path: root/Chemical_Engineering_Thermodynamics_by_Y_V_C_Rao/ch12.ipynb

{
 "metadata": {
  "name": ""
 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 12 : Vapor liquid Equilibrium"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.1  Page No : 423"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "%matplotlib inline\n",
      "import math \n",
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "\n",
      "# Variables\n",
      "T = 60.\t\t\t #temperature of the system in degree celsius\n",
      "P = [237.60,265.20,317.50,333.00,368.70,387.20];\t\t\t #Pressure data in Torr (from Danneil et al.)\n",
      "x1 = [0.0870,0.1800,0.4040,0.4790,0.7130,0.9070];\t\t\t #mole fraction of benzene in the liquid phase corresponding to the given pressure (no unit) (from Danneil et al.)\n",
      "y1 = [0.1870,0.3400,0.5780,0.6420,0.7960,0.9220];\t\t\t #mole fraction of benzene in the vapour phase corresponding to the given pressure (no unit) (from Danneil et al.)\n",
      "antoine_const_benzene = [6.87987,1196.760,219.161];\t\t\t #Antoine's constants for Benzene from Table A.7\n",
      "antoine_const_heptane = [6.89386,1264.370,216.640];\t\t\t #Antoine's constants for heptane from Table A.7\n",
      "\n",
      "# Calculations\n",
      "P1_s = 10**(antoine_const_benzene[0]-(antoine_const_benzene[1]/(T+antoine_const_benzene[2])));\n",
      "P2_s = 10**(antoine_const_heptane[0]-(antoine_const_heptane[1]/(T+antoine_const_heptane[2])));\n",
      "l = len(P);\t\t\t #iteration parameter\n",
      "i = 0;\t\t\t #iteration parameter\n",
      "gaamma1 = zeros(l)\n",
      "gaamma2 = zeros(l)\n",
      "ln_gaamma1_expt = zeros(l)\n",
      "ln_gaamma2_expt = zeros(l)\n",
      "gE_RTx1x2 = zeros(l)\n",
      "while i<l:\n",
      "    gaamma1[i] = (y1[i]*P[i])/(x1[i]*P1_s);\t\t\n",
      "    gaamma2[i] = ((1-y1[i])*P[i])/((1-x1[i])*P2_s);\n",
      "    ln_gaamma1_expt[i] = math.log(gaamma1[i]);\n",
      "    ln_gaamma2_expt[i] = math.log(gaamma2[i]);\n",
      "    gE_RTx1x2[i] = ((x1[i]*ln_gaamma1_expt[i])+((1-x1[i])*ln_gaamma2_expt[i]))/(x1[i]*(1-x1[i]));\t\t\t # Calculations of gE/RT using Eq.(11.36) (no unit)\n",
      "    i = i+1;\n",
      "\n",
      "plot(x1,gE_RTx1x2,'o');\t\t\n",
      "suptitle('Plot of gE/RTx1x2 vs x1')\n",
      "xlabel('x1')\n",
      "ylabel('gE/RTx1x2');\n",
      "A21 = 0.555\n",
      "A12 = 0.315\n",
      "j = 0\n",
      "ln_gaamma1 = zeros(l)\n",
      "ln_gaamma2 = zeros(l)\n",
      "P_calc = zeros(l)\n",
      "y1_calc = zeros(l)\n",
      "gaamma1 = zeros(l)\n",
      "gaamma2 = zeros(l)\n",
      "while j<l:\n",
      "    ln_gaamma1[j] = ((1-x1[j])**2)*(A12+(2*(A21-A12)*x1[j]));\n",
      "    ln_gaamma2[j] = (x1[j]**2)*(A21+(2*(A12-A21)*(1-x1[j])));\n",
      "    gaamma1[j] = math.exp(ln_gaamma1[j])\n",
      "    gaamma2[j] = math.exp(ln_gaamma2[j])\n",
      "    P_calc[j] = (gaamma1[j]*x1[j]*P1_s)+(gaamma2[j]*(1-x1[j])*P2_s)\n",
      "    y1_calc[j] = (gaamma1[j]*x1[j]*P1_s)/P[j];\t\t\t \n",
      "    j = j+1;\n",
      "\n",
      "# Results\n",
      "print 'Data for the plot of gE/RTx1x2 vs x1: ';\n",
      "\n",
      "for i in range(l):\n",
      "    print 'P = %f Torr\\t x1 = %f\\t y1 = %f \\t lngamma1) = %f\\t\\t lngamma2) =\\\n",
      "     %f\\t\\t gE/RTx1x2 = %f'%(P[i],x1[i],y1[i],ln_gaamma1_expt[i],ln_gaamma2_expt[i],gE_RTx1x2[i]);\n",
      "\n",
      "print 'Results: ';\n",
      "for i in range(l):\n",
      "    print 'x1 = %f \\t gamma1 = %f \\t gamma2 = %f \\t P_Exptl. = %f \\\n",
      "    Torr\\t P_Calc = %f Torr\\t y1_Exptl = %f \\t y1_calc = %f '%(x1[i],gaamma1[i],gaamma2[i],P[i],P_calc[i],y1[i],y1_calc[i]);\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "Data for the plot of gE/RTx1x2 vs x1: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "P = 237.600000 Torr\t x1 = 0.087000\t y1 = 0.187000 \t lngamma1) = 0.265459\t\t lngamma2) =     0.004741\t\t gE/RTx1x2 = 0.345243\n",
