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diff --git a/Introduction_To_Chemical_Engineering_Thermodynamics_by_G._Halder/Ch9.ipynb b/Introduction_To_Chemical_Engineering_Thermodynamics_by_G._Halder/Ch9.ipynb new file mode 100644 index 00000000..9ed9282e --- /dev/null +++ b/Introduction_To_Chemical_Engineering_Thermodynamics_by_G._Halder/Ch9.ipynb @@ -0,0 +1,1078 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9 - Solutoin thermodynamic properties" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.1 Page: 338" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.1 - Page: 338\n", + "\n", + "\n", + "Partial molar volume of water is 2.76e-05 cubic m/mol\n", + "\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "print \"Example: 9.1 - Page: 338\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "V1_bar = 52.37*10**(-6)## [partial molar volume of ethanol, cubic m/mol]\n", + "y1 = 0.5## [mole fraction of ethanol]\n", + "Density = 800.21## [kg/cubic m]\n", + "M1 = 46*10**(-3)## #[Molecular wt. of ethanol,kg/mol]\n", + "M2 = 18*10**(-3)## [Molecular wt. of water,kg/cmol]\n", + "#*************#\n", + "\n", + "y2 = 1 - y1## [mole fraction of water]\n", + "M = y1*M1 + y2*M2## [Molecular wt. of mixture, kg/mol]\n", + "V = M/Density## [Volume of mixture, cubic m/mol]\n", + "# From Eqn. 9.9:\n", + "V2_bar = (V - y1*V1_bar)/y2## [partial molar volume of water, cubic m/mol]\n", + "print \"Partial molar volume of water is %.2e cubic m/mol\\n\"%(V2_bar)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.2 Page: 338" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.2 - Page: 338\n", + "\n", + "\n", + "Volume of alcohol required is 1.223 cubic m while volume of water required is 0.842 cubic m\n", + "\n" + ] + } + ], + "source": [ + "print \"Example: 9.2 - Page: 338\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "Vol = 2## [Volume of the mixture, cubic m/mol]\n", + "y1 = 0.4## [mole fraction of alcohol, cubic m/mol]\n", + "V1_bar = 38.3*10**(-6)## [partial molar volume of alcohol, cubic m/mol]\n", + "V2_bar = 17.2*10**(-6)## [partial molar volume of water, cubic m/mol]\n", + "V1 = 39.21*10**(-6)## [molar volume of alcohol, cubic m/mol]\n", + "V2 = 18*10**(-6)## [molar volume of water, cubic m/mol]\n", + "#*************#\n", + "\n", + "# From Eqn. 9.9:\n", + "V = y1*V1_bar + (1 - y1)*V2_bar## [molar volume of the solution]\n", + "n = Vol/V## [number of moles of solution]\n", + "n1 = y1*n## [number of moles of alcohol required]\n", + "n2 = (1 - y1)*n## [number of moles of water required]\n", + "V_alcohol = V1*n1## [Volume of alcohol required, cubic m]\n", + "V_water = V2*n2## [Volume of water required, cubic m]\n", + "print \"Volume of alcohol required is %.3f cubic m while volume of water required is %.3f cubic m\\n\"%(V_alcohol,V_water)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.3 Page: 339" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.3 - Page: 339\n", + "\n", + "\n", + "Mass of water added is 1138 g\n", + "\n", + "The volume of vodka obtained after conversion is 3047 cubic cm\n", + "\n" + ] + } + ], + "source": [ + "print \"Example: 9.3 - Page: 339\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "Vol = 2000## [cubic cm]\n", + "y1_1 = 0.96## [mass fraction of ethanol in laboratory alcohol]\n", + "y2_1 = 0.04## [mass fraction of water in laboratory alcohol]\n", + "y1_2 = 0.56## [mass fracion of ethanol in vodka]\n", + "y2_2 = 0.44## [mass fraction of water in vodka]\n", + "Vbar_water1 = 0.816## [cubic cm/g]\n", + "Vbar_ethanol1 = 1.273## [cubic cm/g]\n", + "Vbar_water2 = 0.953## [cubic cm/g]\n", + "Vbar_ethanol2 = 1.243## [cubic cm/g]\n", + "Density_water = 0.997## [cubic cm/g]\n", + "#***************#\n", + "\n", + "# Solution (i)\n", + "# From Eqn 9.9\n", + "Va = y1_1*Vbar_ethanol1 + y2_1*Vbar_water1## [Volume of laboratory alcohol, cubic cm/g]\n", + "mass = Vol/Va## [g]\n", + "# Let Mw be the mass of water added in laboratory alcohol.