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-{
- "metadata": {
- "name": ""
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 5 : Properties of Real Gases"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.1 page no: 109"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "V = 0.6 #m**3 vessel\n",
- "T = 473. #K temperature\n",
- "N = 1. * 10 ** 3 #mol\n",
- "R = 8.314 #Pa * m**3/molK\n",
- "\n",
- "# Calculation \n",
- "P = N * R * T / (V * 10**5) \n",
- "\n",
- "# Result\n",
- "print \"(a)Pressure calculated using ideal gas equation = %.2f bar\"%P\n",
- "a = 0.4233 #N * m**4 / mol**2\n",
- "b = 3.73 * 10**-5 #m**3/mol\n",
- "P1 = (R*T/(V/N - b)-a/(V/N)**2)/10**5 \n",
- "print \"(a)Pressure calculated using van der waals equation = %.2f bar\"%P1\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(a)Pressure calculated using ideal gas equation = 65.54 bar\n",
- "(a)Pressure calculated using van der waals equation = 58.13 bar\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.2 pageno : 110"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "P = 10.**7 #Pa \n",
- "T = 500. #K molar volume\n",
- "R = 8.314 #Pa * L / mol K\n",
- "N = 1000.\n",
- "\n",
- "# Calculation \n",
- "V = N * R * T / ( P * 1000) \n",
- "\n",
- "# Result\n",
- "print \"(a)Volume of CO2 calculated using ideal gas equation = %.4e m**3\"%V\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(a)Volume of CO2 calculated using ideal gas equation = 4.1570e-04 m**3\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.3 pageno : 111"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "V = 0.6 * 10**-3 #m**3\n",
- "T = 473. #K vellel of volume\n",
- "Tc = 405.5 #K temperature\n",
- "Pc = 112.8 * 10 ** 5 #Pa pressure\n",
- "R = 8.314 \n",
- "\n",
- "# Calculation \n",
- "a = 0.4278 * (R**2) * (Tc ** 2.5)/Pc \n",
- "b = 0.0867 * R * Tc / Pc \n",
- "P1 = (R*T/(V - b) - a/((T**0.5)*V*(V + b)))/10**5 \n",
- "\n",
- "# Result\n",
- "print \"Pressure developed by gas = %.2f bar\"%P1\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pressure developed by gas = 57.87 bar\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.4 pageno : 112"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "P = 10.**6 #Pa\n",
- "T = 373. #K molar volume\n",
- "Tc = 405.5 #K temperature\n",
- "Pc = 112.8 * 10 ** 5 #Pa pressure\n",
- "R = 8.314 \n",
- "\n",
- "# Calculation \n",
- "a = 0.4278 * (R**2) * (Tc ** 2.5)/Pc \n",
- "b = 0.0867 * R * Tc / Pc \n",
- "#P1 = (R*T/(V - b) - a/((T**0.5)*V*(V + b)))/10**5 \n",
- "#10**6=((8.314*373)/(V-2.59*10**-5))-8.68/((373**0.5)*V*(V+2.59*10**-5) \n",
- "#solving this we get,\n",
- "V = 3.0 * 10**-3 #m**3/mol\n",
- "\n",
- "# Result\n",
- "print \"molar volume of gas = %.e m**3/mol\"%V\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "molar volume of gas = 3e-03 m**3/mol\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.5 pageno : 112"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "B = -2.19 * 10**-4 #m**3/mol virial coefficients\n",
- "C = -1.73 * 10**-8 #m**6/mol**2\n",
- "P = 10. #bar molar volume\n",
- "T = 500. #K\n",
- "\n",
- "# Calculation \n",
- "#virial equation is given as, Z = PV/RT = 1 + B/V + C/V**2\n",