        "P = 265.200000 Torr\t x1 = 0.180000\t y1 = 0.340000 \t lngamma1) = 0.246143\t\t lngamma2) =     0.013576\t\t gE/RTx1x2 = 0.375599\n",
        "P = 317.500000 Torr\t x1 = 0.404000\t y1 = 0.578000 \t lngamma1) = 0.148307\t\t lngamma2) =     0.065399\t\t gE/RTx1x2 = 0.410716\n",
        "P = 333.000000 Torr\t x1 = 0.479000\t y1 = 0.642000 \t lngamma1) = 0.130700\t\t lngamma2) =     0.083082\t\t gE/RTx1x2 = 0.424313\n",
        "P = 368.700000 Torr\t x1 = 0.713000\t y1 = 0.796000 \t lngamma1) = 0.049771\t\t lngamma2) =     0.218778\t\t gE/RTx1x2 = 0.480259\n",
        "P = 387.200000 Torr\t x1 = 0.907000\t y1 = 0.922000 \t lngamma1) = 0.005014\t\t lngamma2) =     0.433207\t\t gE/RTx1x2 = 0.531539\n",
        "Results: \n",
        "x1 = 0.087000 \t gamma1 = 1.346332 \t gamma2 = 1.000884 \t P_Exptl. = 237.600000     Torr\t P_Calc = 238.297793 Torr\t y1_Exptl = 0.187000 \t y1_calc = 0.193066 \n",
        "x1 = 0.180000 \t gamma1 = 1.309835 \t gamma2 = 1.005243 \t P_Exptl. = 265.200000     Torr\t P_Calc = 265.912990 Torr\t y1_Exptl = 0.340000 \t y1_calc = 0.348175 \n",
        "x1 = 0.404000 \t gamma1 = 1.198147 \t gamma2 = 1.044870 \t P_Exptl. = 317.500000     Torr\t P_Calc = 320.705660 Torr\t y1_Exptl = 0.578000 \t y1_calc = 0.597076 \n",
        "x1 = 0.479000 \t gamma1 = 1.159413 \t gamma2 = 1.072467 \t P_Exptl. = 333.000000     Torr\t P_Calc = 335.157916 Torr\t y1_Exptl = 0.642000 \t y1_calc = 0.653147 \n",
        "x1 = 0.713000 \t gamma1 = 1.055628 \t gamma2 = 1.236286 \t P_Exptl. = 368.700000     Torr\t P_Calc = 369.484272 Torr\t y1_Exptl = 0.796000 \t y1_calc = 0.799482 \n",
        "x1 = 0.907000 \t gamma1 = 1.006511 \t gamma2 = 1.521729 \t P_Exptl. = 387.200000     Torr\t P_Calc = 387.326500 Torr\t y1_Exptl = 0.922000 \t y1_calc = 0.923362 \n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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LbZq/vz/0ej0MBgMiIiKULJOIiCR4KrViq9WK9PR0FBcXY+TIkYiMjERsbCwMBoPdcm1t\nbViyZAni4+PtpqtUKpjNZowYMUKpEomIyAkORxhWqxVr1qzBk08+iX379tnNW7FiRZcrLikpQXBw\nMPz8/ODp6Ynk5GQYjcYOy+Xm5iIpKQk+Pj4d5nXnJeVERKQMh4GxcOFClJSUQKvVIjMzE4899pht\n3qWHjhyxWCzQarW27xqNBhaLxW6ZmpoabN26Fenp6QB+HFVcpFKpEBMTA71ej5dffln+FxERkSIc\nHpIqLS3F0aNHAQCPPPIIfv/73+PXv/413n77bakVX7rzd2Tx4sV44YUXoFKpIISwG1EcOHAAvr6+\nOHfuHOLj4xEYGIgZM2Z0WEdWVpbtc3R0NKKjo6XqIyLqL8xmM8xm81WvRyUcHPcJCgrCkSNH7KYt\nX74chYWFOHv2LI4dO3bFFe/duxfZ2dn45z//CQD429/+hubmZixdutS2zNixY20hUVtbi8GDB+PV\nV1/FnDlz7Na1atUqAMCf/vQn++L/P2iIiEhed/edDg9J6fV6fPTRR3bTnn32Wfzud7/DiRMnulxx\neHg4KisrUVNTg5aWFhQUFCAhIcFuma+++grHjx/H8ePHkZSUhLVr12LOnDloaGhAQ0MDAKC+vh4m\nkwnBwcFO/zgiIuo5Dg9J5efndzp94cKFWLhwYZcrVqvVWLt2LeLi4tDe3o7U1FSEhYUhLy8PAJCW\nluaw7enTpzFv3jyoVCo0NDQgJSWlw6iDiIhcy+EhqYuWLVuGrKwseHr+mC3ff/89Fi9ejNdff90l\nBV4JD0kRETmvxw9JXdTW1oaIiAgcOnQIhYWFiIiIQFhYWLeKJCKivqvLEQYAfPTRR5g9ezaGDx+O\nPXv24Oabb3ZFbV3iCIOIyHnd3Xd2GRh79uxBeno67rvvPnzyySf43//+h9deew1+fn7dLranMDCI\niJzX3X1nl48GeeKJJ7B582YEBQUBAN577z3ccccd+Pzzz52vkoiI+qwuRxitra22E94XnT9/Hjfc\ncIOihcngCIOIyHmKnfS+PCwAYNu2bU5viIiI+japk96X02q1qK6uVqIep3CEQUTkvB4/h6HT6Rw2\nOnPmjNMbIiKivs1hYJw9exYmkwnDhw/vMG/KlCmKFkVERL2Pw8CYOXMm6urqOrzwCACioqIULYqI\niHqfbp3D6C14DoOIyHmKXSV1+RNrAeCNN95wekNERNS3dRkYy5cvR3p6Ourr63H69GnMnj2bl9US\nEfVDXQbGnj17MHbsWISEhGDatGm45557pF7RSkRE15YuA+O7775DaWkpAgICMGjQIHz99dc8b0BE\n1A91GRiRkZGIi4vDhx9+iNLSUtTU1ODWW291RW1EvZbRWIS4uGWIjs5CXNwyGI1F7i6JSHEOL6v9\n+uuvcdNNN2Hnzp0YPXo0AGDw4MHIzc3Fnj17XFYgUW9jNBZh0aIPUVW10jatqurHd9XPnHmbu8oi\nUpzDy2oNBgMqKipcXY9TeFktuUNc3DIUFq7oZPqfYTI954aKiJyj2GW1RGTPau18YN7U5OHiSohc\ny+EhqZqaGmRmZnaaQiqVCjk5OYoWRtRbeXm1djpdrW5zcSVEruUwMLy9vTFx4kQIIaBSqWzTL/9O\n1N9kZsaiqmqp3TmMgICnkZER78aqiJTHcxhE3WA0FiE3dyeamjygVrchIyOGJ7ypz+jxd3pPnjwZ\nJSUlHaYLIVBQUIDk5GTnq+xhDAwiIuf1+EnvwsJCrFq1Co888gheeeUVtLe34/3330dwcDDeeuut\nqyqWiIj6HocjjJkzZ8LHxweRkZEoLCxEdXU1Bg8ejJdeegmhoaGurrNTHGEQETmvxw9JBQYG4ujR\nowCAtrY2jBo1CidPnoS3t/fVVdqDGBhERM7r8UNSlwaDh4cH/Pz8elVYEBGRazkcYXh4eGDw4MG2\n742NjbbAUKlUuHDhgmsqvAKOMOhyRmMRcnIKYbV6wsurFZmZsbx6iegy3d13OrwPo62NNyFR38Jn\nPBEpy+EhqYkTJ2LRokUwmUxoampyZU1