\n", + "# Material balance on ethanol:\n", + "Mw = mass*y1_1/y1_2 - mass## [g]\n", + "Vw = Mw/Density_water## [Volume of water added, cubic cm]\n", + "print \"Mass of water added is %d g\\n\"%(Mw)#\n", + "\n", + "# Solution (ii)\n", + "Mv = mass + Mw## [Mass of vodka, g]\n", + "Vv = y1_2*Vbar_ethanol2 + y2_2*Vbar_water2## [Volume of ethanol, cubic cm/g]\n", + "V_vodka = Vv*Mv## [Volume of vodka obtained after conversion, cubic cm]\n", + "print \"The volume of vodka obtained after conversion is %.d cubic cm\\n\"%(V_vodka)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.4 Page: 339" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.4 - Page: 339\n", + "\n", + "\n", + " Mathematics is involved in proving but just that no numerical computations are involved.\n", + "\n", + "\n", + " For prove refer to this example 9.4 on page 339 of the book.\n" + ] + } + ], + "source": [ + "print \"Example: 9.4 - Page: 339\\n\\n\"\n", + "\n", + "# Mathematics is involved in proving but just that no numerical computations are involved.\n", + "# For prove refer to this example 9.4 on page number 339 of the book.\n", + "\n", + "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n", + "print \" For prove refer to this example 9.4 on page 339 of the book.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.5 Page: 340" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.5 - Page: 340\n", + "\n", + "\n", + " Mathematics is involved in proving but just that no numerical computations are involved.\n", + "\n", + "\n", + " For prove refer to this example 9.5 on page 340 of the book.\n" + ] + } + ], + "source": [ + "print \"Example: 9.5 - Page: 340\\n\\n\"\n", + "\n", + "# Mathematics is involved in proving but just that no numerical computations are involved.\n", + "# For prove refer to this example 9.5 on page number 340 of the book.\n", + "\n", + "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n", + "print \" For prove refer to this example 9.5 on page 340 of the book.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.6 Page: 341" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example - 9.6 and Page number - 341\n", + "\n", + "\n", + "The expression for the partial molar volume of methanol(2) is\n", + "V2_bar = V2 + a*x_1**(2) [cubic cm/mol]\n", + "\n", + "\n", + "The partial molar volume of methanol at infinite dilution is 37.5 cubic cm/mol\n" + ] + } + ], + "source": [ + "print \"Example - 9.6 and Page number - 341\\n\\n\"\n", + "\n", + "#Given\n", + "T = 25+273.15## [K]\n", + "P = 1## [atm]\n", + "# Component 1 = water\n", + "# Component 2 = methanol\n", + "a = -3.2## [cubic cm/mol] A constant\n", + "V2 = 40.7## [cubic cm/mol] Molar volume of pure component 2 (methanol)\n", + "# V1_bar = 18.1 + a*x_2**(2)\n", + "\n", + "# From Gibbs-Duhem equation at constant temperature and pressure we have\n", + "# x_1*dV1_bar + x_2*dV2_bar = 0\n", + "# dV2_bar = -(x_1/x_2)*dV1_bar = -(x_1/x_2)*a*2*x_2*dx_2 = -2*a*x_1*dx_2 = 2*a*x_1*dx_1\n", + "\n", + "# At x_1 = 0: x_2 = 1 and thus V2_bar = V2\n", + "# Integrating the above equation from x_1 = 0 to x_1 in the RHS, and from V2_bar = V2 to V2 in the LHS, we get\n", + "# V2_bar = V2 + a*x_1**(2) - Molar volume of component 2(methanol) in the mixture \n", + "\n", + "print \"The expression for the partial molar volume of methanol(2) is\\nV2_bar = V2 + a*x_1**(2) [cubic cm/mol]\\n\\n\"\n", + "\n", + "# At infinite dilution, x_2 approach 0 and thus x_1 approach 1, therefore\n", + "x_1 = 1## Mole fraction of component 1(water) at infinite dilution\n", + "V2_bar_infinite = V2 + a*(x_1**(2))##[cubic cm/mol]\n", + "\n", + "print \"The partial molar volume of methanol at infinite dilution is %.1f cubic