- "#V = (RT/P)*(1 + B/V + C/V**2)\n",
- "# now by assuming different values for V on RHS and checking for corresponding V on LHS, we have to assume such value of V on RHS by which we get the same value for LHS V\n",
- "#by trial and error we get,\n",
- "V = 3.92 * 10**-3 #m**3\n",
- "\n",
- "# Result\n",
- "print \"Molar volume of methanol = %.3e m**3\"%V\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Molar volume of methanol = 3.920e-03 m**3\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.6 pageno : 120"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "T = 510. #K molar volume\n",
- "P = 26.6 #bar \n",
- "Tc = 425.2 #K temperature\n",
- "Pc = 38. #bar pressure\n",
- "Zc = 0.274 # compressibility factor\n",
- "R = 8.314 \n",
- "\n",
- "# Calculation \n",
- "Pr = P / Pc \n",
- "Tr = T / Tc \n",
- "\n",
- "# Result\n",
- "print \"Pr = \",Pr\n",
- "print \"Tr = %.2f\"%Tr\n",
- "\n",
- "#From fig. 5.4 and 5.5 from the text book\n",
- "Z = 0.865 \n",
- "D = 0.15 \n",
- "Z1 = Z + D * ( Zc - 0.27) \n",
- "V = R * T * Z1 / (P * 10**5) \n",
- "print \"Molar volume of n-butane = %.4e m**3/mol\"%V\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pr = 0.7\n",
- "Tr = 1.20\n",
- "Molar volume of n-butane = 1.3798e-03 m**3/mol\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.7 pageno : 120"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "T = 510. #K molar volumes\n",
- "P = 26.6 #bar\n",
- "Tc = 425.2 #K temperature\n",
- "Pc = 38. #bar pressure\n",
- "w = 0.193 # acentric factor\n",
- "R = 8.314 \n",
- "\n",
- "# Calculation \n",
- "Pr = P / Pc \n",
- "Tr = T / Tc \n",
- "\n",
- "# Result\n",
- "print \"Pr = \",Pr\n",
- "print \"Tr = %.2f\"%Tr\n",
- "\n",
- "#From fig. 5.6 and 5.7 from the text book\n",
- "Z0 = 0.855 \n",
- "Z1 = 0.042 \n",
- "Z = Z0 + w*Z1 \n",
- "print \"Z = %.4f\"%Z\n",
- "V = R * T * Z / (P * 10**5) \n",
- "\n",
- "print \"Molar volume of n-butane = %.4e m**3/mol\"%V\n",
- "\n",
- "# note : answer may vary because of rounding error."
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pr = 0.7\n",
- "Tr = 1.20\n",
- "Z = 0.8631\n",
- "Molar volume of n-butane = 1.3758e-03 m**3/mol\n"
- ]
- }
- ],
- "prompt_number": 14
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.8 pageno : 122"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from numpy import *\n",
- "# variables \n",
- "P = 6000. #kPa ethane\n",
- "T = 325. #K ethane\n",
- "xn2 = 0.4 # gas mixture\n",
- "xethane = 0.6 \n",
- "an2 = 0.1365 #N m**4 / mol**2 nitrogen\n",
- "\n",
- "# Calculation \n",
- "bn2 = 3.86 * 10**-5 #m**3/mol\n",
- "aethane = 0.557 #N m**4 / mol**2\n",
- "bethane = 6.51 * 10**-5 #m**3/mol\n",
- "Pcn2 = 3394. #kPa\n",
- "Tcn2 = 126.2 #K\n",
- "Pcethane = 4880. #kPa\n",
- "Tcethane = 305.4 #K\n",
- "R = 8.314 \n",
- "\n",
- "\n",
- "# Result\n",
- "V = R * T / (P*1000) \n",
- "print \"(a)Molar volume by ideal gas equation = %.3e m**3/mol\"%V\n",
- "\n",
- "\n",
- "a = (xn2 * (an2**0.5) + xethane * (aethane**0.5))**2 \n",
- "b = (xn2*bn2 + xethane*bethane) \n",
- "#substituting the above values in van der waals equation, and solving, we get\n",
- "#V^3 - 5.0484*10^-4V^2+5.9117*10^-8V-3.2214*10^-12=0\n",
- "#Using co-efficients from the above equation,\n",