E3ZKTU2gXFgBQVbUSubk73VQR0bXFYWAcOHAAiYmJ2L17\nN6KiopCQkIA1a9bgiy++cGV9RNL4jCciZTk8JDVw4EDcfvvtuP322wH8+Gwpk8mEZcuW4csvv8Qt\nt9yCV155xWWFEnWFz3giUpbDk95X0tzcjNLSUre/SIknvelSnZ3DCAh4GmvWxPMcBtElevw+jKlT\np6K4uBgAkJqaio0bN9rmhYWFoby8vJul9hwGBl2Oz3gi6lqPXyVVX19v+1xZWWk3jztp6q1mzryN\nAUGkEEVfoGQymaDT6RAUFITs7GyHy5WWlsLT0xNbtmxxui0REbmGwxHG999/j/feew9CCLvPF+d1\nxWq1Ij09HcXFxRg5ciQiIyMRGxsLg8Fgt1xbWxuWLFmC+Ph4p9sSEZHrOAyM2267Ddu3bwcAREVF\n2T5f/N6VkpISBAcHw8/PDwCQnJwMo9HYYaefm5uLpKQklJaWOt2WiIhcx2FgbNiwAQCwevXqDvO8\nvb1x8OBBREREOFyxxWKBVqu1fddoNDCbzXbL1NTUYOvWrdi1axdKS0ttb/KTaUtERK7lMDAuKisr\nw8cff4zZs2cDAIxGIyZMmID169dj1qxZyMrK6rSdzGtcFy9ejBdeeMF2xv7iIS++ApaIqPfpMjC+\n+eYbHDp0yPbgwRUrVuDOO+9EUVERJkyY4DAwNBoNqqurbd+rq6vtRg3Aj2GUkpICAKitrcWOHTsw\ncOBAqbYXXbr96OhoREdHd/WTiIj6FbPZ3DNHaUQXxo0bJ1paWmzfW1paREBAgBBCiNDQUIftGhsb\nxejRo4XFYhHNzc1i0qRJoqyszOHy999/v9iyZYtTbSXKJyKiy3R339nlCOPuu+9GREQE5s6dCyEE\ntm/fjvnz56OxsRHjx4932E6tVmPt2rWIi4tDe3s7UlNTERYWhry8PABAWlqa022JiMh9pB4Nsm/f\nPuzbtw8qlQpTpkxx+yNBLuKd3kREzuvxR4P0BQwMIiLn9fgrWomIiC7FwCAiIikMDCIiksLAICIi\nKQwMIiKSwsAgIiIpDAwiIpLCwCAiIikMDCIiksLAICIiKQwMIiKSwsAgIiIpDAwiIpLS5fswyP2M\nxiLk5BTCavWEl1crMjNjMXPmbe4ui4j6GQZGL2c0FmHRog9RVbXSNq2qaikAMDSIyKV4SKqXy8kp\ntAsLAKiqWonc3J1uqoiI+isGRi9ntXY+CGxq8nBxJUTU3zEwejkvr9ZOp6vVbS6uhIj6OwZGL5eZ\nGYuAgKV20wICnkZGRoybKiKi/orv9O4DjMYi5ObuRFOTB9TqNmRkxPCENxF1W3f3nQwMIqJ+prv7\nTh6SIiIiKQwMIiKSwsAgIiIpDAwiIpLCwCAiIikMDCIiksLAICIiKQwMIiKSwsAgIiIpDAwiIpLC\nwCAiIikMDCIiksLAICIiKQwMIiKSomhgmEwm6HQ6BAUFITs7u8P8rVu3Qq/XIyQkBDqdDiaTyTbP\n398fer0eBoMBERERSpZJREQSFHsfhtVqRWBgIIqLizFy5EhERkZi3bp1MBgMtmXq6+tx3XXXAQA+\n+eQTzJo1CydPngQAjBkzBmVlZRgxYoTj4vk+DCIip/W692GUlJQgODgYfn5+8PT0RHJyMoxGo90y\nF8MCAOrq6jBq1Ci7+QwDIqLeQ7HAsFgs0Gq1tu8ajQYWi6XDch988AHGjx+PhIQErFmzxjZdpVIh\nJiYGer0eL7/8slJlEhGRJE+lVqxSqaSWS0xMRGJiIvbu3YsFCxbg888/BwAcOHAAvr6+OHfuHOLj\n4xEYGIgZM2Z0aJ+VlWX7HB0djejo6J4on4jommE2m2E2m696PYoFhkajQXV1te17dXW13YjjctOm\nTUNrayvOnDmDkSNHwtfXFwDg4+ODpKQklJaWdhkYSjIai5CTUwir1RNeXq3IzIzFzJm3uWTbRERX\n4/I/ppcvX96t9SgWGOHh4aisrERNTQ18fX1RUFCAvLw8u2VOnDgBf39/AEB5eTmam5vh6+uLhoYG\nAMDgwYNRX18Pk8mExx9/XKlSu2Q0FmHRog9RVbXSNq2qaikAMDSIqN9QLDDUajXWrl2LuLg4tLe3\nIzU1FWFhYbbQSEtLQ35+Pt566y0AgLe3N/Lz86FSqXD69GnMmzcPKpUKDQ0NSElJwZw5c5QqtUs5\nOYV2YQEAVVUrkZv7ZwYGEfUbil1W6wquuqw2OjoLe/ZkdZgeFZUFs7njdCKi3qzXXVZ7LfHyau10\nulrd5uJKiIjch4EhITMzFgEBS+2mBQQ8jYyMGDdVRETkejwkJcloLEJu7k40NXlArW5DRkYMz18Q\nUZ/U3X0nA4OIqJ/hOQwiIlIUA4OIiKQwMIiISAoDg4iIpDAwiIhICgODiIikMDCIiEgKA4OIiKQw\nMIiISAoDg4iIpDAwiIhICgODiIikMDCIiEgKA4OIiKQwMIiISAoDg4iIpDAwiIhICgODiIikMDCI\niEgKA4OIiKQwMIiISAoDg4iIpDAwiIhICgODiIikMDCIiEgKA4OIiKQwMIiISAoDg4iIpDAwiIhI\nCgODiIikMDCIiEiKooFhMpmg0+kQFBSE7OzsDvO3bt0KvV6PkJAQ6HQ6mEwm6bZERORiQiFNTU3C\n399fWCwW0dLSIiZNmiTKy8vtlqmrq7N9Pnz4sLjpppuk2wohhILl9zm7d+92dwm9BvviJ+yLn7Av\nftLdfadiI4ySkhIEBwfDz88Pnp6eSE5OhtFotFvmuuuus32uq6vDqFGjpNuSPbPZ7O4Seg32xU/Y\nFz9hX1w9xQLDYrFAq9Xavms0Glgslg7LffDBBxg/fjwSEhKQk5PjVFsiInIdxQJDpVJJLZeYmIjP\nPvsM27dvR2pqKn4cLRERUW/jqdSKNRoNqqurbd+rq6vtRg2XmzZtGlpbW3H27FlotVqptgEBAdLB\n1B8sX77c3SX0GuyLn7AvfsK++FFAQEC32ikWGOHh4aisrERNTQ18fX1RUFCAvLw8u2VOnDgBf39/\nAEB5eTmam5vh6+uLYcOGddkWAL788kulyiciossoFhhqtRpr165FXFwc2tvbkZqairCwMNuOPy0t\nDfn5+XjrrbcAAN7e3sjPz4dKpXLYloiI3EcleNKAiIgk9Ik7vWVu4svMzERwcDDCwsJQUVHh4gpd\np6u+2LhxI/R6PXQ6HSZNmoSysjI3VOkasjd3lpaWwtPTE++9954Lq3Mtmb4wm82IiIhAaGgooqKi\nXFyh63TVF6dPn8b06dMRHByMX/3qV50e7r4WPPDAAxg5ciR0Op3DZZzeb/bkzSBKkLmJb/PmzWLu\n3LlCCCHKy8tFSEiIO0pVnExflJSUiAsXLgghhNixY4cIDQ11R6mKk725s7W1Vdx+++1i5syZYvPm\nzW6oVHkyfXHq1CkRHBwszpw5I4QQ4vz58+4oVXEyfbF06VLx1FNPCSGEOHfunLj++utFU1OTO8pV\nVFFRkSgvLxcTJkzodH539pu9foQhcxPfv/71L6SmpgIADAYDWltbr8n7NmT6IiIiAkOHDgUA3Hrr\nraipqXFHqYqTvbkzNzcXSUlJ8PHxcUOVriHTF/n5+UhOToavry8AYMSIEe4oVXEyfaHVanHhwgUA\nwIULF+Dj4wMvLy93lKuoadOmYfjw4Q7nd2e/2esDQ+Ymvv5yo5+zvzMvLw9z5851RWkuJ9MXNTU1\n2Lp1K9LT0wHI3xvU18j0xeeff45vvvkGkZGR0Ov1eO2111xdpkvI9MVDDz2ETz/9FL/4xS8QEhKC\nNWvWuLrMXqE7+03FrpLqKbL/k4vLzt1fizsHZ36T2WzG+vXrsW/fPgUrch+Zvli8eDFeeOEFqFQq\nCCGu2ZtCZfqira0NlZWV2LVrFxoaGnDLLbcgMjISwcHBLqjQdWT64vnnn0doaCjMZjOqqqoQExOD\nQ4cO2Ubm/Ymz+81eP8KQuQHw8mUsFgs0Go3LanQV2ZshDx8+jIULF2Lbtm1XHJL2ZTJ9UVZWhpSU\nFIwZMwZbtmzBo48+im3btrm6VMXJ9MVNN92E2NhYeHt744YbbkBUVBQOHz7s6lIVJ9MXxcXFmD9/\nPoAfb2CEs8NnAAACeklEQVQbM2YMPvvsM5fW2Rt0a7/ZY2dYFNLY2ChGjx4tLBaLaG5uFpMmTRJl\nZWV2y2zevFkkJiYKIYQoKysTer3eHaUqTqYvTp48KQICAsT+/fvdVKVryPTFpe6//36xZcsWF1bo\nOjJ9UV5eLqZPny5aW1tFfX29CAoKEhUVFW6qWDkyffHoo4+KrKwsIYQQp0+fFjfeeKPtYoBrzfHj\nx6940tvZ/WavPyQlcwPgXXfdhd27dyM4OBheXl54/fXX3Vy1MmT64i9/+Qu+++4723H7gQMH4uDB\ng+4sWxEyfdFfyPSFwWBAfHw89Ho9WlpasHDhQoSGhrq58p4n0xfPPPMM7rvvPgQFBaGtrQ0rVqyw\nXQxwLbnnnnuwZ88e1NbWQqvVYvny5WhpaQHQ/f0mb9wjIiIpvf4cBhER9Q4MDCIiksLAICIiKQwM\nIiKSwsAgIiIpDAwiIpLCwCBSSHx8PIYPH47Zs2e7uxSiHsHAIFLIk08+iY0bN7q7DKIew8Agukql\npaUICQmB1WpFfX09JkyYgCNHjuCOO+7AkCFD3F0eUY/p9Y8GIertwsPDMWfOHCxbtgyNjY1ITU1F\nUFCQu8si6nEMDKIe8Mwzz2DSpEnw9vZGbm6uu8shUgQPSRH1gNraWtTX16Ourg6NjY226dfie1mo\n/2JgEPWAtLQ0rFixAvfeey+WLFlim85ne9K1hIekiK7Sm2++CS8vL6SkpKC9vR1TpkzB7t278eyz\nz+Lo0aOoq6uDVqvF+vXrERMT4+5yibqNjzcnIiIpPCRFRERSGBhERCSFgUFERFIYGEREJIWBQURE\nUhgYREQkhYFBRERSGBhERCTl/wBGhb+in7ykegAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2dcf110>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.3  Page No : 430"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *\n",
      "# Variables\n",
      "T = 25.     \t\t\t #temperature of the system in degree celsius\n",
      "A12 = 2.0522;\t\t\t #three suffix Margules parameters for the system (no unit)\n",
      "A21 = 1.7201;\t\t\t #three suffix Margules parameters for the system (no unit)\n",
      "P = [118.05,207.70,246.35,259.40,261.50,262.00,261.90,258.70,252.00];\t\t\t #Pressure data in Torr (from Tasic et al.)\n",
      "x1 = [0.0115,0.1125,0.3090,0.5760,0.6920,0.7390,0.7575,0.8605,0.9250];\n",
      "y1 = [0.1810,0.5670,0.6550,0.7050,0.7250,0.7390,0.7460,0.8030,0.8580];\n",
      "antoine_const_acetone = [7.11714,1210.595,229.664];\t\t\t #Antoine's constants for acetone from Table A.7\n",
      "antoine_const_chexane = [6.85146,1206.470,223.136];\t\t\t #Antoine's constants for cyclohexane from Table A.7\n",
      "\n",
      "# Calculations\n",
      "P1_s = 10**(antoine_const_acetone[0]-(antoine_const_acetone[1]/(T+antoine_const_acetone[2])));\n",
      "P2_s = 10**(antoine_const_chexane[0]-(antoine_const_chexane[1]/(T+antoine_const_chexane[2])));\n",
      "\n",
      "l = len(P)\n",
      "ln_gaamma1 = zeros(l)\n",
      "ln_gaamma2 = zeros(l)\n",
      "gaamma1 = zeros(l)\n",
      "gaamma2 = zeros(l)\n",
      "P = zeros(l)\n",
      "y1_calc = zeros(l)\n",
      "j = 0;\t\n",
      "\n",
      "while j<l:\n",
      "    ln_gaamma1[j] = ((1-x1[j])**2)*(A12+(2*(A21-A12)*x1[j]));\t\n",
      "    ln_gaamma2[j] = (x1[j]**2)*(A21+(2*(A12-A21)*(1-x1[j])));\t\n",
      "    gaamma1[j] = math.exp(ln_gaamma1[j]);\t\t\t \n",
      "    gaamma2[j] = math.exp(ln_gaamma2[j]);\t\t\t \n",
      "    P[j] = (gaamma1[j]*x1[j]*P1_s)+(gaamma2[j]*(1-x1[j])*P2_s)\n",
      "    y1_calc[j] = (gaamma1[j]*x1[j]*P1_s)/P[j];\t\t\t \n",
      "    j = j+1;\n",
      "\n",
      "# Results\n",
      "print 'P-x-y data: ';\n",
      "print 'x1 \\t  gamma1\\t  gamma2 \\t P Torr \\t y1  ';\n",
      "for i in range(l):\n",
      "    print '%0.4f \\t %f \\t %f \\t %f  \\t %f '%(x1[i],gaamma1[i],gaamma2[i],P[i],y1_calc[i])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P-x-y data: \n",
        "x1 \t  gamma1\t  gamma2 \t P Torr \t y1  \n",
        "0.0115 \t 7.372871 \t 1.000314 \t 116.059350  \t 0.168694 \n",
        "0.1125 \t 4.747283 \t 1.029662 \t 212.486878  \t 0.580377 \n",
        "0.3090 \t 2.415459 \t 1.231286 \t 255.363338  \t 0.674908 \n",
        "0.5760 \t 1.350072 \t 1.942786 \t 259.940648  \t 0.690796 \n",
        "0.6920 \t 1.163087 \t 2.513451 \t 261.385489  \t 0.711020 \n",
        "0.7390 \t 1.112223 \t 2.812451 \t 261.416681  \t 0.726019 \n",
        "0.7575 \t 1.095373 \t 2.942991 \t 261.232545  \t 0.733436 \n",