cm/mol\"%(V2_bar_infinite)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.7 Page: 342" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.7 - Page: 342\n", + "\n", + "\n" + ] + }, + { + "data": { + "image/png": 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9uEZgTcXFX7PGc42gTbVa/+fTTycLwXz+83DDDcko4KeeSm6rtxFotVwUybnI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\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f9070c5aed0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "For X1 = 0.5\n", + "\n", + "Partial molar volume of component 1 is 3.38e-05 cubic m/mol\n", + "\n", + "Partial molar volume of component 2 is 1.70e-05 cubic m/mol\n", + "\n", + "\n", + "\n", + "For X2 = 0.75\n", + "\n", + "Partial molar volume of component 1 is 3.83e-05 cubic m/mol\n", + "\n", + "Partial molar volume of component 2 is 1.72e-05 cubic m/mol\n", + "\n" + ] + }, + { + "data": { + "image/png": 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RGtjjnZrLre403AAFvD/fD1h/o4hEi0g9oAGw1Nv2cOA04IEs3yvwX3YPYF0Q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\nrkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f9070ba6bd0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print \"Example: 9.7 - Page: 342\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "# Data = [X1 V*10**6(cubic m/mol)]#\n", + "from numpy import mat\n", + "Data = mat([[0, 20],[0.2, 21.5],[0.4, 24.0],[0.6, 27.4],[0.8, 32.0],[1, 40]])\n", + "#************#\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, title, xlabel, ylabel, show, grid\n", + "plot(Data[:,0],Data[:,1])\n", + "title(\"Example 9.7\")\n", + "xlabel(\"Mole fraction\")\n", + "ylabel(\"Molar Volume*10**(6)\")\n", + "grid()#\n", + "show()\n", + "# Solution (i)\n", + "print \"For X1 = 0.5\\n\"\n", + "# A tangent is drawn to the curve at X1 = 0.5.\n", + "# The intercept at X2 = 0 or X1 = 1, gives V1_bar.\n", + "V1_bar1 = 33.8*10**(-6)## [cubic m/mol]\n", + "# The intercept at X2 = 1 or X1 = 0, gives V2_bar.\n", + "V2_bar1 = 17*10**(-6)## [cubic m/mol]\n", + "print \"Partial molar volume of component 1 is %.2e cubic m/mol\\n\"%(V1_bar1)#\n", + "print \"Partial molar volume of component 2 is %.2e cubic m/mol\\n\"%(V2_bar1)#\n", + "print \"\\n\"\n", + "\n", + "# Solution (ii)\n", + "print \"For X2 = 0.75\\n\"\n", + "# A tangent is drawn to the curve at X1 = 0.75.\n", + "# The intercept at X2 = 0 or X1 = 1, gives V1_bar.\n", + "V1_bar2 = 36.6*10**(-6)## [cubic m/mol]\n", + "# The intercept at X2 = 1 or X1 = 0, gives V2_bar.\n", + "V2_bar2 = 12.4*10**(-6)## [cubic m/mol]\n", + "point1 = mat([[0, V1_bar1],[ 1 ,V2_bar1]])\n", + "point2 = mat([[0, V1_bar2],[1, V2_bar2]])\n", + "plot(point1[:,0],point1[:,1],point2[:,0],point2[:,1])\n", + "#legend(\"X1 = 0.5\"%(\"X1 = 0.75\"\n", + "xlabel(\"Mole fraction\")\n", + "ylabel(\"Molar Volume\")\n", + "print \"Partial molar volume of component 1 is %.2e cubic m/mol\\n\"%(V1_bar)#\n", + "print \"Partial molar volume of component 2 is %.2e cubic m/mol\\n\"%(V2_bar)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.8 Page: 352" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.8 - Page: 352\n", + "\n", + "\n", + " Mathematics is involved in proving but just that no numerical computations are involved.\n", + "\n", + "\n", + " For prove refer to this example 9.8 on page 352 of the book.\n" + ] + } + ], + "source": [ + "print \"Example: 9.8 - Page: 352\\n\\n\"\n", + "\n", + "# Mathematics is involved in proving but just that no numerical computations are involved.\n", + "# For prove refer to this example 9.8 on page number 352 of the book.\n", + "\n", + "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n", + "print \" For prove refer to this example 9.8 on page 352 of the book.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.9 Page: 352" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.9 - Page: 352\n", + "\n", + "\n", + " Mathematics is involved in proving but just that no numerical computations are involved.