{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Acentric factor\n",
    "\n",
    "Definition of acentric factor:\n",
    "$$\\omega = -\\left(\\log_{10}\\frac{p_s}{p_c}\\right)_{T_r =0.7}-1$$\n",
    "We introduce a new scaled variable\n",
    "$$\\Theta = \\frac{T_c}{T}-1 $$\n",
    "So if $T_r=0.7$, $\\Theta=0.4285714285714286$\n",
    "\n",
    "At $\\Theta=1/0.7-1$, \n",
    "$$p_s = p_c\\cdot 10^{1-\\omega}$$\n",
    "In general, $\\log_{10}\\frac{p_s}{p_c}$ is close to a linear function of $\\theta$\n",
    "\n",
    "At the critical point, $\\Theta = 1$, and $\\log_{10}(p_s/p_c)=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEVCAYAAAD+TqKGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xd4VNXWx/HvoklTUbx2rFeKXRTEHnu914KKXcGCYgEb\n2AX1qldBQRBFQGmKhSJIUUENCgpKDR30IoKKWAAlICVZ7x87aOCFkDKZczLz+zwPj0nmzDmL84ys\nrL3O3tvcHRERkS0pF3UAIiISb0oUIiJSICUKEREpkBKFiIgUSIlCREQKpEQhIiIFil2iMLM6ZjYl\n358VZnZH1HGJiKQri/M8CjMrB3wPNHT3RVHHIyKSjmJXUWziNOAbJQkRkejEPVFcBrwRdRAiIuks\ntkNPZlaJMOx0oLv/HHU8IiLpqkLUARTgbGDS5pKEmcUzu4mIxJy7W1HfE+ehp8uB/lt60d1T+s+j\njxb2uEcjjzUuf3QvdC90Lwr+U1yxTBRmVo3QyB4UdSxRadcu6ghERIJYDj25ezawU9RxROnRR6OO\nQEQkiGVFIdC2beGOy8jIKM0wyhTdi7/pXvxN96LkYvvUU0HMzMti3EXRtm3hk4WISGGYGV6MZrYS\nRUyZQYr/FUUkyYqbKDT0FFPqUYhIXKiiEBFJE6ooUoz6EyKywcKFcN99kJsbzfWVKGJK8yhEJCcH\nOnaEI4+E6tWjSxSxnEch6lGIpLtp0+CGG6BaNRg3DurUiS4W9ShERGJk9eowovDqq/DUU9CsWXgK\nMhHUo0gx6lGIpJ/Ro+GQQ+DbbyErC66/PnFJoiRUUcSU5lGIpI9ffoG774bMTOjaFc49t3Suo4oi\nxahHIZL63KFfPzj4YNhxR5g5s/SSREmoohARicCCBXDLLfDjj9CjBzRoUPrXVEWRYtSjEElN69dD\n+/YhMZx8MkycmJwkURKqKGJKPQqR1DNpEtx4Yxhm6tYN9t8/uddXRZFi1KMQSR3Z2aFZfc450KoV\njBqV/CRREqooRERK0QcfwM03w3HHwfPPwz/+EV0sqihSjHoUImXb0qVw5ZWhYf3yy+HppiiTREko\nUcSU1noSKZvcoXfvMHFu991h+nQ488yooyqZWK71ZGY1gB7AQYADzdx9fLRRJZd6FCJlz/z5YZhp\n+XIYORLq1486osSIZY/CzHoDY9z9VTOrAFRz9xX5XlePQkRiY+1aeOaZsNLrgw/C7bdDhRj+Gp4y\nPQoz2x44wd1fBXD39fmTRLpQj0KkbBg3Do44AiZMCI+/3nlnPJNEScSuojCzw4FuwCzgMGAS0NLd\nV+U7JuUrCs2jEIm35cuhTRsYNgw6dYLGjeOxgF9BUqaiIPRN6gNd3b0+kA3cF21IyacehUg8ucPb\nb8NBB0G5cmF9posvjn+SKIk4FkiLgcXu/lXe9wPYTKJom29sJiMjg4yMjGTEljQaehKJn4ULoUWL\n8N933oFjj406ooJlZmaSmZlZ4vPEbugJwMw+BW5w93lm1hao4u5t8r2e8kNPbdsqWYjExfr1YXjp\nqafgrrvgnnugUqWooyq64g49xTVRHEZ4PLYS8A3QNN2eelKPQiQeNqzPtMMOYeLcAQdEHVHxFTdR\nxHHoCXefBsR8PcXSpR6FSLRWroSHH4b+/cOjr1dfndp9iILEsqLYmnSoKEQkOu+9B7fdFpYBb98e\ndtop6ogSI5WeehLUnxCJwg8/hCeY7roLXnsNevVKnSRREkoUMaW1nkSSJzcXXnoJDjsM6taFrCw4\n5ZSoo4qPWPYoRD0KkWTJyoLmzcOciMzMMD9CNqYehYikpexseOyxMMT0n//A9deHZJHK1KNIMepR\niJSeESPg4INh8eKwDPiNN6Z+kigJVRQxpXkUIon3ww9hK9JJk0JP4owzoo4ouVRRpBj1KEQSJycH\nunYNzeratWHGjPRLEiWhikJEUtrUqaFZXalSmFmdzs1qVRQpRj0KkZLJzoZ77w2Vw003wZgx6Z0k\nSkIVRUypRyFSfMOGhZnVJ5wAHTrAzjtHHVE8pNRaT6IehUhxfP89tGwJ06ZBjx5w2mlRR5QaNPQU\nUxp6Eim8nBzo0iU0q+vVC5PolCQSR4kippQoRApn6lQ45piw69xnn8Hjj0OVKlFHlVrUo4gp9ShE\nCvbHH2GI9vXX4cknoWlTTZrbGj31lGLUoxDZPHcYPBgOPBB++y3MiUiH5TeipIpCRMqMhQvD00xf\nfx1mVmdkRB1R2aKKIsWoRyHyt3Xrwi5zRx4JjRqFvoSSRPKooogp9ShEgs8/DzOrd989LMOx//5R\nR1R2pdQ8CjP7FvgdyAHWuXvDaCNKPvUoJN399hvcdx8MHw7PPQeXXpq+e1ZHLa5DTw5kuPsR6Zgk\nQENPkr7coW/fsNzGNtvArFnQpImSRJRiWVHkSeuPRdu2ShaSfubOhVtugeXLYehQaNAg6ogEYtqj\nMLP/ASsIQ0/d3L37Jq+rRyGSQv78M8yF6NoVHn4Ybr0VKsT519gyKqV6FMBx7v6jmf0DGGVmc9z9\ns/wHtM3363ZGRgYZKfYIhHoUki5GjYIWLcLyG9OmwR57RB1R6sjMzCQzM7PE54llRZGfmT0KrHT3\nDvl+lvIVhUiq+/FHuOsuGD8eOneG886LOqLUlzLzKMysqpltm/d1NeAMYHq0USWf+hOSqnJyQmI4\n9FDYd1+YOVNJIu5iV1GY2b7A4LxvKwCvu/tTmxyT8hWFehSSir76Cm6+GbbdNsysrlcv6ojSS8r0\nKNx9AXB41HFETT0KSSXLl8ODD8LAgfDss3DVVXrctSyJ3dCTBBp6klTgHlZ3PfDAMOQ0axZcfbWS\nRFmjRBFTShRS1s2ZEzYPat8eBg2Cl1+GHXeMOiopjtj1KApDPQqR+Fq9OsyJeOkleOihsNqr5kTE\nQ8r0KCRQj0LKopEjQ2KoX19zIlKJKgoRKbHFi+HOO2HyZHjxRTjrrKgjks1JmXkUEqhHIWXBunVh\nZdfDD4e6dcNuc0oSqUcVRUypRyFxN3ZsWHpjl11CFVG7dtQRydaookgx6lGkn4GzBtJieIuow9iq\nn3+GZs3gsstCs/rDD5UkUp0SRUxp6Cl9rFm/hjtG3sG9o+6l2RHNog5ni3Jz4ZVXwj4RNWqEORHa\nTCg96KmnmNJ+FOlhwbIFNBnQhD2224PJzSdTo3KNqEParMmTwz4R5cuH1V4POyzqiCSZ1KOIKfUo\nUt+QOUO4adhN3HfcfbRq1AqL4a/mK1aE/SHeegueegquuw7KaRyizNI8ihSjHkXqWpezjvtG38eA\n2QMYctkQGu3ZKOqQ/h936N8f7rknrOw6axbUrBl1VBIVVRQiSbRoxSKaDGjCDlV2oM8FfahZNX7/\n+s6eHXaYW7YszK5uFL88JsWkp55SjPoTqWfE/BEc1f0ozq9zPu9d/l7skkR2Ntx/P5xwAlxwQVgS\nXElCQBVFbKlHkTrW5azj4U8epl9WP/o37s8Je58QdUgbcYfBg8PM6uOPD4v47bZb1FFJaVCPIsWo\nR5EaFq1YxOUDL6d6pepMaT6Ff1T7R9QhbWT+fLjjDli4EHr1gpNPjjoiiSMNPcWUhp7KvhHzR9Cg\newPOPeBcRlw5IlZJYvVqeOQROOYYOOUUmDpVSUK2TIkippQoyq4NTzXd9N5NvH3J29x/wv2Us/j8\nrzZsWJg0N3t2SBD33guVKkUdlcSZehQxpR5F2bRhqKlapWr0vbAvO1fbOeqQ/rJgAbRsGTYU6tIF\nzjgj6ogk2VLuqSczK29mU8zsvahjiYJ6FGXPhqGmcw44h5FXjoxNklizBp54Ao46Co4+GqZPV5KQ\nooltRWFmdwFHAtu6+783eS3lKwopO9blrOOhjx/i9emv80bjNzhx7xOjDukvH3wQNhI66CDo2BH2\n2SfqiCRKKVVRmNmewDlADyB+6xokgXoUZcN3K77jpF4