        "0.8605 \t 1.029233 \t 3.827737 \t 256.608420  \t 0.796964 \n",
        "0.9250 \t 1.008121 \t 4.546617 \t 248.599211  \t 0.866162 \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.4  Page No : 432"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "T = 25. \t\t\t #temperature of the system in degree celsius\n",
      "A = 2.0684;\t\t\t #the van Laar parameters for the system (no unit)\n",
      "B = 1.7174;\t\t\t #the van Laar parameters for the system (no unit)\n",
      "P = [118.05,207.70,246.35,259.40,261.50,262.00,261.90,258.70,252.00];\t\t\t #Pressure data in Torr (from Tasic et al.)\n",
      "x1 = [0.0115,0.1125,0.3090,0.5760,0.6920,0.7390,0.7575,0.8605,0.9250];\n",
      "y1 = [0.1810,0.5670,0.6550,0.7050,0.7250,0.7390,0.7460,0.8030,0.8580];\n",
      "antoine_const_acetone = [7.11714,1210.595,229.664];\t\t\t #Antoine's constants for acetone from Table A.7\n",
      "antoine_const_chexane = [6.85146,1206.470,223.136];\t\t\t #Antoine's constants for cyclohexane from Table A.7\n",
      "\n",
      "# Calculations\n",
      "P1_s = 10**(antoine_const_acetone[0]-(antoine_const_acetone[1]/(T+antoine_const_acetone[2])))\n",
      "P2_s = 10**(antoine_const_chexane[0]-(antoine_const_chexane[1]/(T+antoine_const_chexane[2])));\n",
      "l = len(P)\n",
      "j = 0\n",
      "while j<l:\n",
      "    ln_gaamma1[j] = A/(1+((A*x1[j])/(B*(1-x1[j]))))**2\n",
      "    ln_gaamma2[j] = B/(1+((B*(1-x1[j]))/(A*x1[j])))**2\n",
      "    gaamma1[j] = math.exp(ln_gaamma1[j]);\t\t\t\n",
      "    gaamma2[j] = math.exp(ln_gaamma2[j]);\t\t\t\n",
      "    P[j] = (gaamma1[j]*x1[j]*P1_s)+(gaamma2[j]*(1-x1[j])*P2_s)\n",
      "    y1_calc[j] = (gaamma1[j]*x1[j]*P1_s)/P[j];\t\t\t \n",
      "    j = j+1;\n",
      "\n",
      "# Results\n",
      "print 'P-x-y data: ';\n",
      "i = 0;\n",
      "print 'x1 \\t  gamma1 \\t gamma2 \\t PTorr \\t y1 ';\n",
      "for i in range(l):\n",
      "    print '%0.4f \\t %f \\t %f \\t %f  \\t %f '%(x1[i],gaamma1[i],gaamma2[i],P[i],y1_calc[i]);\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P-x-y data: \n",
        "x1 \t  gamma1 \t gamma2 \t PTorr \t y1 \n",
        "0.0115 \t 7.475516 \t 1.000328 \t 116.333233  \t 0.170640 \n",
        "0.1125 \t 4.743506 \t 1.030586 \t 212.468724  \t 0.579965 \n",
        "0.3090 \t 2.395936 \t 1.234218 \t 254.168007  \t 0.672601 \n",
        "0.5760 \t 1.346684 \t 1.937830 \t 259.284960  \t 0.690805 \n",
        "0.6920 \t 1.162537 \t 2.498302 \t 260.842215  \t 0.712164 \n",
        "0.7390 \t 1.112211 \t 2.792268 \t 260.900602  \t 0.727447 \n",
        "0.7575 \t 1.095497 \t 2.920797 \t 260.729035  \t 0.734935 \n",
        "0.8605 \t 1.029539 \t 3.796506 \t 256.244215  \t 0.798334 \n",
        "0.9250 \t 1.008263 \t 4.515793 \t 248.404105  \t 0.866965 \n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.5  Page No : 435"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "\n",
      "# Variables\n",
      "P = 760.\t\t\t #pressure in Torr at which chloroform and methanol form an azeotrope\n",
      "T = 53.5\t\t\t #temperature in degree celsius at which chloroform and methanol form an azeotrope\n",
      "x1 = 0.65\t\t\t #mole fraction of chloroform in the liquid phase (no unit) (corresponding to azeotropic composition)\n",
      "antoine_const_chloroform = [6.95465,1170.966,226.232];\t\t\t #Antoine's constants for acetone from Table A.7\n",
      "antoine_const_methanol = [8.08097,1582.271,239.726];\t\t\t #Antoine's constants for acetone from Table A.7\n",
      "\n",
      "# Calculations\n",
      "x2 = 1-x1\n",
      "P1_s = 10**(antoine_const_chloroform[0]-(antoine_const_chloroform[1]/(T+antoine_const_chloroform[2])));\n",
      "P2_s = 10**(antoine_const_methanol[0]-(antoine_const_methanol[1]/(T+antoine_const_methanol[2])));\n",
      "gaamma1 = P/P1_s\n",
      "gaamma2 = P/P2_s\n",
      "A = math.log(gaamma1)*(1+((x2*math.log(gaamma2))/(x1*math.log(gaamma1))))**2\n",
      "B = math.log(gaamma2)*(1+((x1*math.log(gaamma1))/(x2*math.log(gaamma2))))**2\n",