\n", + "\n", + "\n", + " For prove refer to this example 9.9 on page 352 of the book.\n" + ] + } + ], + "source": [ + "print \"Example: 9.9 - Page: 352\\n\\n\"\n", + "\n", + "# Mathematics is involved in proving but just that no numerical computations are involved.\n", + "# For prove refer to this example 9.9 on page number 352 of the book.\n", + "\n", + "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n", + "print \" For prove refer to this example 9.9 on page 352 of the book.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.10 Page: 354" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.10 - Page: 354\n", + "\n", + "\n", + "Fugacity of the gaseous mixture is 40.095 bar\n" + ] + } + ], + "source": [ + "from math import exp, log\n", + "print \"Example: 9.10 - Page: 354\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "x1 = 0.3## [mole fraction of component 1 in the mixture]\n", + "x2 = 0.7## [mole fraction of component 2 in the mixture]\n", + "phi1 = 0.7## [fugacity coeffecient of component 1 in the mixture]\n", + "phi2 = 0.85## [fugacity coeffecient of component 2 in the mixture]\n", + "P = 50## [bar]\n", + "T = 273 + 100## [K]\n", + "#*************#\n", + "\n", + "phi = exp(x1*log(phi1) + x2*log(phi2))## [fugacity coeffecient of the mixture]\n", + "f = phi*P## [bar]\n", + "print \"Fugacity of the gaseous mixture is %.3f bar\"%(f)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.11 Page: 354" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.11 - Page: 354\n", + "\n", + "\n", + "Fugacity of the gaseous mixture is 45.479 bar\n" + ] + } + ], + "source": [ + "print \"Example: 9.11 - Page: 354\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "x1 = 0.3## [mole fraction of hydrogen in the mixture]\n", + "x2 = 0.25## [mole fraction of nitrogen in the mixture]\n", + "x3 = 0.45## [mole fraction of oxygen in the mixture]\n", + "phi1 = 0.7## [fugacity coeffecient of oxygen in the mixture]\n", + "phi2 = 0.85## [fugacity coeffecient of nitrogen in the mixture]\n", + "phi3 = 0.75## [fugacity coeffecient of oxygen in the mixture]\n", + "P = 60## [bar]\n", + "T = 273 + 150## [K]\n", + "#***********#\n", + "\n", + "phi = exp(x1*log(phi1) + x2*log(phi2) + x3*log(phi3))## [fugacity coeffecient of the mixture]\n", + "f = phi*P## [bar]\n", + "print \"Fugacity of the gaseous mixture is %.3f bar\"%(f)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.12 Page: 356" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.12 - Page: 356\n", + "\n", + "\n", + "Fugacity of liquid water is 1.0012 bar\n" + ] + } + ], + "source": [ + "print \"Example: 9.12 - Page: 356\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "T = 372.12## [K]\n", + "Psat = 100## [kPa]\n", + "P = 300# #[kPa]\n", + "Vspecific = 1.043*10**(-3)##[cubic m/kg]\n", + "M = 18*10**(-3)## [molecular weight of water, kg/mol]\n", + "R = 8.314## [J/mol K]\n", + "#***************#\n", + "\n", + "Psat = Psat/100## [bar]\n", + "P = P/100## [bar]\n", + "Vl = Vspecific*M## [cubic m/mol]\n", + "# Vapour is assumed to be like an ideal gas.\n", + "phi = 1#\n", + "fsat = Psat*phi## [bar]\n", + "fl = fsat*exp(Vl*(P - Psat)*10**5/(R*T))## [bar]\n", + "print \"Fugacity of liquid water is %.4f bar\"%(fl)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.13 Page: 357" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.13 - Page: 357\n", + "\n", + "\n", + "The fugacity of the liquid water is 4.2051 bar\n" + ] + } + ], + "source": [ + "print \"Example: 9.13 - Page: 357\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "Vl = 90.45*10**(-6)## [molar volume of liquid butadiene, cubic m/mol]\n", + "fsat = 4.12## [bar]\n", + "P = 10## [bar]\n", + "Psat = 4.12## [bar]\n", + "T = 313## [K]\n", + "R = 