- "coeff = [1, -5.0484e-4, 5.9117e-8, -3.2217e-12]\n",
- "x = roots(coeff)\n",
- "y = x[0]\n",
- "print \"(b)Molar volume by van der waals equation =\",round((y.real)/1e-4,3),\"*10^-4 m**3/mol\"\n",
- "\n",
- "\n",
- "Prin2 = P/Pcn2 \n",
- "Trin2 = T/Tcn2 \n",
- "Priethane = P/Pcethane \n",
- "Triethane = T/Tcethane \n",
- "# using compressibilty chart, \n",
- "Zn2 = 1 \n",
- "Zethane = 0.42 \n",
- "Z = xn2 * Zn2 + xethane * Zethane \n",
- "V2 = Z * R * T / P * (10**-3)\n",
- "print \"(c)Molar volume based on compressibilty factor = %.2e m**3/mol\"%V2\n",
- "\n",
- "\n",
- "Pri1n2 = xn2*P/Pcn2 \n",
- "Tri1n2 = T/Tcn2 \n",
- "Pri1ethane = xethane*P/Pcethane \n",
- "Tri1ethane = T/Tcethane \n",
- "# using compressibilty chart, \n",
- "Zn21 = 1. \n",
- "Zethane1 = 0.76 \n",
- "Z1 = xn2 * Zn21 + xethane * Zethane1 \n",
- "V3 = (Z1 * R * T / P ) * (10**-3)\n",
- "print \"(c)Molar volume based on daltons law = %.3e m**3/mol\"%V3\n",
- "\n",
- "\n",
- "Tc = xn2 * Tcn2 + xethane * Tcethane \n",
- "Pc = xn2 * Pcn2 + xethane * Pcethane \n",
- "Zc = 0.83 \n",
- "V4 = Zc * R *T / P * (10**-3)\n",
- "print \"(d)Molar volume by kays method = %.3e m**3/mol\"%V4\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(a)Molar volume by ideal gas equation = 4.503e-04 m**3/mol\n",
- "(b)Molar volume by van der waals equation = 3.68 *10^-4 m**3/mol\n",
- "(c)Molar volume based on compressibilty factor = 2.94e-04 m**3/mol\n",
- "(c)Molar volume based on daltons law = 3.855e-04 m**3/mol\n",
- "(d)Molar volume by kays method = 3.738e-04 m**3/mol\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.9 page no : 124"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "# variables \n",
- "P1 = 40. #% ( nitrogen )\n",
- "P2 = 60. #% ( ethane )\n",
- "T = 325. #K ethane\n",
- "\n",
- "# Calculation \n",
- "V = 4.5 * 10**-4 #m**3/mol\n",
- "a1 = 0.1365 #N*m**4/mol**2\n",
- "b1 = 3.86 * 10 ** -5 #m**3/mol\n",
- "a2 = 0.557 #N*m**4/mol**2\n",
- "b2 = 6.51 * 10 ** -5 #m**3/mol\n",
- "Pc1 = 3394. #kPa\n",
- "Tc1 = 126.1 #K\n",
- "Pc2 = 4880. #kPa\n",
- "Tc2 = 305.4 #K\n",
- "R = 8.314 \n",
- "Pideal = R * T / (V * 1000) #kPa\n",
- "\n",
- "# Result\n",
- "print \"(a)Pressure of Gas by the ideal gas equation = %.f kPa\"%Pideal\n",
- "y1 = P1/100. \n",
- "y2 = P2/100. \n",
- "a = (y1 * (a1**(1./2)) + y2 * (a2**(1./2)))**2 \n",
- "b = y1 * b1 + y2 * b2 \n",
- "Pv = ((R * T / (V - b)) - a / (V**2))/1000 \n",
- "print \"(b)Pressure of Gas by Van der waals equation = %.f kPa\"%Pv\n",
- "Tc = y1*Tc1 + y2*Tc2 \n",
- "Pc = y1*Pc1 + y2*Pc2 \n",
- "Vc = R * Tc / Pc #Pseudo critical ideal volume\n",
- "Vr = V / Vc #Pseudo reduced ideal volume\n",
- "Tr = T / Tc #Pseudo reduced temperature\n",
- "\n",
- "#From fig 5.3, we get Pr = 1.2\n",
- "Pr = 1.2 \n",
- "Pk = Pr * Pc \n",
- "print \"(c)Pressure of Gas by the Kays method = %.f kPa\"%Pk\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(a)Pressure of Gas by the ideal gas equation = 6005 kPa\n",
- "(b)Pressure of Gas by Van der waals equation = 5080 kPa\n",
- "(c)Pressure of Gas by the Kays method = 5143 kPa\n"
- ]
- }
- ],
- "prompt_number": 22
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-04-04 01:11:06 +0000