      "x1 = linspace(0.1,0.9,9)\n",
      "l = len(x1)\n",
      "gaamma1 = zeros(l)\n",
      "gaamma2 = zeros(l)\n",
      "P  = zeros(l) \n",
      "y1 = zeros(l)\n",
      "j = 0\n",
      "while j<l:\n",
      "    ln_gaamma1[j] = A/(1+((A*x1[j])/(B*(1-x1[j]))))**2\n",
      "    ln_gaamma2[j] = B/(1+((B*(1-x1[j]))/(A*x1[j])))**2\n",
      "    gaamma1[j] = math.exp(ln_gaamma1[j]);\t\t\t \n",
      "    gaamma2[j] = math.exp(ln_gaamma2[j]);\t\t\t \n",
      "    P[j] = (gaamma1[j]*x1[j]*P1_s)+(gaamma2[j]*(1-x1[j])*P2_s)\n",
      "    y1[j] = (gaamma1[j]*x1[j]*P1_s)/P[j];\t\t\t \n",
      "    j = j+1;\n",
      "\n",
      "# Results\n",
      "print 'VLE data: ';\n",
      "print 'x1 \\tgamma1 \\t\\t gamma2  \\t P Torr \\t y1 ';\n",
      "for i in range(l):\n",
      "    print '%0.1f \\t %f \\t %f \\t %f \\t %f '%(x1[i],gaamma1[i],gaamma2[i],P[i],y1[i]);\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "VLE data: \n",
        "x1 \tgamma1 \t\t gamma2  \t P Torr \t y1 \n",
        "0.1 \t 2.391069 \t 1.005464 \t 578.375597 \t 0.242663 \n",
        "0.2 \t 2.151801 \t 1.024547 \t 649.357212 \t 0.389019 \n",
        "0.3 \t 1.928361 \t 1.062974 \t 699.744047 \t 0.485280 \n",
        "0.4 \t 1.722251 \t 1.130135 \t 732.594248 \t 0.551969 \n",
        "0.5 \t 1.535159 \t 1.242383 \t 751.239893 \t 0.599745 \n",
        "0.6 \t 1.369108 \t 1.430331 \t 759.122391 \t 0.635183 \n",
        "0.7 \t 1.226766 \t 1.756665 \t 759.153131 \t 0.663976 \n",
        "0.8 \t 1.112114 \t 2.365222 \t 751.206494 \t 0.695188 \n",
        "0.9 \t 1.031997 \t 3.639052 \t 721.331744 \t 0.755801 \n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.6  Page No : 443"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "y1 = 0.3;\t\t\t #mole fraction of ethane in the vapour phase (no unit)\n",
      "T = 30. \t\t\t #temperature in degree celsius\n",
      "\n",
      "# Calculations\n",
      "y2 = 1-y1\n",
      "P_guess = 1\n",
      "K1 = 3.4\n",
      "K2 = 1.1\n",
      "x1_calc = y1/K1\n",
      "x2_calc = y2/K2;\n",
      "tot = x1_calc+x2_calc\n",
      "if tot == 1:\n",
      "    P = P_guess\n",
      "    x1 = x1_calc\n",
      "    x2 = x2_calc\n",
      "else:\n",
      "    P = 1.5\n",
      "    K1 = 2.4\n",
      "    K2 = 0.8\n",
      "    x1 = y1/K1\n",
      "    x2 = y2/K2\n",
      "\n",
      "# Results\n",
      "print 'The Dew pressure and the liquid composition of a binary vapour mixture of\\\n",
      " ethane and propane was found to be P = %0.2f MPa\\t x1 = %0.3f\\t x2 = %0.3f \\t'%(P,x1,x2);\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Dew pressure and the liquid composition of a binary vapour mixture of ethane and propane was found to be P = 1.50 MPa\t x1 = 0.125\t x2 = 0.875 \t\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.7  Page No : 443"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "x1 = 0.4;\t\t\t #mole fraction of ethane in the liquid phase (no unit)\n",
      "P = 1.5;\t\t\t #pressure in MPa\n",
      "\n",
      "# Calculations\n",
      "x2 = 1-x1\n",
      "t_guess = 10.\n",
      "K1 = 1.8;\t\n",
      "K2 = 0.5;\t\n",
      "y1_calc = K1*x1\n",
      "y2_calc = K2*x2\n",
      "tot = y1_calc+y2_calc\n",
      "if tot == 1:\n",
      "   t = t_guess\n",
      "   y1 = y1_calc\n",
      "   y2 = y2_calc\n",
      "else:\n",
      "    t = 9.\n",
      "    K1 = 1.75\n",
      "    K2 = 0.5;\n",
      "    y1 = K1*x1\n",
      "    y2 = K2*x2\n",
      "\n",
      "# Results\n",
      "print 'The bubble temperature and the vapour composition of a binary vapour mixture\\\n",
      " of ethane and propane was found to be t = %d degree celsius y1 = %f\\t y2 = %f\\t'%(t,y1,y2);\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The bubble temperature and the vapour composition of a binary vapour mixture of ethane and propane was found to be t = 9 degree celsius y1 = 0.700000\t y2 = 0.300000\t\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.8  Page No : 449"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "%matplotlib inline\n",
      "# Variables\n",
      "P = [350.00,446.00,518.00,574.50,609.00,632.50,665.00,681.50,691.50]\n",
      "x1 = [0.0550,0.1290,0.2120,0.3130,0.4300,0.5200,0.6380,0.7490,0.8720]\n",
      "y1 = [0.3500,0.5110,0.5990,0.6500,0.6970,0.7260,0.7590,0.8130,0.8830]\n",
      "antoine_const_propanol = [8.37895,1788.020,227.438];\t\t\t \n",
      "antoine_const_cbenzene = [7.17294,1549.200,229.260];\t\t\t \n",
      "T = 95.\t\t\t #temperature of the system in degree celsius\n",
      "\n",
      "# Calculations\n",
      "P1_s = 10**(antoine_const_propanol[0]-(antoine_const_propanol[1]/(T+antoine_const_propanol[2])));\n",
      "P2_s = 10**(antoine_const_cbenzene[0]-(antoine_const_cbenzene[1]/(T+antoine_const_cbenzene[2])));\n",
      "l = len(P)\n",
      "lngamma1_gamma2 = zeros(l)\n",
      "gaamma1 = zeros(l)\n",
      "gaamma2 = zeros(l)\n",
      "i = 0\n",
      "while i<l:\n",
      "    gaamma1[i] = (y1[i]*P[i])/(x1[i]*P1_s)\n",
      "    gaamma2[i] = ((1-y1[i])*P[i])/((1-x1[i])*P2_s)\n",
      "    lngamma1_gamma2[i] = math.log(gaamma1[i]/gaamma2[i])\n",
      "    i = i+1;\n",
      "\n",
      "plot(x1,lngamma1_gamma2);\n",
      "suptitle('Plot of ln(gamma1/gamma2) vs x1')\n",
      "xlabel('x1')\n",
      "ylabel('ln(gamma1/gamma2)');\n",
      "area_above = 1515.\n",
      "area_below = 1540.\n",
      "consistency_parameter = abs((area_above-area_below)/(area_above+area_below));\t\t\t\n",
      "\n",
      "# Results\n",
      "print 'Values of lngamma1./gamma2: ';\n",
      "print 'x1 \\t gamma1 \\t gamma2 \\t lngamma1./gamma2';\n",
      "\n",
      "for i in range(l):\n",
      "    print '%0.4f \\t %f \\t %f \\t %f '%(x1[i],gaamma1[i],gaamma2[i],lngamma1_gamma2[i]);\n",
      "\n",
      "print 'The value of the consistency parameter = %f'%(consistency_parameter);\n",
      "if consistency_parameter<0.02 or consistency_parameter == 0.02:\n",
      "    print 'The VLE data is thermodynamically consistent';\n",
      "else:\n",
      "    print 'The VLE data is not thermodynamically consistent';\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "Values of lngamma1./gamma2: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "x1 \t gamma1 \t gamma2 \t lngamma1./gamma2\n",
        "0.0550 \t 3.266913 \t 0.968851 \t 1.215489 \n",
        "0.1290 \t 2.591375 \t 1.007704 \t 0.944514 \n",
        "0.2120 \t 2.146767 \t 1.060854 \t 0.704889 \n",
        "0.3130 \t 1.749940 \t 1.177901 \t 0.395847 \n",
        "0.4300 \t 1.447924 \t 1.302845 \t 0.105581 \n",
        "0.5200 \t 1.295263 \t 1.453040 \t -0.114944 \n",
        "0.6380 \t 1.160398 \t 1.781713 \t -0.428812 \n",
        "0.7490 \t 1.085022 \t 2.043343 \t -0.632987 \n",
        "0.8720 \t 1.027071 \t 2.543757 \t -0.906931 \n",
        "The value of the consistency parameter = 0.008183\n",
        "The VLE data is thermodynamically consistent\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['f', 'draw_if_interactive', 'new_figure_manager', 'test']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pVMC//gUEBCidiKjyZCsc0dHRmDt3LurUqQOr/37FUqlUuHjxYuWSyoCFg0yp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\nEREZhIWDiIgMwsJBREQGYeEgIiKD/H+2fJxBMvlw7wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x39ce190>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.9  Page No : 464"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "%matplotlib inline\n",
      "# Variables\n",
      "\n",
      "P = 760.\t\t\t                            #pressure of the system in Torr\n",
      "antoine_const_benzene = [6.87987,1196.760,219.161];\t\t\t #Antoine's constants for Benzene from Table A.7\n",
      "t = linspace(60,100,9);\t\t\t #temperature range in degree celsius\n",
      "\n",
      "P2_s = [149.40,187.58,233.71,289.13,355.21,433.51,525.84,634.00,760.00];\n",
      "x1 = linspace(0,1,6)\n",
      "\n",
      "# Calculations\n",
      "l = len(t)\n",
      "i = 0\n",
      "P1_s = zeros(l)\n",
      "P_tot =  zeros(l)\n",
      "\n",
      "while i<l:\n",
      "    P1_s[i] = 10**(antoine_const_benzene[0]-(antoine_const_benzene[1]/(t[i]+antoine_const_benzene[2])));\n",
      "    P_tot[i] = P1_s[i]+P2_s[i];\n",
      "    i = i+1;\n",
      "\n",
      "T = (((t[2]-t[1])*(760-P_tot[1]))/(P_tot[2]-P_tot[1]))+t[1]\n",
      "\n",
      "P1_s_three_phase = 10**(antoine_const_benzene[0]-(antoine_const_benzene[1]/(T+antoine_const_benzene[2])));\n",
      "P2_s_three_phase = 760-P1_s_three_phase;\n",
      "y1_three_phase = P1_s_three_phase/760\n",
      "\n",
      "trange1 = linspace(T,T+11,11)\n",
      "n = len(trange1)\n",
      "i = 0\n",
      "y1 = zeros(n)\n",
      "P1_s_calc = zeros(n)\n",
      "while i<n:\n",
      "    if i == 1:\n",
      "        y1[i] = y1_three_phase\n",
      "    else:\n",
      "         P1_s_calc[i] = 10**(antoine_const_benzene[0]-(antoine_const_benzene[1]/(trange1[i]+antoine_const_benzene[2])));\n",
      "         y1[i] = (P1_s_calc[i])/P\n",
      "    i = i+1;\n",
      "\n",
      "trange2 = [70,75,80,85,90,95,100]\n",
      "P2_s_range = [233.71,289.13,355.21,433.51,525.84,634.00,760.00]\n",
      "p = len(trange2);\t\t\t\n",
      "i = 0\n",
      "y_one = zeros(p)\n",
      "# Calculations of the vapour composition of benzene in the two phase region (L2+V) using Eq.(12.61) (no unit)\n",
      "y_one[i] = y1_three_phase;\n",
      "trange2[i] = T;\n",
      "i = i+1;\n",
      "\n",
      "while i<p:\n",
      "    y_one[i] = (P-P2_s_range[i])/P;\n",
      "    i = i+1;\n",
      "k=len(x1)    \n",
      "t_3phase = zeros(k)\n",
      "i = 0\n",
      "k = len(x1)\n",
      "while i<k:\n",
      "    t_3phase[i] = T\n",
      "    i = i+1;\n",
      "\n",
      "# Results\n",
      "plot(y1,trange1);\n",
      "plot(y_one,trange2);\n",
      "plot(x1,t_3phase);\n",
      "suptitle('t-x-y diagram for benzene-water sytem at 760 Torr')\n",
      "xlabel('x1,y1')\n",
      "ylabel('t (degree celsius)');\n",
      "q = len(t)\n",
      "i = 1;\t\t\n",
      "print ' Calculationss performed for determining the three phase equilibrium temperature';\n",
      "print 'tdegree celsius \\t P1_s Torr \\t P2_s Torr \\t P1_s+P2_s Torr ';\n",
      "for i in range(q):\n",
      "    print '%d \\t \\t \\t %.2f \\t %0.2f \\t %.2f '%(t[i],P1_s[i],P2_s[i],P_tot[i]);\n",
      "\n",
      "print 'The three phase equilibrium temperature = %0.2f degree celsius '%(T);\n",
      "print 'The vapour phase composition of benzene at the three phase equilibrium point = %0.4f '%(y1_three_phase);\n",
      "\n",
      "# Note: answer are slightly different because of rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        " Calculationss performed for determining the three phase equilibrium temperature"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "tdegree celsius \t P1_s Torr \t P2_s Torr \t P1_s+P2_s Torr \n",
        "60 \t \t \t 391.63 \t 149.40 \t 541.03 \n",
        "65 \t \t \t 465.92 \t 187.58 \t 653.50 \n",
        "70 \t \t \t 550.98 \t 233.71 \t 784.69 \n",
        "75 \t \t \t 647.87 \t 289.13 \t 937.00 \n",
        "80 \t \t \t 757.67 \t 355.21 \t 1112.88 \n",
        "85 \t \t \t 881.54 \t 433.51 \t 1315.05 \n",
        "90 \t \t \t 1020.65 \t 525.84 \t 1546.49 \n",
        "95 \t \t \t 1176.21 \t 634.00 \t 1810.21 \n",
        "100 \t \t \t 1349.47 \t 760.00 \t 2109.47 \n",
        "The three phase equilibrium temperature = 69.06 degree celsius \n",
        "The vapour phase composition of benzene at the three phase equilibrium point = 0.7028 \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['draw_if_interactive']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jBSUFouT7/dbvDFwzkEbVG7G873KqlK+idSQhij2zFQg3Nzdjcbh37x5xcXE0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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x39910d0>"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}