nkbU0iynNp8QmSXz3HTRuHJYB79gR3n1X\nSUKKL5aJAngeuBfIjTqQqLRrF3UEsjVD5w6lQfcGnF/nfIZfMTwWTzWtWRP2q65fPyzcN3MmnHtu\n1FFJWRe7eRRmdh6w1N2nmFnGlo5rm+9X7oyMDDIytnhomaQeRXytzVkb1mqaNYBBlw7iuL2Oizok\nIAwz3X471KsXZlXvu2/UEUnUMjMzyczMLPF5YtejMLMngauB9UBlYDtgoLtfk+8Y9SgkEguWLeCy\ngZexc7Wd6XV+r1gsw/Hdd2FW9dSp8MILqiBky1KmR+HuD7h7LXffF7gM+Dh/kkgX6lHEz6DZgzi6\nx9E0OagJQy8bGnmS0DCTJEvsKor8zOwk4O50fOpJ8yji48/1f3LPh/cwfP5w3mz8JkfveXTUIfH+\n+2HpjXr1QrNaw0xSGKW+1pOZVQOuBA4GyhOGhXKBlcB44B13T2jz2d3HAGMSec6yQj2KeJj36zya\nDGjCP3f8J1OaT4l8B7qFC8MwU1YWdOqkCkKSo1AVhZmdDhwIDHP3bzZ5zYDDgNOA0e4+tTQC3eSa\nKV9RSPT6ZfXjzg/u5LGMx7j5qJsj3YHuzz/Dqq4dO4ZKonVrqFw5snCkjCq1isLMKgML3H3U5l7P\n+xd7KjDVzA4pagCyedozOzrZa7O5feTtjFs0jtFXj+awXaPdIHrYsLD0xmGHwcSJmg8hyRfrHsWW\npENFoR5FNKb/NJ0mA5rQYI8GvHjOi1SvVD2yWL75Blq1gnnzwtNMZ54ZWSiSIiJ76snMbsz771El\nPZf8TT2K5HJ3uk3sxil9TuG+4++j9wW9I0sSq1bBww+HdZmOPz6szaQkIVFKxIS73/P6FGk7i7o0\naNgpeZb/uZyb3ruJeb/O47Omn1F3p7qRxLFhp7m77gr7REydCnvuGUkoIhtJxDyKL4AXgMMTcC7J\no0SRHBMWT6B+t/rsUm0Xxt8wPrIkMWdOqBoeeSTsNNe/v5KExEeRexRmdjdhwb5dgSHAo+6+rhRi\nKygG9SikRHI9l/aft6fDFx3odl43Lqh7QSRx/PEHPP44vPYaPPgg3HorVKwYSSiSBpK5Z/Zcd++Q\nN9x0CvAw8EgxziMFUI+i9Py08ieuefcastdm89WNX7HX9nslPQZ3eP11aNMGTj899CF23TXpYYgU\nSnEqihuAH4BP3X2lmf3L3ZO6uVA6VBRSOkb/bzTXvnstTQ9vStuMtlQol/x1MadMCYv3/fkndO4c\n+hEiyZDMiqIWUANoamY1gQpmtj2wh7v/txjnk83QPIrEWpezjoc/eZh+Wf3oc0EfTt3v1KTH8Ouv\n8NBDMGhQ2HGuWTMoXz7pYYgUWXEqivpAFXcfl/f9/sCxwA3uflLiQ9xsDClfUahHkTgLli3g8oGX\nU7NqTXqd3yvp+0bk5MArr4TEf+ml8NhjsMMOSQ1BBCjdmdl1gFx3nw/g7pPzv563pMc3Zja6qBeX\nLVOPIjHemvEWt4+8nfuPv59WjVolfRmOsWPDMNO228KHH4bZ1SJlzVYrCjOrAGQAdQhzJb5y94ml\nH1qBMaV8RSElk702m5bvt+TThZ/Sv3F/jtz9yKRe/4cfQqP6k0/g2WfhsstClSgSpVKbme3u6919\ntLu/6O4vAeXM7BYzu9XMTstLJJJg6k8U37Ql0ziq+1GszVnLpJsmJTVJrFkD//0vHHpomAcxZw5c\nfrmShJRtJVrryczqAicBlYDvgQ/cPTtBsRV03ZSvKNSjKDp354UJL/DEZ0/w/JnPc9WhVyX1+sOH\nh7WZ6tWD556Df/4zqZcX2apkPvX0F3efA8zJC2B34DzgrZKcUwL1KIrm5+yfaTqkKUuzlzL++vHs\nv+P+Sbv2vHkhQXzzTVi87+yzk3ZpkaQo8hIeZna3mX1kZjPN7Ekzqwjg7j+4u5JEgmjoqfBG/280\nh3c7nIN3PpixzcYmLUn8/nvYF+LYY+GUU8KkOSUJSUXFWetprrufStjp7iPCzGxJMCWKrVubs5Y2\no9pw7bvX0vuC3jx92tNUKl+p1K+bmwt9+oQhpp9/hhkz4J57oFLpX1okEpqZHVPqURRs/q/zuWLQ\nFexSbRdeO/+1pM2N+OqrsMNcTk6YVX109NtnixRayszMzttRbwywDaFJPsTd7y/pecsa9Sg2z93p\nM60Pbd6/mwdPfpTbGt6WlLkRS5bA/ffDBx/Af/4D114L5RKx9rJIGRDLmdlmVtXdV+U9ejsWuMfd\nx+Z7PeUrCvn/Vvy5gluG3kSjvp9wXXZttvt47NbfVEJr10KnTuGR12bNwhIc221X6pcVKRWlOTN7\nG2Bbd/8FCpyZPcrM9nL374oaxKbcfVXel5WA8sBvJT1nWaO1njb2xaIvaPXapfQZmMs/t69D+Tf6\nl/o1hw+HO++EOnXg88+hdu1Sv6RILBWqojCz84DtgMHuvnozr+8AXALMdvfPShyUWTlgMrA/8JK7\nt97k9ZSvKNSjCNbnrufJz55kXp/n6TEUKt9+Z9i4oRRX05szJ+wy97//QceOcNZZpXYpkaQq1R6F\nuw8zs92AO81sZ6AyUBHIAVYBi4Hu7r6iqAFs4Xq5wOF5vY8PzCzD3TPzH9M236/bGRkZZGRkJOLS\nsaEeBXy7/Fuue/sKbh38PQ/MqEqFgf3hxBNL7XrLl4dNhPr0Cf2I227Tk0xStmVmZpKZmVni85R0\nZvZewC7AT4kYctrCNR4GVrt7+3w/S/mKIt31n96fTn1v5d0hVdml3pFYz1ehZs1SuVZODvTsGbYh\n/fe/wxLgO+9cKpcSiVTSZ2abWXPCk0krgRPMLNfdOxb3fPnOuxOw3t2Xm1kV4HSgXUnPW9aka4/i\njzV/cNuIW9ll0Cg+G+FUfPwBuOWWUlssacwYaNkStt8eRo6EI44olcuIlGnFrijM7DR3H53v+5Pd\n/ZMSB2R2CNCbMBmwHNDX3Z/d5JiUryjSsUcxfvF4bn7jCl4eUZ6GSytQ7q234ZBDSuVa334L994b\n5kU8+yxcfLEW7pPUF8VaT7+bWXugKrACGFGCc/3F3acD9RNxrrIsnXoUGxrWXwzsxNh3K1H9nPNh\nxHNQtWrCr7VyJTz9NLz8clifqU8fqFIl4ZcRSSkl6lFEJR0qinSxYNkCrhl4Jdd9uJTrMldQ/qWX\noXHjhF8nNxdefz00qTMyQrLYc8+EX0Yk1qLoUeye/1vgZHfvV9zzycZSvUfh7vTL6scz77Rk+Mia\n1Kq+BzbpE6hVK+HX+uKLUD0AvPMOHHNMwi8hktJK0qM4H7gWmJb3ozrufkWiAtvKtVO+okjlHsWy\n1ctoMaIFNT8cx/ODsql4Ryt44IGEz41YtCjsMvfpp/DUU3DllVp2Q9Jb0isKdx9iZhPcfUleAHqg\nMIFStUeR+W0mzd++mp5janDsrHKUG/JeWKc7gbKz4ZlnoEsXuPVW6N4dqlVL6CVE0kpx9qNos+Fr\nd19iZrXMrA9qQCdUqg07bVgS/MnOlzLpFeP4GodSbuq0hCaJ3Fzo1w/q1g2bCU2ZAo89piQhUlLF\nKcRrmtlwMzsw7/u7gSeA3RIXlqRSopj982yOeeVoavcdzvu9c6ne9snQWd5++4Rd44svQu+hUyd4\n803o3x/22ithpxdJa8VJFF+6+7nAAXnf7w18AyxNWFRCuxSYYujuvPjli1zywvG823ctzeZvS7kv\nv4SrEreX9cKFcPnlcMklYZhpwgQ47riEnV5EKF6iOMLMbgXq5S0xvhdh7ScV+AlU1nsUP/7xI+e8\ncQ7f9unE1FfKUev0i7FPP4X99kvI+VeuDEt+168fVnedOxeuuUbNapHSUJz9KHYBjgamA/sBM4Gm\nwCR3/zDhEW4+hpR/6qksGzx7MHcPvpm3xtfiqBm/YX37JuzX/Nxc6N07JIlTToEnnyyVJ2pFUlIy\nn3r6GdgJaA1kuftHwFPFOI8UoCzOo/hjzR+0er8Vv4z9kJmDK1Pl2ANhSueE9SIyM+Huu2GbbWDw\nYGjYMCGnFZGtKE5FcQ/wPaEnUQuo6e4dSiG2gmJI+YqirM2jGPfdOK4bdDVPT67Jhe9/S7lOL4Tm\nQQJ8/XVYl2nKlLDT3KWXal0mkeJIZkUx392H5Ltwk2KcQ7airPQo1uaspV1mOz78uDtffPAPdqpe\nDSZOSsgjR8uW/b0/xD33hCeZKldOQNAiUiTFaf3908wamtl+ZpZB2IVOEqwsDDvN/nk2x/RoxA6D\nRjDhlVx2uvRa+OijEieJdeugc+fQpM7Ohpkz4b77lCREolKciqIbcA/QAJgBlJHffcuWOPcocj2X\nLl92odPItnz4+f7stzgb+3BUiTdzcIdhw8Iw0157hZxTSquMi0gRlHj1WDM7090/SFA8hb2mehQR\nWbRiEU2HNKVe1o881/83Kja+JDQOSrhW95QpoVG9ZEnYH+Kcc9SHEEm0Uu1RmFkLwgKAqzbzcj1g\n16JeWAoWtx6Fu9N/Rn/avNeSAdPq0HDscuzVXnDmmSU67w8/hEddR4wIf+cbb4QKJdklRUQSrrD/\nS84Djnf3dZu+YGZnJzYkgXgNO/266ldajGjB+kkTmTd4e6ocshtkDSnRHtbZ2dC+PbzwQkgOc+cm\ndEUPEUmgQjWz3X30pknCzC7Oe21kaQSW7uKSKEbOH8kRXQ/l6pE/MKDnH1R5qC28/Xaxk0RODrz2\nWmhUz54NkyaFTYSUJETiqyT7UVzr7r0THE9hr60eRSlbuXYl9354LzPGD+W993ekRvWaYUr03nsX\n+5yjR4fHXKtVg+eeg6OPTmDAIrJVxe1RxG5lnLxlyz8xs5lmNsPM7og6pihE2aMY9904Dn/pMBqO\nmMaYbmuocUVT+PjjYieJmTPh3HOhefPQjxg7VklCpCyJY9twHXCnu081s+rAJDMb5e6zow4smaIY\nelqzfg2PZj7KiM9e5bNP92a35ashcwwcdFCxzvfTTyHhDRoU9qoeNCgsvyEiZUvsKgp3X+LuU/O+\nXgnMBnYv+F2pJ9mJYuqSqTTo3oAdRnzMlJdht2PPCGt2FyNJrFoFTzwR3lq1KsyZA3feqSQhUlaV\npEdxjbv3SXA8m15jH2AMcFBe0tjwc/UoEmR97nqeGfcMPT/pwIdf1mW/eT9jffpAo0ZFPldODvTt\nG4aXjjsurOy6v+bti8RG0vfMBgaU4L1blTfsNABomT9JbNA236/cGRkZZGRklGY4SZeMHsWcX+Zw\n7bvXcvK8dcx9YxsqXHAEvPXfYu0dOmpUaFRvuy0MGFCsPCMiCZaZmUlmZmaJz1PimdmlwcwqAsOA\nke7ecTOvp3xFUZpyPZfOEzrz3KjHGD7tIA768lvs1VfhtNOKfK6sLGjdGr75JkzQvvBCzagWiatU\neurJgJ7ArM0liXRRWj2KBcsWcGqfU5kzpAfzX6vOwdX3w7Kyipwkvv8emjWDM86A886DWbPgoouU\nJERSUewqCjM7HvgUyAI2BHe/u7+f75iUrygS3aNwd7pP7s5jHzzA4OkHcdSY+VjXrnDBBUU6z++/\nh8rh5ZfD465t2miynEhZEUWPolS4+1hiWOkkWyJ7FN///j3XD72ef8xayNcDt6fyoTtD1kDYaadC\nn2PdOnjllbA/xFlnwdSp2oJUJF3ErqIojHSoKBLB3emb1Zf7R9xN/9kHcsIHc7COHeGyywo9RuT+\n9zyIffcN1cThh5dy4CJSKlKmopCgpPtRLFm5hObDmlMpaxZfD9mBKvtvD9Omwa6FX+h33LiwN8Sq\nVdClS+hHiEj6UUURU8XtUbg7b898m7uH30Hv2XU4ZcQcrH17uPrqQlcRc+aECmLy5DBx7soroVza\nDwaKlH2qKFJMcXoUS7OX0mJ4C9ZPnczc93agWq3qYUegPfYo1PuXLAlVzMCBoZJ4440S70ckIilA\nvyfGVFGHnQbMGkD9Lodw44ifGNz9D6rd2RqGDy9Ukvjjj3C9gw6C6tXD3hCtWytJiEigiiKmCtuj\n+Dn7Z24beRurJk9gzns7UH2PamHMqBCPJK1bB927hyeZTj017A2xzz4ljVxEUo16FDFVmB7FwFkD\naTXsVrrP3J8zR8zDnn46zILbSi/CPSyz8cADsN9+YeOgI45IYPAiEkvqUaSYgnoUv6z6hdtG3Maq\nieOZPXx7qu+5XaGriDFjwrDSunXw0kvFWrVDRNKMKooyZtDsQbQa2oLu0/fljA+/wZ55Bq69dqtV\nRFZWeJJp9uzwJNNll+lJJpF0kzJrPUmwaX/il1W/cPnAy+n32p3M7r0tZy6viU2ZAtddV2CSWLgw\n5JHTT4czzwyJ4oorlCREpPBUUcRU/h7FgFkDuGfobfScujenfPIt1qFDmNxQQIL49Vd46il47TW4\n9dawBPh22yUpeBGJJfUoUsyjj4Z5EbeNuI1y4ycwa2hlqh66J0wbUuDs6lWroFMn6NABLrkEZsyA\n3XZLYuAiknKUKGLI3al78Vs06tSS3hNrcfwXa7AXOod/+bdg/Xp49VVo1y7sLvf551C7dhKDFpGU\npUQRM0tWLuGW4bew4PmTmLWkIpWPrwvT39/iSq8bFu174IEwt27wYGjYMMlBi0hKU6KIiQ0rvbYb\nchf9v6zF0RMGU3nYAXDuuVt8zyefwH33wdq18MILYdE+bRwkIommRBEDi39fTPNhzdlv3CxmD65A\npX8fzaNt/txikpgyJTzqOn9+eNS1SRM9xSQipUdPPUXI3ek5pSfth7ThnbG7c/DCVVj3HnDyyZs9\n/uuv4eGHITMTHnoIbrwRKlVKbswiUnZpHkUZs2DZAk7vcxoLuz7J9JeMQ448G8ua/leSyD+PYsmS\n8Ihro0Zh4b7588P3ShIikgyqKJIs13N58csX6fnuIwzM3IX9VlXCevSEBg02Os4Mli+HZ54J+1Nf\nd10YbirC7qUiIhtJqXkUZvYqcC6w1N0PiTqeRJn7y1xufLcZF37yIxPfhwp3XR0WXqpYcaPjVq8O\nM6kPOADOOy/0JPbaK6KgRSTtxTJRAK8BnYE+UQeSCOtz19Ph8w4MHfQUA0btwK419sTGjYC6dTc+\nbj306hXmQjRoEHoRBx4YScgiIn+JZY/C3T8DlkUdRyJk/ZTFCS81ZPcO3fi0T3l2a9EaGzNmoySx\nYdnvgw/C2oIlAAAMZklEQVSG118PXx96qJKEiMRDbHsUZrYP8N7mhp7KQo9izfo1PPHpE0wZ0Jm+\n71elxqENsRdf3GjHOXcYPTr0HtzhySf/ngtR3D2zRUS2JKV6FIXRNt9jQRkZGWRkZEQWy6bGLx5P\ny7euo+37a2g7swrlX3gBGjfeaDbchAlhNvWiRWEuxMUXbzwXojh7ZouI5JeZmUlmZmaJz6OKIoGy\n12bz0McPseLNXnQZWY4q/74Ie/ZZqFHjr2NmzYIHH4SJE+GRR8LTTJv0skVESoXmUUTso/99xOlP\nH8iVbQfS/YudqPrOYKx797+SxMKF0LQpZGSERfvmzQsT5raUJAqzX7aISDLEMlGYWX/gc6C2mS0y\ns6ZRx7Qly1Yv44bBzfik9SVkdlzOUWc2pfy06XDiiQAsXQotW0L9+mGn0vnzw94QVaoUfN527ZIQ\nvIhIIcSyR+Hul0cdQ2EMmj2ILq/eTI9h5dhrhzpUGNvzr0eVVqyA9u2ha1e46qqws9zOOxf+3OpR\niEhcxLZHUZCoexRLVi7hrndv4cQ+n3L9pBwqPvnfMI5UrhyrV0OXLvDss3DOOWEIaZ99IgtVROQv\n6lEkgbvTa2ovbrurLp3bZHLj9hlUnDEbmjdnXU45unULs6k//zxMluvVq/hJQj0KEYkLVRSFtGDZ\nAlq/0ZRr+2ZxxuJtqPRydzjvPHJz4e23w6que+8d5kIkYuMgzaMQkURLu3kUyZKTm0PnCS/w9fMP\n02u0UeXa6yn3+BN4teqMHBHmQlSqFBbuO/XUxF1XPQoRiQtVFAWYsXQGj71yJfe/vpB629Si8qu9\noX59xo4NCeLXX8NkuQsu0M5yIhJ/6lEk0Jr1a3jsgwcZftXR9O7wPw67uR2VJ01lWvn6nHtueIrp\n+ushKwsuvLB0koR6FCISF6ooNvHFoi94uf1l/GfAb9SsfzxVur7C12tq8cgjYY/qBx6Am26CbbYp\nlcv/RT0KEUk0VRQltHLtSu5/80YWNj6Vl97KZo8ufVjWbSS3PFlro53lbr+99JMEqEchIvGhigJ4\nf/5IRj16NY+MzGabK65hVev2PPPStnTvHoaY2rSBmjUTdjkRkUiooiiGX1f9Susu57P9ORfxaNYO\nVBr6Gc/t0Y06R23Lb7+FHsQzz0STJNSjEJG4SMuKwt0ZMOV1vr3/Fm4Zvx57oC29q9zNE09X4MQT\n4bHHoHbtBAZcDOpRiEiiaR5FIX3/+/d0bX8p178ykVMOa8Sox/txd8da1K4Nw4aFxfviQD0KEYmL\ntKko3J2+Hz9Pxfse4OzvtmHuDT24adglVK0KTz0Vlv8WEUll6lEU4Jtfv+bp5gdx7kVtOHzPi2my\n/2KaDr6Edu3CukxxTBLqUYhIXKR0RZGTm0Pvdx7igAfbs1/uLnTYaxAD/teQdu3gmmugfPkkBFtM\n6lGISKKpotjErO+n0uOifbjo+vZ8vXNrjvrjW/b4V0PmzQs7zcU5SYB6FCISHylXUazLWUf/ri04\n+onX+HX7g2i+dCj/arE3rVtvtHW1iEja0VNPwIw5nzH3xgs5I2slbSq/yDYn3cQH7Yzdd486sqJr\n21Z9ChGJh5SoKNauX8Pgx6/ixOcHMXK7kxh12CAeaV+DevUiDLKE1KMQkURLqR6FmZ1lZnPMbL6Z\ntSno2JmT3uezQ3fm0M7v88D+g6j95sf0H162kwSoRyEi8RG7isLMygNzgdOA74GvgMvdfXa+Y3zt\n2j8ZeMtFnNp/JK/tej77P96fiy6vrH0hRES2IJUqiobA1+7+rbuvA94Ezt/0oIn778TeQz/n7Vs/\notXswTS+IrWShPoTIhIXcUwUewCL8n2/OO9nG5n8z7OpPeNnbn3mZCpVSlpsSdOuXdQRiIgEcXzq\nqVBjYT+feCCduz4BQEZGBhlxnF5dAupRiEhJZWZmkpmZWeLzxLFH0Qho6+5n5X1/P5Dr7v/Nd0xS\n9swWEUklqdSjmAgcYGb7mFkloAkwNOKYkk49ChGJi9hVFABmdjbQESgP9HT3pzZ5PeUrCs2jEJFE\nS6mZ2e4+EhgZdRxRUo9CROIilhXF1qRDRSEikmip1KMQ1KMQkfhQRRFT6lGISKKpokgx6lGISFyo\nohARSROqKFKMehQiEheqKGJKPQoRSTRVFClGPQoRiQtVFCIiaUIVRYpRj0JE4kIVRUypRyEiiaaK\nIsWoRyEicaGKQkQkTaiiSDHqUYhIXKiiiCn1KEQk0VRRpBj1KEQkLlRRiIikCVUUKUY9ChGJi1hV\nFGZ2CdAWqAs0cPfJWzgu5SsK9ShEJNFSpaKYDlwIfBp1IFErbI8iMzOzVOMoS3Qv/qZ78Tfdi5KL\nVaJw9znuPi/qOOKgsENP+p/gb7oXf9O9+JvuRcnFKlHI39SjEJG4SHqiMLNRZjZ9M3/+lexY4qxd\nu6gjEBEJYtXM3sDMPgHuLqiZneSQRERSQnGa2RVKI5AE2eJfpjh/URERKZ5Y9SjM7EIzWwQ0Aoab\n2cioYxIRSXexHHoSEZH4iFVFsSkzO8vM5pjZfDNrs4VjXsh7fZqZHZHsGJNla/fCzDLMbIWZTcn7\n81AUcZY2M3vVzH4ys+kFHJMun4kC70UafSZqmdknZjbTzGaY2R1bOC5dPhdbvR9F/my4eyz/AOWB\nr4F9gIrAVKDeJsecA4zI+/poYHzUcUd4LzKAoVHHmoR7cQJwBDB9C6+nxWeikPciXT4TuwKH531d\nHZibrv9WFOF+FOmzEeeKoiHwtbt/6+7rgDeB8zc55t9AbwB3nwDUMLNdkhtmUhTmXkABDwCkCnf/\nDFhWwCHp8pkozL2A9PhMLHH3qXlfrwRmA7tvclg6fS4Kcz+gCJ+NOCeKPYBF+b5fnPezrR2zZynH\nFYXC3AsHjs0rq0eY2YFJiy5e0uUzURhp95kws30IVdaETV5Ky89FAfejSJ+NOD8eW9gu+6ZZMRW7\n84X5O00Garn7KjM7G3gXqF26YcVWOnwmCiOtPhNmVh0YALTM+036/x2yyfcp/bnYyv0o0mcjzhXF\n90CtfN/XIvwWUNAxe+b9LNVs9V64+x/uvirv65FARTPbMXkhxka6fCa2Kp0+E2ZWERgI9HP3dzdz\nSFp9LrZ2P4r62YhzopgIHGBm+5hZJaAJMHSTY4YC1wCYWSNgubv/lNwwk2Kr98LMdjEzy/u6IeHR\n59+SH2rk0uUzsVXp8pnI+zv2BGa5e8ctHJY2n4vC3I+ifjZiO/Tk7uvN7DbgA8JTPz3dfbaZNc97\nvZu7jzCzc8zsayAbaBphyKWmMPcCuBi4xczWA6uAyyILuBSZWX/gJGCnvMmZjxKeBEurzwRs/V6Q\nJp8J4DjgKiDLzKbk/ewBYC9Iv88FhbgfFPGzoQl3IiJSoDgPPYmISAwoUYiISIGUKEREpEBKFCIi\nUiAlChERKZAShYiIFEiJQkRECqREISIiBVKiEEkCM6tgZnWijkOkODQzW9KKmdUAbids/rQ9UNnd\nexTxHLWBToQVNy8BFgJfAjcBDdw9dzPvOS3vOCvqe/PeXw5o7+53FSVWkUSI7VpPIqXkVcKyy4sA\nzOx+M2vs7gOLcI7DgX+7+zozuxB4xt3nmtmKLf1DD9Rx99FmdmlR32tmOxDWJjqpCDGKJIyGniRt\nmFkDoPyGJJGnO9C2iKean7fTIEBtd5+b9/WcAt6zIQkU+b3uvszdnwN+L2KcIgmhikLSSQNgnpnN\nI2+VVaA/sJuZVXH31YU5ibtPATCzA4Bv8v186uaOz1vG+avivFckDpQoJJ1UBtYCl7j7NAAzO5zQ\nH9gGWJ23JeTpW3h/b3dfnu/7hoT+wtYc6e4vbfKzwr5XJHJKFJJOxgOtNiSJPN8BP29IAO4+C5hV\nyPM1AD4qxHGbG+Ld6L1mVpWwR8Cm23Vmu/uAQsYjUiqUKCRtuPvnec3rPdx9wzaYNwPtNhyzlYqi\nj7svy/d9A+Dpgq6Z90js3M28tNF787al7LP1v4VI8ilRSLq5ErjDzGYC1YAf3P3NDS8WpqIws8OA\nM4BDgQvNbCBhWOsYYDt3757v8AzCtpRbfK+7L93K9aoRhsfqmVkroLu7Zxfy7ytSYppHIZIAZtYZ\nuMM3+R/KzG53984RhSWSEHo8ViQxpgBHmNlRG35gZrsD32/5LSJlgyoKkVJiZk2AYRomkrJOiUJE\nRAqkoScRESmQEoWIiBRIiUJERAqkRCEiIgVSohARkQIpUYiISIGUKEREpEBKFCIiUqD/A7+mOHWg\nuAd+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1044ef150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import CoolProp, numpy as np, matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "PropsSI = CoolProp.CoolProp.PropsSI\n",
    "for fluid in ['Ethane','Water','R125']:\n",
    "    Tc = PropsSI('Tcrit',fluid)\n",
    "    pc = PropsSI('pcrit',fluid)\n",
    "    Ts = np.linspace(PropsSI('Ttriple',fluid),Tc)\n",
    "    ps = PropsSI('P','T',Ts,'Q',0,fluid)\n",
    "    plt.plot(Tc/Ts-1,-np.log10(ps/pc),label = fluid)\n",
    "plt.axvline(1/0.7-1,dashes=[2,2])\n",
    "plt.xlabel('$\\Theta=T_c/T-1$')\n",
    "plt.ylabel('$-\\log_{10}(p/p_c)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, we can express the slope of the line as:\n",
    "$$ m = \\frac{(\\omega+1)-0}{(1/0.7-1)-0}$$\n",
    "or\n",
    "$$ -\\log_{10}(p/p_c) = \\frac{\\omega+1}{1/0.7-1}\\Theta $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEVCAYAAAD+TqKGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmcjeX7wPHPPYxtZFeWklL2IlIKNUmylfwUopSUtZAW\nfMvWJkUlFbJLZN+NtY6yJuvYd9mJQdbZrt8f98hYZj/LM+dc79drXubMec7z3HN6Otdc93UvRkRQ\nSimlEhLk6wYopZRyNg0USimlEqWBQimlVKI0UCillEqUBgqllFKJ0kChlFIqUY4LFMaYEsaYdfG+\nzhhjOvi6XUopFaiMk+dRGGOCgEPAQyJywNftUUqpQOS4jOI6NYDdGiSUUsp3nB4omgDjfN0IpZQK\nZI7tejLGZMJ2O5UWkRO+bo9SSgWqjL5uQCJqA2tuFiSMMc6Mbkop5XAiYlL6Gid3Pb0IjE/oSRHx\n66+ePZN7XE+ft9UpX/pe6Huh70XiX6nlyEBhjAnBFrKn+rotvtK7t69boJRSliO7nkTkPJDP1+3w\npZ49fd0CpZSyHJlRKOjVK3nHhYaGerIZ6Yq+F1fpe3GVvhdp59hRT4kxxkh6bHdK9OqV/GChlFLJ\nYYxBUlHM1kDhUMaAn/+KSikvS22g0K4nh9IahVLKKTSjUEqpAKEZhZ/R+oRS6or9+6FrV4iN9c31\nNVA4lM6jUErFxMA330DFipA9u+8ChSPnUSitUSgV6DZsgNdfh5AQWLYMSpTwXVu0RqGUUg5y8aLt\nURgxAvr0gddes6Mg3UFrFH5GaxRKBZ5Fi+C++2DfPti4EVq2dF+QSAvNKBxK51EoFTj++QfeeQdc\nLvjhB6hb1zPX0YzCz2iNQin/JwJjx0LZspAnD2ze7LkgkRaaUSillA/s3Qtt28KRIzBsGFSq5Plr\nakbhZ7RGoZR/io6Gfv1sYHjiCfjrL+8EibTQjMKhtEahlP9ZswbeeMN2Mw0ZAsWKeff6mlH4Ga1R\nKOU/zp+3xeo6daBTJ1i40PtBIi00o1BKKQ+aPx/atIEqVeDrryF/ft+1RTMKP6M1CqXSt+PHoVkz\nW7AePNiObvJlkEgLDRQOpWs9KZU+icDo0XbiXKFCEB4OTz/t61aljSPXejLG5AKGAWUAAV4TkZW+\nbZV3aY1CqfRn507bzXT6NISFQYUKvm6ReziyRmGMGQ0sEZERxpiMQIiInIn3vNYolFKOERkJX3xh\nV3r94AN46y3I6KY/w2NjYeJEyJkTatdO27n8pkZhjMkJVBOREQAiEh0/SAQKrVEolT4sWwYPPACr\nVtnhr2+/7b4gATBpEnz1FeTI4b5zppTjMgpjTHlgCLAFKAesATqKyIV4x/h9RqHzKJRyttOnoUsX\nmD0bBgyAhg3dt4Dfn3/CoEHw448QFGS/3HFuv8kosHWTCsAPIlIBOA909W2TvE9rFEo5k4jtCipT\nxn6Ab94Mzz/vviARG2t3s3vkEXvODBl8v4KsE4vZB4GDIrI67vFkbhIoesXrmwkNDSU0NNQbbfMa\n7XpSynn274d27ey/kybBo4+657yHDtmRjg8/bJcW//VX95zX5XLhcrnSfB7HdT0BGGN+B14XkR3G\nmF5AVhHpEu95v+966tVLg4VSThEdbbuX+vSBzp3h3XchU6a0nzc21mYl06bZGkeXLpA7d9rPm5DU\ndj05NVCUww6PzQTsBloE2qgnrVEo5QxX1mfKndtOnLv33rSfMyrKFqjHj7eLArqz+J2Y1AYKJ3Y9\nISIbAIevp+hZWqNQyrfOnYPu3e2H+RdfwMsvp71WEB0NMTEQHAynTsEvv3gvSKSFE4vZCu12UsqX\nZs2yxeqICNi0CZo3T3uQWLzYnnPSJNvd1LcvlCzpnvZ6mgYKh9JAoZT3HT5sRzB17gwjR8KoUZAv\nX9rOefCg/TdbNhg40K7/lN44skaRFK1RKKXcKTbW7g/Rowe0bm1nV2fNmrZznj8PDRrYrOTPP30/\nxBX8rEahtEahlLds3GiDQ1AQuFy2eygtdu60WUju3Hbl2Hr1nBEk0kK7nhxKu56U8qzz5+1w1Bo1\n4LXX4I8/0h4kvv/eTpRbt84+btDAFq7TOw0UDqWBQinPmTsXypa19YPwcDv8NSiVn4anT9vNicAu\n2rd9O1Sv7r62OoHWKBxKaxRKud/hw3Yr0jVr7FpKNWum7XwnT0Lp0rYA/v337mmjJ/nTWk8KrVEo\n5U4xMfDDD1CuHBQvboe8pjZIREfD8OE2G8mb1wad9BAk0kIzCqWUX1u/3harM2WyM6vTWofo1MnW\nIIYMST/zIK7QjMLPaI1CqbQ5fx7ee89mDq1awZIlqQ8SS5ZA//72+08/taOj0luQSAsNFA6le2Yr\nlXqzZ9ugcPSo7WZq2TL1xeqDB22xu1Ah+zgkJP0Pd00pnUfhUFqjUCrlDh2Cjh1hwwYYNswOfU2N\nPXvs5Lvu3aFECdi2LfWBxh8E8K/ubNr1pFTyxcTAd9/ZYnWpUnYSXWqDBNgRUcWLQ+HC9nEgBwnQ\nYrZj6X4USiXP+vW2BpEliy0wlyqV8nP8+y/062czkmHD3N9Gp9Bitp/RGoVSifv3X7t439NP21FN\nLlfKg0R0tP337Flbi/jwQ7c30y9ooHAorVEodXMidke40qXtng6pLVb/8ovdhGjHDtvFNHw4FC3q\nkSane9r1pJRKN/bvhzffhF27bB0hNDRlrxex2UPOnDB0qM1Aqlb1SFMdSbue/IzWJ5S6KirK7jJX\nsSJUrmzrEikNErt2QbVqdm4F2CGvgRQk0kIzCofStZ6UspYvtzWIQoXsMhzFiqXs9bt329dERNid\n65o1gwwZPNNWp/Or/SiMMfuAs0AMECUiD/m2Rd6nNQoV6E6dgq5dYc4c+OoraNQo5RPdOna0tYi1\na20donlzz7TV3zm160mAUBF5IBCDBGjXkwpcIvDTT3ZmdebMsGULNG6c/CBx4oR9DdhVXXfuvDof\nQqWOUwMFQIBNkr+WBgoViLZvhyefhK+/hpkz7R7TOXMm//XLltk1mK7sD1GtGuTI4Zm2BhJH1iiM\nMXuAM9iupyEiMvS657VGoZQfuXQJPvvM1iC6d4f27SFjMjvGIyNh4kRo2tSe5+hRuPtuz7Y3vfKr\nGgVQRUSOGGPyAwuNMdtE5I/4B/SK9yd3aGgooSkdAuFwWqNQgWLhQmjXzi6/sWFDyruJnnwSbrkF\n6ta1+1RrkLjK5XLhcrnSfB5HZhTxGWN6AudEpH+8n/l9RqGUvztyxM6sXrnSdjHVq5e814lAWJjN\nOGrWtDWJ/Pk921Z/4TfzKIwx2Ywxt8R9HwLUBMJ92yrv0xqF8lcxMTYw3H8/3HUXbN6c/CABMH06\nvPvu1eK2BgnPc1xGYYy5C5gW9zAj8LOI9LnuGL/PKLRGofzR6tXQpo3tKho0KPlrM23ZYleHHTDg\naoBIbg1DXeU3NQoR2QuU93U7fE1rFMqfnD4NH3wAU6bAl1/CSy8lf7iriF0dtkED+31wsGfbqm7k\nuIwiOQIho1DKH4jAuHF22Yxnn7Ujm/LkSfp1J09Cnz52LkWLFvY8gbarnCf4TY1CWVqjUOndtm12\n86B+/WDqVBg8OOkgceXvvyVL4MIFqFXLPtYg4VuaUTiU1ihUenXxos0cBg2y+zu8+WbS9YSYGPjx\nRxgxwq7tpN1LnuE3NQplaY1CpUdhYTYwVKiQvDkRsbE2SGTIAFu32qxDg4TzaEahlEqzgwfh7bft\n4nvff3+1yygxy5fboNKuHbz+uufbqLRG4Xe0RqHSg6gou7Jr+fJ2jaVNm5IOEv/8Y/+NjYX//c/u\nTqecTTMKh9IahXK6pUttNnDbbTaLKF488eMvXoSXX7YL/23YkPKtS1XaaUbhZ7RGEXimbJlCuznt\nfN2MJJ04Aa+9Bk2a2GL1ggWJB4mDB+08iqxZ7VyIVas0SKQ3+p/LobTrKXBcjr5Mh7AOvLfwPV57\n4DVfNydBsbF2ZFKZMpArl50tndRmQiNG2MX+Vqywj5s1g2zZvNNe5T466smhevXSYBEI9kbspfHk\nxhTOUZi1rdeSK0suXzfpptauhbZt7eikhQvth39CLlyAP/+0e1pXqwYbN+rGQemd1igcSmsU/m/G\nthm0mt2KrlW60qlyJ4wDZ5WdOWP3h5gwwc6UfvXVxLuNTp+G++6DJ56A0aN1opzT6DwKP6M1Cv8V\nFRNF10Vdmbx1MjOazKDy7ZV93aQbiMD48XaV1nr1bDdT3rwJHztlCjzyiM0cfvsN7rnHu+1VnqUZ\nhVJedODMARpPbkzurLkZ89wY8mZL4NPXh7ZutTvMRUTY2dWVk4hj3brZrUdHjbJLhyvn0lFPfkbr\nE/5n7s65PDj0QeqXqM+sF2c5LkicP28/9KtVg+ees0uCJxQk1qyxy36Dfc1ff2mQ8GcaKByqd29f\nt0C5y5WuplazWjH5hcl0qdqFIHPj/3rHzh0jMibS6+0TsYv2lS4Nf/8N4eHQoUPC6zMdPWqHuWbK\nZB/nyKHDXf2d/ud1KK1R+IcDZw7wxOgnWH90Petar6PandVuety0rdO4b9B9LP17qVfbt3Mn1Klj\n50OMGgU//wwFC9543JEjdnLd9u1QoADs2WP3iFCBQQOFQ2nXU/o3d+dcKg2tRN176zK32Vzyh9y4\nZ2dUTBQABbIXYP5L86l+V3WvtO3iRejRwxagq1eH9evtSKWE9Otn5z9c2XZUd5cLLFrMdiidR5F+\nRcVE0f237ozdOJZxDcfx2J2P3XCMiDD4r8F8s+obNrbZSOaMmb3WvtmzbddSxYrw9ddw++03HnPp\nkq1B7NplV3RV/kGHx/qZ3r01UKRHB84c4MUpLxKSKYS1rddya8itCR679/RepjWe5rUgsXcvdOxo\nNxQaPBhq1rzxmNhYW284edJOmtN7UIGDu56MMRmMMeuMMbN83RZf0BpF+nOlq6nOvXUIaxZ2Q5CI\niY2h//L+9HL1whjDF099Qen8pT3ersuX4ZNP4MEH4eGHbbH6ZkFi1iw7WW7zZjsfYuJEW+BWyskZ\nRUdgC3CLrxviC/qXXPoRFRPFh79+yM/hPzPxhYk37WoC2HxiM/N2z2NwXe/15cyfb/d8KFPGDmkt\nWvTGYy5csPWHAwdsLUKDg7qeI2sUxpjbgVHAp0BnEXnmuue1RqEc4e8zf9NkchNyZsnJmOfG3FCw\njoyJ5MtlX9Ls/mYUzVXUe+36224ktH49fPst1K174zH790ObNnDrrXa5DeX//G3C3dfAe0Csrxvi\nKzqPwvlmbp9JpaGVqF+iPnOazrnpqKbuv3Zn+cHlBAd5Z3/Py5ftftUVKtiF+zZvvjFIHDpk/82R\nwy7PMXSoV5qm0jHHdT0ZY+oBx0VknTEmNKHjesX7czs0NJTQ0AQPTZe0RuFckTGRdq2mLZOZ2mgq\nVYpUueb5i1EXmbtzLg1LN6RXaC+yZMzilQX/5s+Ht96CUqXsrOq77rrxmA8/tMtyrF0Ld95pl+pQ\n/svlcuFyudJ8Hsd1PRljPgNeBqKBLEAOYIqINI93jN93PSln2huxlyZTmnBryK2Mqj/qhmU4omOj\nqfhjRYrnLc74huPJGOT5v8WS6mY6e9bOpi5eHBYvtktt5L8x+VEBwG+6nkTkfyJyh4jcBTQBfo0f\nJAKF1iecZ+rWqTw87GEal2nMzCYzrwkS5yLPceDMATIGZWTSC5OY9MIkjweJ5HQzrV4N994LkybZ\nx08+qUFCpZzjMor4jDGPA++IyLPX/dzvMwrdj8I5LkVf4t0F7zJn5xx+afgLD9/+8DXPhx8L59lf\nnqV1xdZ0rdrVK22aN89OmitVCr755tpuppgYmDkT6te3E+d277bDXpVKbUaR7EBhjAkBmgFlgQzY\nbqFY4BywEpgkIl4pPgdCoNBRT86w4+QOGk9uzD157mHoM0Ov2YHuQtQFsgVn48ylM6w8uJKn73na\n4+3Zv992M23cCAMG3Hw009NP25Vgp0+HfPk83iSVjng0UBhjngJKA7NFZPd1zxmgHFADWCQi61Pa\niJQKhEChfG/sxrG8Pf9tPgr9iDYPtrmmID1351xaz27NrBdnUb5AeY+35dIlO8fhm29sJvH++5Al\ny9Xnly6FyEi7btPBg3bCnO4up67nsSU8jDFZgL0isvBmz8d9Yq8H1htjNMF1E80ofOd85HneCnuL\nZQeWsejlRZQrcOMG0REXI/ipwU9eCRKzZ9ulN8qVs/s+XD9pbs4cu7Lrt9/axzdbu0mptHB0jSIh\ngZBRaI3CN8KPhdN4cmMqFa7E93W+J3um7IBdxG/i5omMWD+CsGZhN91Pwt1274ZOnWDHDhsEno7X\ns7Vvn120r08fe6/ExEBm760rqNIpn416Msa8Effvg2k9l7pK51F4l4gw5K8hVB9Tna5VuzL6udH/\nBQmwcyfGbRrHR6EfeTxIXLgA3bvbdZmqVrVrM8UPEiLQtCmEhEB0tF3yW4OE8qQ0ZxTGmMbAROAB\nEVnrllYlfU2/zyiU95y+dJpWs1qx4+QOfnn+F0rmKwnY4DFq/SiyBmelSdkmHm+HCEybBp07230i\nvvzyajfSv//aJcGLFoXmza+u8qpUSvhyHsUK4FvA8521AUTrE96x6uAqKgypwG0ht7Hy9ZX/BQmA\nBbsX8N3q7yiVr5TH27Ftm80aevSwO82NH39trWHhQru7XNWq9rEGCeVNKc4ojDHvAHWAAsAMoKeI\nRHmgbYm1we8zCq1ReFasxNJveT/6r+jPkHpDeK7kc//9fNT6UTQu05hswdmIkRiPTpz791/4+GMY\nORI++MAuqREcbDOG8ePtchuLF2vXknIPb25ctF1E+scNi60OdAd6pOI8KhFao/CcY+eO0Xx6c85H\nnmf1G6spkrPIf8+1nd2WTSc2UbNYTUIyhZDReCZIiNj9qbt0gaeesnWIAgXsz2Ni7B8KLhd8+qkG\nCeV7qckoXgcOA7+LyDljzDMi4tXNhQIho1CesWjPIl6Z/gotyregV2gvMgZlJDo2mg1HN1CxUEWO\nnjtK/mz5yRCUwWNtWLfOLt536RIMHGjrEVd+3qkTNG5sh7sq5W7ezCjuAHIBLYwxeYGMxpicQGER\n6ZuK86mb0HkU7hV/H+sxz43hybufBOwaTU+MfoJCtxRieuPpFMhewGNtOHnSrt46dardce611yBD\nBjhzBnLmtN1Qr7xii9VKOUlqMooKQFYRWRb3uBjwKPC6iDzu/ibetA1+n1FojcJ99kbs5cUpL5I3\nW15G1R9F/pD8RMZEEhkTSfZM2Vm0ZxFP3vWkx5YCj4mBH3+0gb9RI/joI8id2y7q17YtLFsGW7bY\noKGUJ3ls1JMxpoQx5t4rj0Vk7ZUgEfd4t4j8hF3pVbmJ1ijcY8KmCf+t+Dr7xdnkD8nPxmMbqfhj\nRUasGwFAjbtreCxILF1q96oePx4WLLBdTbGxNovIlMl2O61apUFCOVuSGYUxJiMQCpTALgK4WkT+\n8nzTEm2T32cUKm3OR56n47yO/L7/d8Y3HE/FQhUREYwxbPtnG2sOr6HpfU09FiAOH7aF6t9+s/Mh\nmjSxWeIvv9g9rIcOhQYNPHJppRLksYxCRKJFZJGIfC8ig4AgY0xbY0x7Y0yNuECi3EzrE6m34egG\nHhz6IJExkaxptYaKhSryx/4/KDe4HAfOHKBkvpI0u7+ZR4LE5cvQt6/dHOj22+38iOeft1kDQPny\nsHKlBgmVvqRpZrYxpiTwOJAJOATMF5HzbmpbYtf1+4xCaxQpJyJ8u+pbPvnjE75++mteuv+l/577\n8NcPebDQg//Nl/CEOXPsqKVSpeCrr+Cee2yBumJFKF3azrrWFV2VL3l8P4pkNKAQUE1EJrjlhIlf\ny+8DhY56SpkT50/QYkYLjp8/zviG4ymWpxgLdy9kzs45fFPrG49ee8cOGyB277bLgNeqZesRZcva\n5b7Dw3XjIOUMXlvCwxjzjjFmsTFmszHmM2NMMICIHPZGkAgUGiSSb9GeRZQfUp6yt5Zl6WtLKZan\nGBEXI+i8oDO176ntseuePWv3hXj0UbsPRHg41K5tZ1p36GDrFKBBQqV/qRkeW09EZsebmf24iHh1\nZrZmFArsiq7df+3O2PCxjH5uNDXursGMbTModEshKhWu9F/x2t1iY2HsWOjWDWrWtEt9nzkDv/8O\nb7wBp05Bjhx2VVelnMSbiwIWMMbUAUJEZDGwOhXnUEno3dvXLXC2nSd3UmVEFTaf2Mz61uupcXcN\nxm4cy3sL3yM2bkdeTwSJ1auhShW7F8TUqXaNpowZITTUZhgAefJokFD+xXEzs+N21FsCZMYWyWeI\nSLe0nje90XkUNycijNkwhi7z3uGDJ3rSvlJ7Fu9dTI27a9CwVEMalmpI1uCsbr/u0aM2g5g/366/\n9MwzdthrrlxQogTs3Xvt1qRK+ZPUZBQzgBUi8oKIVAdaAAa7omyaicgl4AkRKQ/cDzxhjKnqjnOn\nJ9rtdKMzl87QbFITznR/jx0LSvLWw2/RclZLOi/ozD8X/iFrcFa3B4nISBsQypaF/PntcNcWLeCz\nz+D0advFBBoklH9LzoS7zMAtIvJPEscVADKJyN9ua5wx2bDZxSsisiXez7VGEWBWHFhBp5GNGDMl\nlnty3s3xIV9RsFQlNhzdQKn8pciUIZPbrzlnDrz9ts0Y+va1s6zDw+3sahEd6qrSH48OjzXG1ANy\nANNE5OJNns8NvABsFZE/UtqIm5wvCFgLFAMGicj71z3v94FC51FY0bHRfPbHZ+wY8zXDZkJMm9Y0\nKLaanCF5mPTCJI9cc9s2u8vcnj12V7nateHQIVuo7t0bKlXyyGWV8jiPrh4bN8qpIPC2MeZWIAsQ\nDMQAF4CDwFAROZPSBiRwvVigfFztY74xJlREXPGP6RXvz+3Q0FBCQ0PdcWnH0BoF7Du9j1cnNqX9\ntEP8b1M2zKSxZKhWlRfWj6LFAy3cfr3Tp+3Q1jFjbD2ibFm72muhQlCuHMyd6/ZLKuVRLpcLl8uV\n5vOkdWZ2EeA24Jg7u5yuu0Z34KKI9Iv3M7/PKALd+PDxDPipPdNnZCPb3SVoXPtfXn6iE03va2o/\nscuWhSJFkj5RMsTEwPDhdhvSZ5+1/95+OwwYYDcTeuEF3XpU+Qevz8w2xrTGjkw6hx0FFSsiaZ4C\na4zJB0SLyGljTFZgPtA7bijulWP8PlAEao3i38v/8ubc9tw2dSGfzr1E8MefMrfGneyO2EP7h9oT\nNPA7+wk+YYJdljWNliyBjh3tfhAffGADRlAQjBunNQjlf3wRKGqIyKJ4j58Qkd9SdbJrz3sfMBo7\nIisI+ElEvrzuGL8PFIFYo1h5cCVtxjVl8NwM3H84hndfK0yfTrPJmTkHLF9uJzCcPAlZs0K2bGm6\n1r598N57dl5E9+52E6HTp2HIELv7XEiIe34npZzEmzvcXXHWGNMPyAacAdzSgysi4UAFd5wrPQuk\nGsWVgvWKKQNYOj0T2evU58WWR3iqbH1yBGe31eSICPvnf968abrWuXPw+ecweLBdn+n+++0yHI8/\nbhfx69rVTb+UUn7EbYsCelMgZBSBYm/EXppPacarC47z0q8n+f39xjz1/mA7geHUKVskWLECHnoo\nTbv7xMbCzz/bInXVqnYtpkcfhbAwW+644w43/lJKOZQ3l/C4csFC8b4KG2NeSvpVKrn8vT4hIvy0\n4See7V+RnwedoOmhPFRpm4mIutVh+3a7NvfAgfbgRx5JU5BYscKe4rvv7LpMy5fDrFn2udq1NUgo\nlZS01CjqA68AG+J+VEJEmrqrYUlc2+8zCn+uUURcjKDd3HbkXbCMLyefJrpdG27p1YcL50+TLUde\n2820aJHd8ScNFeUDB+wuc0uWQLNmdjZ1ZCRs3AiVK7vxF1IqnfB6RiEiM4B2ItJbRHoDnVJ7LnUj\nf61RuPa5qDzwftqP2MSns87TpGlmNrf+PwgLI1uZ8vZTPHduOyY1lUHi/Hn7/pUvb+sOFSva/SH+\n+cfWwDVIKJUyqVlmvEv8xf+MMXcAnwLjRGSem9uXUBv8PqPwN1eWBF83byQTpmUk9yNPcOyLnmTO\nk59cWXPDTz/ZPqA0TJyMjbXDWrt1gzJloGVLG29274a77tK5EEp5M6PIa4yZY4wpHff4HeAToGAq\nzqUS4E81iq0ntvLIjw9z75jZTB52lk+qxHBhxBBum/UruZ5tZPvYXn45TUHiSh1iwAB45x3YsAGi\no+1zxYppkFAqLVKTUTwvIpONMfVFZIYxZhrwPFBLROZ4pJU3tsHvMwp/qFGICD+s/oFBs3owZ9Ft\nFCEniz9uQeXHmpI9ytjJC92722FHqbR/vx3S6nLBww/beXhBQXD5MmTP7r