{ "metadata": { "name": "", "signature": "sha256:8a4a2e9c3fff1b1819d5290ddbbc5e41fcd04a943a3cffb4a3e2d4883b56476a" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 11 : Solution Thermodynamics Theroy" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.4 page no : 168" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import poly1d,roots\n", "\n", "\n", "#H = 400x1 + 600x2 + x1x2(40x1 + 20x2) Given\n", "#Substituting x2 = 1-x1\n", "H = poly1d([600, -180, 0, -20],'x1','c') \t\t\t#(A)\n", "#K = dH/dx1\n", "K = poly1d([-180, 0, -60],'x1','c')\n", "\n", "# Calculations\n", "#Using Eqn 11.15 H1 = H+x2*K\n", "#substituting x2 = 1-x1\n", "H1 = poly1d([420, 0, -60, 40],'x1','c') \t\t\t#(B)\n", "\n", "#Similarly for H2\n", "\n", "H2 = poly1d([600 ,0 ,0, 40],'x1','c') \t\t\t#(C)\n", "#Now to calculate H1_inf and H2_inf \n", "#x1 = 0 in (B)\n", "H1_inf = 420;\t\t\t#[J/mol]\n", "#x2 = 0 in (C) i.e. x1 = 1\n", "H2_inf = 640;\t\t\t#[J/mol]\n", "\n", "# Results\n", "print (H1,'H1 = ');\n", "print (H2,'H2 = ');\n", "print ('J/mol',H1_inf,'H1_inf = ')\n", "print ('J/mol',H2_inf,'H2_inf = ')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(poly1d([ 1, -400, -10800, 1008000, 0]), 'H1 = ')\n", "(poly1d([ 1, -640, 24000, 0, 0]), 'H2 = ')\n", "('J/mol', 420, 'H1_inf = ')\n", "('J/mol', 640, 'H2_inf = ')\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.5 page no : 170" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel,subplot\n", "\n", "from numpy import array,exp,round,linspace\n", "import math \n", "\n", "# Variables\n", "#Using Eqn 11.30\n", "#G = t(T)+RT ln f\n", "#G` = t(T)+rt ln f`\n", "#Hence ln(f/f`) = (1/RT)*(G-G`)\n", "#G = H-TS\n", "#G` = H-TS`\n", "#ln (f/f`) = (n/R)*(((H-H`)/T)-(S-S`)) (A)\n", "R = 8.314;\n", "n = 18.015;\n", "f_ = 1;\t\t\t#[kPa]\n", "P_ = f_;\n", "H_ = 3076.8;\t\t\t#[J/g]\n", "S_ = 10.3450;\t\t\t#[J/g/K]\n", "T = 573.15;\t\t\t#[K]\n", "\n", "P = array([10, 50, 100, 200, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500, 7000, \\\n", " 7600, 8000, 8400,0]);\n", "H = array([3076.6, 3075.7, 3074.2, 3072.1, 3064.8, 3052.1, 3038.9, 3025 ,3010.4, 2995.1, 2979 ,2962, \\\n", " 2944.2, 2925.5, 2905.8, 2885 ,2862.9, 2839.4, 2808.8, 2786.8, 2763.1,0]); \n", "S = array([9.282, 8.5380, 8.2166, 7.8937, 7.4614, 7.1251, 6.9207, 6.7696, 6.6470, 6.5422, \\\n", " 6.4491, 6.3642, 6.2852, 6.2105, 6.1388, 6.0692, 6.0008, 5.9327, 5.8503, 5.7942, 5.7366,0]);\n", "\n", "# Calculations and Results\n", "K = round(exp((n/R)*(((H-H_)/T)-(S-S_))),0);\n", "\n", "f = K*f_;\n", "P[21] = 8592.7;\t\t\t#[kPa]\n", "P_sat = P[21]\n", "f[21] = 6738.9;\n", "f_sat = f[21]\n", "\n", "si = round(f/P,4);\n", "si_sat = si[21]\n", "\n", "Vl = round(1.403*n,2)\t\t\t#[cm**3/mol]\n", "#Umath.sing Eqn 11.41\n", "P_new = linspace(8592.7,10000,10);\n", "f_new = round(f_sat*exp(Vl*(P_new-P_sat)/(R*1000*T)),1);\n", "si_new = f_new/P_new;\n", "\n", "subplot(211)\n", "plot(P/1000,f/1000,'b')\n", "plot(P_new/1000,f_new/1000,'g')\n", "\n", "dotsx = [0 ,P_sat/1000];\n", "dotsy = [f_sat/1000, f_sat/1000];\n", "plot(dotsx,dotsy,'b--')\n", "\n", "dotsx = [0, f_sat/1000];\n", "dotsy = [P_sat/1000 ,P_sat/1000];\n", "plot(dotsy,dotsx,'g--')\n", "\n", "dotsx = [11,8];\n", "dotsx = [6,6];\n", "plot(dotsx,dotsy,'w')\n", "\n", "suptitle('f vs P')\n", "xlabel('P X 10**-3 /kPa')\n", "ylabel('f X 10**-3 /kPa')\n", "\n", "subplot(222)\n", "plot(P/1000,si,'r')\n", "plot(P_new/1000,si_new,'g')\n", "dotsx = [0, P_sat/1000];\n", "dotsy = [si_sat ,si_sat];\n", "plot(dotsx,dotsy,'g--')\n", "dotsx = [0.55, si_sat];\n", "dotsy = [P_sat/1000, P_sat/1000];\n", "plot(dotsy,dotsx,'r--')\n", "\n", "suptitle('si vs P')\n", "xlabel('P X 10**-3 /kPa')\n", "ylabel('si')\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.7 page no : 171" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "T = 200.;\t\t\t#[K]\n", "P = 30.;\t\t\t#[bar]\n", "R = 83.14;\n", "x1 = 0.4;\t\t\t#[N2]\n", "x2 = 1-x1;\t\t\t#[CH4]\n", "\n", "B11 = -35.2;\t\t\t#[cm**3/mol]\n", "B22 = -105.;\t\t\t#[cm**3/mol]\n", "B12 = -59.8;\t\t\t#[cm**3/mol]\n", "\n", "# Calculations\n", "delta_12 = round((2*B12)-B11-B22,1);\n", "si_1 = round(math.exp((P/(R*T))*(B11+(x2**2*delta_12))),4);\n", "si_2 = round(math.exp((P/(R*T))*(B22+(x1**2*delta_12))),4);\n", "\n", "B = round((x1**2*B11)+(2*x1*x2*B12)+(x2**2*B22),2);\n", "Z = round(1+((B*P)/(R*T)),2);\n", "\n", "# Results\n", "print 'Fugacity Coefficients are ',si_2,si_1\n", "print 'Second Viral coefficient is ',B\n", "print 'Compressibility Factor is ',Z\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity Coefficients are 0.8324 0.9511\n", "Second Viral coefficient is -72.14\n", "Compressibility Factor is 0.87\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.8 page no : 176" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "T = 473.15;\t\t\t#[K]\n", "P = 70.;\t\t\t#[bar]\n", "Tc = 420.;\t\t\t#[K]\n", "Pc = 40.43;\t\t\t#[bar]\n", "omega = 0.191;\n", "\n", "# Calculations\n", "#By interpolation in Tables E.15 and E.16\n", "si_0 = 0.627;\n", "si_1 = 1.096;\n", "#Using Eqn(11.64)\n", "si = round(si_0*(si_1**omega),3);\n", "f = round(si*P,1);\n", "\n", "# Results\n", "print 'Fugacity coefficient is ',si\n", "print 'fugacity is ',f,'bar'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity coefficient is 0.638\n", "fugacity is 44.7 bar\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.9 page no : 179" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import array,exp,round\n", "import math \n", "\n", "# Variables\n", "P = 25.;\t\t\t#[KPa]\n", "T = 323.15;\t\t\t#[K]\n", "R = 83.14;\n", "x1 = 0.5;\n", "x2 = 1-x1;\n", "\n", "# Calculations\n", "ij = array([11,22,12]);\n", "Tc_ij = array([535.5,591.8,563.0]);\n", "Pc_ij = array([41.5,41.1,41.3]);\n", "Vc_ij = array([267,316,291]);\n", "Zc_ij = round((Pc_ij*Vc_ij)/(R*Tc_ij),3);\n", "omega_ij = array([0.323,0.262,0.293]);\n", "\n", "Tr_ij = round(T/Tc_ij,3);\n", "B0 = round(0.083-(0.422/(Tr_ij**1.6)),3)\n", "B1 = round(0.139-(0.172/(Tr_ij**4.2)),3)\n", "B_ij = round((R*Tc_ij/Pc_ij)*(B0+(omega_ij*B1)),0);\n", "\n", "delta_12 = (2*B_ij[2])-B_ij[0]-B_ij[1];\n", "R = 8314;\n", "si_1 = round(exp((P/(R*T))*(B_ij[0]+(x2**2*delta_12))),3);\n", "si_2 = round(exp((P/(R*T))*(B_ij[2]+(x1**2*delta_12))),3);\n", "\n", "Ans = [ij,Tc_ij,Pc_ij,Vc_ij,Zc_ij,omega_ij,Tr_ij,B0,B1,B_ij];\n", "\n", "# Results\n", "print ' ij Tcij Pcij Vcij Zcij Wij Trij B0 B1 Bij'\n", "print Ans\n", "print 'Fugacity Coefficients are ',si_2,si_1\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " ij Tcij Pcij Vcij Zcij Wij Trij B0 B1 Bij\n", "[array([11, 22, 12]), array([ 535.5, 591.8, 563. ]), array([ 41.5, 41.1, 41.3]), array([267, 316, 291]), array([ 0.249, 0.264, 0.257]), array([ 0.323, 0.262, 0.293]), array([ 0.603, 0.546, 0.574]), array([-0.865, -1.028, -0.943]), array([-1.3 , -2.045, -1.632]), array([-1378., -1872., -1611.])]\n", "Fugacity Coefficients are 0.985 0.987\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 11.10 page no : 181" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "T0 = 298.15;\t\t\t#[K]\n", "T = 323.15;\t\t\t#[K]\n", "Cp_E = -2.86;\t\t\t#[J/mol/K]\n", "Ho_E = 897.9;\t\t\t#[J/mol]\n", "Go_E = 384.5;\t\t\t#[J/mol]\n", "\n", "# Calculations\n", "#(a) Derivations\n", "#G_E = -a*(T ln T - T)+ bT + c\n", "#S_E = a ln T - b\n", "#H_E = aT + c\n", "#Where\n", "#a = Cp_E\n", "#c = Ho_E-aT0\n", "#b = ((Go_E+a(T ln T0 - T0)-c)/T0)\n", "#(b)\n", "a = Cp_E;\n", "c = round(Ho_E-(a*T0),1);\n", "b = round((Go_E+(a*((T0*math.log(T0))-T0)-c))/T0,4);\n", "G_E = round((-a*(T*math.log(T)-T))+(b*T)+c,1);\n", "S_E = round((a*math.log(T))-b,3);\n", "H_E = round((a*T)+c,1);\n", "\n", "# Results\n", "print 'G_E = ',G_E,'J/mol'\n", "print 'S_E = ',S_E,'J/mol/K'\n", "print 'H_E = ',H_E,'J/mol'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "G_E = 344.4 J/mol\n", "S_E = 1.492 J/mol/K\n", "H_E = 826.4 J/mol\n" ] } ], "prompt_number": 16 } ], "metadata": {} } ] }