8.314## [J/mol K]\n", + "#************#\n", + "\n", + "fl = fsat*exp(Vl*(P - Psat)*10**5/(R*T))## [bar]\n", + "print \"The fugacity of the liquid water is %.4f bar\"%(fl)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.14 Page: 357" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.14 - Page: 357\n", + "\n", + "\n", + "The fugacity of the gas is 1411 atm \n", + "\n", + "The fugacity coeffecient of the gas is 1.411 atm\n" + ] + } + ], + "source": [ + "print \"Example: 9.14 - Page: 357\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "b = 0.0391## [cubic dm/mol]\n", + "P1 = 1000## [atm]\n", + "T = 1000 + 273## [K]\n", + "R = 0.0892## [L bar/K mol]\n", + "#deff('[Vreal] = f1(P)','Vreal = R*T/P + b')#\n", + "#deff('[Videal] = f2(P)','Videal = R*T/P')#\n", + "def f1(P):\n", + " Vreal = R*T/P + b\n", + " return Vreal\n", + "\n", + "def f2(P):\n", + " Videal = R*T/P\n", + " return Videal\n", + "\n", + "def f(P):\n", + " f12 = f1(P)-f2(P)\n", + " return f12\n", + "\n", + "#**************#\n", + "\n", + "# We know that:\n", + "# RTlog(f/P) = integral('Vreal - Videal',P,0,P)\n", + "\n", + "from sympy.mpmath import quad\n", + "f = P1*exp((1/(R*T))*quad(f,[0,P1]))## [atm]\n", + "phi = f/P1#\n", + "print \"The fugacity of the gas is %d atm \\n\"%(f)#\n", + "print \"The fugacity coeffecient of the gas is %.3f atm\"%(phi)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.15 Page: 359" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.15 - Page: 359\n", + "\n", + "\n", + "Fugacity of liquid butadiene at 313 K & 10 bar is 8.109 bar\n" + ] + } + ], + "source": [ + "print \"Example: 9.15 - Page: 359\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "Vl = 73*10**(-6)## [cubic m/mol]\n", + "P = 275## [bar]\n", + "Psat = 4.360## [bar]\n", + "T = 110 + 273## [K]\n", + "R = 8.314## [J/mol K]\n", + "#**************#\n", + "\n", + "# Acetone vapour is assumed to behave like ideal gas.\n", + "phi = 1#\n", + "fsat = Psat## [bar]\n", + "fl = fsat*exp(Vl*(P - Psat)*10**5/(R*T))## [bar]\n", + "print \"Fugacity of liquid butadiene at 313 K & 10 bar is %.3f bar\"%(fl)# " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.16 Page: 362" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.16 - Page: 362\n", + "\n", + "\n", + "The entropy change of mixiong is 0.749 cal/K mol\n" + ] + } + ], + "source": [ + "print \"Example: 9.16 - Page: 362\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "V1 = 2.8## [Volume of Oxygen, L]\n", + "V2 = 19.6## [Volume of hydrogen, L]\n", + "R = 1.987## [cal/K mol]\n", + "#**************#\n", + "\n", + "n1 = V1/22.4## [moles of Oxygen]\n", + "n2 = V2/22.4## [moles of Hydrogen]\n", + "n = n1 + n2## [total number of moles]\n", + "x1 = n1/n## [mole fraction of Oxygen]\n", + "x2 = n2/n## [mole fraction of Hydrogen]\n", + "# From Eqn. 9.88:\n", + "deltaS_mix = - (R*(x1*log(x1) + x2*log(x2)))## [cal/K mol]\n", + "print \"The entropy change of mixiong is %.3f cal/K mol\"%(deltaS_mix)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.17 Page: 363" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.17 - Page: 363\n", + "\n", + "\n", + " Mathematics is involved in proving but just that no numerical computations are involved.\n", + "\n", + "\n", + " For prove refer to this example 9.17 on page 363 of the book.\n" + ] + } + ], + "source": [ + "print \"Example: 9.17 - Page: 363\\n\\n\"\n", + "\n", + "# Mathematics is involved in proving but just that no numerical computations are involved.\n", + "# For prove refer to this example 9.17 on page number 363 of the book.\n", + "\n", + "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n", + "print \" For prove refer to this example 9.17 on page 363 of the book.