7fRSl/4M2M4gFjTHug\nlDGmGFAEu/aTTlFyo/Reozjy7xHqjKvDrpH9+X3gOTbemQWzcCE1lh4m+9TZdkbbhAmpDhLnztl1\nmCpUgOLF4c47bfdSVBQEB2uQUMqdUpNR3AY8DIQDdwObsXtSrBGRBW5v4c3b4PcZRXo2bes03pnW\nhgkr7+CBjScY9U51mrX5gaxTZ8L48Xac6u23p+rcsbEwerRdbqNQIWje3M6JiI7WXeWUSoo3M4oT\nQD7gfaC4iBwVkT7eChKBIj3WKP69/C8tZ7Rk+LB2/DbwX4oE5yXjkt95/WghskYDjRrBtGmpDhIu\nl13ie+hQO6u6UCGoXt0+p0FCKc9JTUbxLnAIOI7dFjWviPT3QNsSa4PfZxTprUax7O9lvDr1ZT5f\nm5das7Yy763aPNPzZzLVfRbuvhu++CLV/UG7dsG779qJcgUKwMqVaV7qSamA5M21nnbGzaG4cuHG\nqTiHSkJ6qVFExkTS29WbuYsHMW2qoUyBOzBhi2h48iRkyGQziKyp2540IsLuDzF6tA0UISHw4oup\nPp1SKpVS0/V0jzHmIWPM3caYUOwudMrN0kPX09YTW3lkWGVyT53LooFnOflkZWKHDoV69WDrVntQ\nKj7Vo6Ls6h3FisGUKXY70m7d7FpN9erp8t9KeVtqup6yA+8ClYBNQE8RueSBtiXWBr/venLyfhSx\nEst3f37KZ5ltAAAVT0lEQVRH/7ndmb6kIOWPBxHd40OCa9e1GzscOJCqBZREYPZsOw+iaFFo0gTO\nnoW2bSFzZvf/HkoFGq/vRxHvwk+LyPw0nSTl1/T7QOHUGsWBMwdoMaMFd63ZQ6/R+zhbpwalqj5n\n+8qmToVq1VJ13nXrbOawcSNkyWLnRwQHu7nxSgU4j9YojDHtsAsAXrjJ06WAAim9sEqc02oUIsL4\nTeN5Z0Z7pm0sxcPLLhPxxTcUbtXBrpHRoAEUTPnk/MOH7cJ98+dD797w3HO2DqFBQinnSFZGYYyp\nASwRkaibPFdbRMI80bhE2uP3GYWTnLxwknZz23Fy+WIGjougwIOh5M5ZwG4Pt2kTZMqU4nOePw/9\n+tkvEbv0RsuWHmi8Uuo/Hp1HISKLrg8Sxpjn457zapAIFE6pT4TtDKPc92V5OewwYaNjKNj9S3LP\nWgR168KaNSkOEjExdl/qu+6y9e4pU2DpUg0SSjlZWvajeEVERru5Pcm9tt9nFL6uUZyLPEfn+Z1Z\n+fs4hk+J5sFby2GyZLULKvXtm/QJbmLRIujc2fZUlS4Nq1bpYn1KeZPX96PwFGPMHcaY34wxm40x\nm4wxHXzdJl/wZY1i2d/LKPfD/VQOC2fFj7GUbvUB5udxUKsWfPJJis+3ebPddrRlS+jRAxYvhj//\n1CChVHrhuIzCGFMAKCAi6+OG4q4BnhORrfGO8fuMwhcuR1+m66KuTHcNZvLC3FQ8d4sdlzphApQq\nleLzHTtmA97YsbY4PWXK1SU3lFLe5zcZRdzaUevjvj8HbAUK+bZV3uftGsX6o+upNLQSOWYvZN0Q\nKFOjqR1+1LkzlCyZonNduGBnUhcrZpfaWLMGjhzRIKFUepWWjKK5iIxxc3uuv0ZRYAlQJi5oXPm5\n32cU3qpRRMdG08vVi6GLv+TXNWUpHX4UU6mSXXojhVOgY2LsRnX/+x+cOgWtWtnRTDqTWiln8OZa\nT1dMTsNrkxTX7TQZ6Bg/SFzRK96f3KGhoYSmYXc0J/JGjWLbP9t4Zfor3PPXHrZODuaW+vdjjsVC\nmzYp/nSfOdMGhkKF7Ly7smV1TwilfM3lcuFyudJ8njTPzPYEY0wwMBsIE5FvbvK832cUnhQrsXzy\n+yd8/2tfFm+qQBnXFswHH9huJpEUBYmNG+H99+0IpjJlbD2iaFHPtV0plXp+U6MwxhhgOLDlZkEi\nUHiqRrE3Yi+ho0L5bezHhA/NSJljgrn99qsFhGQGiQMH7BbXjzxiF+o7etTOh9AgoZT/cVxGYYyp\nCvwObASuNK6biMyLd4zfZxTurlGICH2X9WWAqy+zwstSYd5GgkaOhGeesRdL5s4/Z8/aaRQ//AC3\n3GI3q3v2Wfe1UynlOb6oUXiEiCzFgZmOt7mzRnHo7CEaTGhA0Jq1hM/LQ77Lu6BiRZtFJHNRpago\nu/3ogAFQs6btckrFArFKqXTIcRlFcgRCRuEOIsLAPwfS99ePGbe+GI8u2ErwD4OhalW7HWkyuplE\nYNIk+PBD+7hJEztpTrceVSr98ZuMQllp3Y/i6Lmj1PypJsEbN7N1fkFyHN0Ir71m50Yk05w59iWX\nL8PEiTaTUEoFHs0oHCq1NQoRYXz4eN4Pe5vvl+Wi7vITZOz3Fdx7L1Spkqxz/PUXfPqp/bdCBRgx\nAvLmTXlblFLOohmFn0lNjeLQ2UPUHFuT7Fv3sGtGbrIc22dnwDVqlKzXHz0Kzz8Py5fbTYTGjdP9\nqZVSWjR2rJR2O03eMpmHfniAN+ecZNn4rGR5uYVdeS8ZQeLUKRsYypSBfPlgxQro31+DhFLK0ozC\noZJbozhw5gA1x9ak0O7j7PnZkPn8BQgPtxs+JCEqCj7+GD77DO65x67JpPMglFLX04zCoXr3TvqY\nKVumUOH7+2gz5zgLRguZH37UrumdRJAQsQGiVCnbzfTdd3YTIQ0SSqmb0YzCoRKrUew7vY+64+pS\nducZDo+G4Lx5YP2vyZrYsGQJNGwI587ByJEpGgSllApQOuopnZm6dSqvTHiRz//MQZvlUWQoX96u\nwpcnT6KvmzXLdjEdO2bX/OvY0W41oZQKHDrqyc9cX6PYfWo3r896nWIrd3BqXDDBFe+DzT9B4cKJ\nnmf/fmjdGhYsgMaNweXSAKGUShnNKBwq/jyKEetG8ObU1/nur9to4TqNqVUrybGre/bAq6/Cpk3Q\nti288YbWIJQKdJpR+JmePWHria10W9yNe8JWcXL2LWQNfRT2fAcFCyb4ugsX7HpMPXrYkUwrVkCJ\nEl5suFLK7+ioJwcSEaIf+5CHBpSh1fB1fDn2OFn/r5HddDqBIHHpErzyil3Cad06WLvWjmTSIKGU\nSivNKBxmb8ReOi/ozOlej3AkIhfZa1SDfX0SHNEkYmvZHTrYbOLrr22Xk1JKuYsGCocQEVrPbs2k\nFcNYNacwJbZNI/tnMdCtW4Kv+fpr+OgjKFIEhg+3i/YFaY6olHIzDRQOcPDsQVrPakXl8Us5+Fdu\nQmrXoGf1MwkGibVr7VPLltnupgEDdNlvpZTn6KgnH4qJjaH5tOYs+Wsym0ZmJeepC5gpU+yuczfx\n22/QooVdm6lPHzuSKVMmLzdaKZVu+c2e2YFib8Reqg9/jAKjp7JrWDZy1aiHOX78vyARfw7F339D\n+/bw3HNQrBjs2GEfa5BQSnmDZhReFhkTSaNJjTjnWsjssbFkzpwNM28eVKp0zXHGwD//QP36dojr\nW2/ZXeby5fNRw5VS6Z5fZRTGmBHGmGPGmHBft8Wdtv+znfL976X4z/OYOyEDWWrXwxw5ckOQiIiA\nJ56wi/Zdvgy//w7ffKNBQinlG04tgY4EBgJjfN0Qd7gQdYFXpr3CbZPmsnFmJBmKl8SsmAQlS15z\nXHQ0vP8+fPstlCtnl9soXdo3bVZKqSscGShE5A9jTFFft8MdNhzdwJM/VqHLH7F0XhlEhpZv2HW9\n441jjY2FgQNh0CC45Rb4/ns4ckSDhFLKGRwZKPzB6Yun6baoK8UGjOHI0mgy1qyF2TbomkX8RGDu\nXLtYnwhMmgS1a9v6hDEp3+VOKaU8Id0Gil7xPkVDQ0MJDQ31WVuuN23rNFr93JgBv2ahyTohqNdH\n0KWL/fSP8/PPNoM4fhw6d4bu3SE4+Oo5UrNntlJKxedyuXC5XGk+j2NHPcV1Pc0Skftu8pwjRz0d\nO3eMz12fULnXMJ7dJmR58WXMl19Crlz/HbNli90saNMmu+zGF19cGyCUUspT/GrUU3rUf3l/Hupd\nmNc6/0SjrYasP47ADB36X5BYswZCQ+1X/fpw+LBdgiOhIKHdTkopp3BkRmGMGQ88DuQFjgM9RGRk\nvOcdk1GcunCK7tM70uCjCTxyJCMhnd6Drl3/2yvi+HG75PePP8JDD8G8edckGAmKvx+FUkq5g1/t\nRyEi6WIn566LujJ/en9+H5OBkMw5CQqbAY8+CtgA0bw5rFxp12Patg2KF0/+ubVGoZRyCkdmFEnx\ndUZx9NxReo5uQZ1Bi6h5KDNZP+pj19QICuLiRTv6tWdPu431mDFQvbrPmqqUUv/RGoUXxMbG0mZ2\nG95uVZRBHebzTEwxsm7ZCW+9RWR0EG++CbfeCsuX22U3Dh5MfZDQGoVSyik0o0imvRF7+aTfM9SZ\nsYWnT+Uh+6dfQosWxMbCxIl22e+TJ+0w1/feS/v1tEahlHI3v6pROEl0TDQvT32JJ7+axrBVkcQ+\n8wwZVo5DQrIzZLCdHlG4MAwbZrMHk+L/BDenNQqllFNoRpGITcc30bNXKB3nnaZ88B3k6D8Q6tXj\njz/ggw9g+3Y7k3rQoP8GOSmllGNpjcKNLkZd5PUJL3Gx0gNMGnyKR1t9RI4tu/gjZz3uugtq1YKW\nLe1ciFGjPBMktEahlHIKzSius3T/Ur7o8ST9w6IpckdZMo8ayyZzH599BosX24X6Ro6EokU9cvn/\naI1CKeVumlGk0elLp+n+/QsUeeBxJk8U7h48iX9mbqB6x/u4/37Imxd277bbkXo6SIDWKJRSzqEZ\nBTBizTCWfdqGLxZCzpLlOPNTGD2/u5Vx46BaNbsm05NPuu1ySinlE5pRpMLxc8f58sPqNKzaij5/\n5iDrnBV0eWwNt5W9lYULITwcZszwTZDQGoVSyikCMqMQET5f3JvIzz6my3KDebouHxefyPCxmalS\nxW5D2q6d+4a6pobWKJRS7qbzKJLp0NlDzOlQi/a/bOZwxeLM7buAV7sXIXI+TJ4M9er5uoWW1iiU\nUk4RMBmFiNBzcnvu/XQwL242bHmqEw139CNffkPLltC0KWTL5qEGK6WUA2iNIhG7T+5i6lO383bz\nQRQp+BiPlYigwoL+PPa4YflyeP115wUJrVEopZzCrzOKmNgYev74Io17TaHkySB63/YDo80b9OgB\nTz8NRYp4obGppDUKpZS7aY3iOlv+XsPBZ0PptOMcv1RoQtV/hlE0bwgr59q1mZxOaxRKKafwu4wi\nKiaKvp/Xo8PHC4klK3UyhRH65mO0bQt33OHlhiqllINojQLYvGERC8pl59W+C+ma+12Kh5zlnZGP\n8dln6S9IaI1CKeUUfpFRXI66xJR36tLou1/ZmfVWPqi2nk++KkjJkhCUTkOh1iiUUu7mVxmFMaaW\nMWabMWanMaZLYseuX/ATrjIhlBvn4t2cnzKszTEmzCpI6dLpN0iA1iiUUs7huIzCGJMB2A7UAA4B\nq4EXRWRrvGPk8uWLLKldleq/rmFK4WJI37U0aprDp7OplVLKyfwpo3gI2CUi+0QkCvgFqH/9Qavu\nzU7+DeF8dP93VFu9i8bN/CtIaI1CKeUUTgwUhYED8R4fjPvZNZbdXYqCm87Qe0N7Chb0Wtu8pndv\nX7dAKaUsJ86jSFZf2KXHGzJo8OcAhIaGEhoa6sk2eZ3WKJRSaeVyuXC5XGk+jxNrFJWBXiJSK+5x\nNyBWRPrGO8Yre2YrpZQ/8acaxV/AvcaYosaYTEBjYKaP2+R1WqNQSjmF4zIKAGNMbeAbIAMwXET6\nXPe832cUOo9CKeVufrXWk4iEAWG+bocvaY1CKeUUjswokhIIGYVSSrmbP9UoFFqjUEo5h2YUDqU1\nCqWUu2lG4We0RqGUcgrNKJRSKkBoRuFntEahlHIKzSgcSmsUSil304zCz2iNQinlFJpRKKVUgNCM\nws9ojUIp5RSaUTiU1iiUUu6mGYWf0RqFUsopNKNQSqkAoRmFn9EahVLKKTSjcCitUSil3E0zCj+j\nNQqllFNoRqGUUgFCMwo/ozUKpZRTOCqjMMa8APQCSgKVRGRtAsf5fUahNQqllLv5S0YRDjQAfvd1\nQ3wtuTUKl8vl0XakJ/peXKXvxVX6XqSdowKFiGwTkR2+bocTJLfrSf8nuErfi6v0vbhK34u0c1Sg\nUFdpjUIp5RReDxTGmIXGmPCbfD3j7bY4We/evm6BUkpZjipmX2GM+Q14J7FitpebpJRSfiE1xeyM\nnmiImyT4y6TmF1VKKZU6jqpRGGMaGGMOAJWBOcaYMF+3SSmlAp0ju56UUko5h6MyiusZY2oZY7YZ\nY3YaY7okcMy3cc9vMMY84O02ektS74UxJtQYc8YYsy7u60NftNPTjDEjjDHHjDHhiRwTKPdEou9F\nAN0TdxhjfjPGbDbGbDLGdEjguEC5L5J8P1J8b4iII7+ADMAuoCgQDKwHSl13TB1gbtz3DwMrfd1u\nH74XocBMX7fVC+9FNeABIDyB5wPinkjmexEo90QBoHzc99mB7YH6WZGC9yNF94aTM4qHgF0isk9E\nooBfgPrXHfMsMBpARFYBuYwxt3m3mV6RnPcCEhkA4C9E5A8gIpFDAuWeSM57AYFxTxwVkfVx358D\ntgKFrjsskO6L5LwfkIJ7w8mBojBwIN7jg3E/S+qY2z3cLl9IznshwKNxafVcY0xpr7XOWQLlnkiO\ngLsnjDFFsVnWquueCsj7IpH3I0X3hpOHxya3yn59VPTH6nxyfqe1wB0icsEYUxuYDhT3bLMcKxDu\nieQIqHvCGJMdmAx0jPtL+oZDrnvs1/dFEu9Hiu4NJ2cUh4A74j2+A/tXQGLH3B73M3+T5HshIv+K\nyIW478OAYGNMHu810TEC5Z5IUiDdE8aYYGAKMFZEpt/kkIC6L5J6P1J6bzg5UPwF3GuMKWqMyQQ0\nBmZed8xMoDmAMaYycFpEjnm3mV6R5HthjLnNGGPivn8IO/T5lPeb6nOBck8kKVDuibjfcTiwRUS+\nSeCwgLkvkvN+pPTecGzXk4hEG2PeBOZjR/0MF5GtxpjWcc8PEZG5xpg6xphdwHmghQ+b7DHJeS+A\n54G2xpho4ALQxGcN9iBjzHjgcSBf3OTMntiRYAF1T0DS7wUBck8AVYCXgI3GmHVxP/sfUAQC774g\nGe8HKbw3dMKdUkqpRDm560kppZQDaKBQSimVKA0USimlEqWBQimlVKI0UCillEqUBgqllFKJ0kCh\nlFIqURoolFJKJUoDhVJeYIzJaIwp4et2KJUaOjNbBRRjTC7gLezmTzmBLCIyLIXnKA4MwK64+QKw\nH/gTaAVUEpHYm7ymRtxxJqWvjXt9ENBPRDqnpK1KuYNj13pSykNGYJddPgBgjOlmjGkoIlNScI7y\nwLMiEmWMaQB8ISLbjTFnEvqgB0qIyCJjTKOUvtYYkxu7NtHjKWijUm6jXU8qYBhjKgEZrgSJOEOB\nXik81c64nQYBiovI9rjvtyXymitBIMWvFZEIEfkKOJvCdirlFppRqEBSCdhhjNlB3CqrwHigoDEm\nq4hcTM5JRGQdgDHmXmB3vJ+vv9nxccs4r07Na5VyAg0UKpBkASKBF0RkA4Axpjy2PpAZuBi3JeRT\nCbx+tIicjvf4IWx9ISkVRWTQdT9L7muV8jkNFCqQrAQ6XQkScf4GTlwJACKyBdiSzPNVAhYn47ib\ndfFe81pjTDbsHgHXb9d5XkQmJ7M9SnmEBgoVMERkeVzxurCIXNkGsw3Q+8oxSWQUY0QkIt7jSsDn\niV0zbkjs9ps8dc1r47alHJP0b6GU92mgUIGmGdDBGLMZCAEOi8gvV55MTkZhjCkH1ATuBxoYY6Zg\nu7UeAXKIyNB4h4dit6VM8LUicjyJ64Vgu8dKGWM6AUNF5Hwyf1+l0kznUSjlBsaYgUAHue5/KGPM\nWyIy0EfNUsotdHisUu6xDnjAGPPglR8YYwoBhxJ+iVLpg2YUSnmIMaYxMFu7iVR6p4FCKaVUorTr\nSSmlVKI0UCillEqUBgqllFKJ0kChlFIqURoolFJKJUoDhVJKqURpoFBKKZUoDRRKKaUS9f/zG7Ie\nUZj93QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1074c4990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import CoolProp, numpy as np, matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "PropsSI = CoolProp.CoolProp.PropsSI\n",
    "for fluid in ['Ethane','Water','R125']:\n",
    "    Tc = PropsSI('Tcrit',fluid)\n",
    "    pc = PropsSI('pcrit',fluid)\n",
    "    acentric = PropsSI('acentric',fluid)\n",
    "    Ts = np.linspace(PropsSI('Ttriple',fluid),Tc)\n",
    "    ps = PropsSI('P','T',Ts,'Q',0,fluid)\n",
    "    line, = plt.plot(Tc/Ts-1,-np.log10(ps/pc),label = fluid)\n",
    "    plt.plot(Tc/Ts-1,(acentric+1)/(1/0.7-1)*(Tc/Ts-1),label = fluid,color = line.get_color(),dashes = [2,2])\n",
    "    \n",
    "plt.axvline(1/0.7-1,dashes=[2,2])\n",
    "plt.xlabel('$\\Theta=T_c/T-1$')\n",
    "plt.ylabel('$-\\log_{10}(p/p_c)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we can clearly see that while this formulation is not perfect, it's not at all bad"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
