 'steam'])\n",
      "\n",
      "plt.xlabel('Temperature $^\\circ$C')\n",
      "plt.ylabel('$\\Delta G$ (kJ/mol)')\n",
      "plt.title('The boiling point is approximately {0:1.2f} $^\\circ$C'.format(bp-273.15))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.text.Text at 0x7f309549ead0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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Tq1YtmjVrluSYr732GpGRkRQpUoR//OMfeHt7s2DBAnbu3EnFihUpXrw4vXr14saNGw9c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\nmd5+Oh2rdHTq+W/ckD7Nliy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       "text": [
        "<matplotlib.figure.Figure at 0x7f30954cf950>"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}

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