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.18 Page: 364" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.18 - Page: 364\n", + "\n", + "\n", + "The free energy change of mixing is -1513.46 J\n", + "\n", + "The enthalpy change of mixing is 0 J\n", + "\n" + ] + } + ], + "source": [ + "print \"Example: 9.18 - Page: 364\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "n1 = 0.7## [moles of helium]\n", + "n2 = 0.3## [moles of argon]\n", + "R = 8.314## [J/mol K]\n", + "T = 273 + 25## [K]\n", + "#******************#\n", + "\n", + "n = n1 + n2## [total moles]\n", + "x1 = n1/n## [mole fraction of helium]\n", + "x2 = n2/n## [mole fraction of argon]\n", + "deltaG_mix = n*R*T*(x1*log(x1) + x2*log(x2))## [J]\n", + "print \"The free energy change of mixing is %.2f J\\n\"%(deltaG_mix)#\n", + "\n", + "# Since the gases are ideal:\n", + "deltaH_mix = 0## [J]\n", + "print \"The enthalpy change of mixing is %d J\\n\"%(deltaH_mix)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.19 Page: 364" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.19 - Page: 364\n", + "\n", + "\n", + "Free Energy change of mixing is -15.37 J\n", + "\n", + "Enthalpy change in mixing is 0.00 J\n", + "\n", + "Entropy Change in mixing is 0.052 J/K\n", + "\n" + ] + } + ], + "source": [ + "print \"Example: 9.19 - Page: 364\\n\\n\"\n", + "\n", + "# Solution\n", + "\n", + "#*****Data******#\n", + "V = 20## [Volume of vessel, L]\n", + "V1 = 12## [Volume of Hydrogen, L]\n", + "V2 = 10## [Volume of Nitrogen, L]\n", + "P = 1## [atm]\n", + "T = 298## [K]\n", + "P1 = 1## [atm]\n", + "P2 = 1## [atm]\n", + "R = 0.082## [L atm/K mol]\n", + "#************#\n", + "\n", + "n1 = P1*V1/(R*T)## [number of moles of Hydrogen]\n", + "n2 = P2*V2/(R*T)## [number of moles of Nitrogen]\n", + "n = n1 + n2## [total number of moles]\n", + "Pfinal = n*R*T/V## [atm]\n", + "p1 = Pfinal*n1## [partial pressure of Hydrogen, atm]\n", + "p2 = Pfinal*n2## [partial pressure of Nitrogen, atm]\n", + "deltaG_mix = R*T*(n1*log(p1/P1) + n2*log(p2/P2))## [J]\n", + "print \"Free Energy change of mixing is %.2f J\\n\"%(deltaG_mix)#\n", + "\n", + "# Since mixing is ideal:\n", + "deltaH_mix = 0## [J]\n", + "print \"Enthalpy change in mixing is %.2f J\\n\"%(deltaH_mix)#\n", + "\n", + "deltaS_mix = - (deltaG_mix/T)## [J/K]\n", + "print \"Entropy Change in mixing is %.3f J/K\\n\"%(deltaS_mix)#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.20 Page: 367" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.20 - Page: 367\n", + "\n", + "\n", + " Mathematics is involved in proving but just that no numerical computations are involved.\n", + "\n", + "\n", + " For prove refer to this example 9.20 on page 367 of the book.\n" + ] + } + ], + "source": [ + "print \"Example: 9.20 - Page: 367\\n\\n\"\n", + "\n", + "# Mathematics is involved in proving but just that no numerical computations are involved.\n", + "# For prove refer to this example 9.20 on page number 367 of the book.\n", + "\n", + "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n", + "print \" For prove refer to this example 9.20 on page 367 of the book.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 9.21 Page: 373" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Example: 9.21 - Page: 373\n", + "\n", + "\n", + " Mathematics is involved in proving but just that no numerical computations are involved.\n", + "\n", + "\n", + " For prove refer to this example 9.21 on page 373 of the book.\n" + ] + } + ], + "source": [ + "print \"Example: 9.21 - Page: 373\\n\\n\"\n", + "\n", + "# Mathematics is involved in proving but just that no numerical computations are involved.\n", + "# For prove refer to this example 9.21 on page number 373 of the book.\n", + "\n", + "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n", + "print \" For prove refer to this example 9.21 on page 373 of the book.\"" + ] + } + ], + "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": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |