path: root/Thermodynamics_by_C_P_Arora/Chapter12.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 12:NON-REACTING MIXTURES OF GASES AND LIQUIDS"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.1, Page No:553"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "M1=28.02; # Molecular mass of N2\n",
      "M2=32; # Molecular mass of O2\n",
      "M3=39.91; # Molecular mass of Ar\n",
      "M4=44; # Molecular mass of CO2\n",
      "M5=2.02; # Molecular mass of H2\n",
      "y1=0.7803; # Part by volume of N2 in dry atmospheric air\n",
      "y2=0.2099; # Part by volume of O2 in dry atmospheric air\n",
      "y3=0.0094; # Part by volume of Ar in dry atmospheric air\n",
      "y4=0.0003; # Part by volume of CO2 in dry atmospheric air\n",
      "y5=0.0001; # Part by volume of H2 in dry atmospheric air\n",
      "R_1=8.3143; # Universal gas constant of air in kJ/kmol K\n",
      "\n",
      "#Calculation for (a)\n",
      "# (a).Average molecular mass and apperent gas constant of dry atmospheric air\n",
      "M=(y1*M1)+(y2*M2)+(y3*M3)+(y4*M4)+(y5*M5); # Average molecular mass\n",
      "R=R_1/M; #Apperent gas constant of dry atmospheric air\n",
      "\n",
      "#Result for (a)\n",
      "print \"(a).Average molecular mass and apperent gas constant of dry atmospheric air\",\"\\nAverage molecular mass = \",round(M,3),\"kmol\"\n",
      "print \"Apperent gas constant of dry atmospheric air =\",round(R,3),\"kJ/kg K\"\n",
      "\n",
      "#Calculation for (b)\n",
      "# (b).The fraction of each component\n",
      "m1=(M1*y1)/M;#The fraction of N2 component\n",
      "m2=(M2*y2)/M;#The fraction of O2 component\n",
      "m3=(M3*y3)/M;#The fraction of Ar component\n",
      "m4=(M4*y4)/M;#The fraction of CO2 component\n",
      "m5=(M5*y5)/M;#The fraction of H2 component\n",
      "\n",
      "#Result for (b)\n",
      "print \"\\n(b).The fraction of N2,O2,Ar,CO2,H2 components are given below respectively \"\n",
      "print \"m1 =\",round(m1,4)\n",
      "print \"m2 =\",round(m2,4)\n",
      "print \"m3 =\",round(m3,4)\n",
      "print \"m4 =\",round(m4,4)\n",
      "print \"m5 =\",round(m5,4)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).Average molecular mass and apperent gas constant of dry atmospheric air \n",
        "Average molecular mass =  28.969 kmol\n",
        "Apperent gas constant of dry atmospheric air = 0.287 kJ/kg K\n",
        "\n",
        "(b).The fraction of N2,O2,Ar,CO2,H2 components are given below respectively \n",
        "m1 = 0.7547\n",
        "m2 = 0.2319\n",
        "m3 = 0.013\n",
        "m4 = 0.0005\n",
        "m5 = 0.0\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.2, Page No:555"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "M1=44; # Molecular mass of CO2\n",
      "M2=32; # Molecular mass of O2\n",
      "M3=28; # Molecular mass of CO\n",
      "M4=28; # Molecular mass of N2\n",
      "y1=0.1; # Part by volume of CO2 in exhaust gas\n",
      "y2=0.06; # Part by volume of O2 in exhaust gas\n",
      "y3=0.03; # Part by volume of CO in exhaust gas\n",
      "y4=0.81; # Part by volume of N2 in exhaust gas\n",
      "R_1=8.3143; # Universal gas constant  in kJ/kmol K\n",
      "\n",
      "#Calculation for (a)\n",
      "# (a).Average molecular mass and apperent gas constant of exhaust gas\n",
      "M=(y1*M1)+(y2*M2)+(y3*M3)+(y4*M4); # Average molecular mass\n",
      "R=R_1/M; #Apperent gas constant of dry atmospheric air\n",
      "\n",
      "#Result for (a)\n",
      "print \"(a).Average molecular mass and apperent gas constant of exhaust gas\",\"\\nAverage molecular mass = \",round(M,3),\"kmol\"\n",
      "print \"Apperent gas constant of exhaust gas =\",round(R,4),\"kJ/kg K\"\n",
      "\n",
      "#Calculation for (b)\n",
      "# (b).The fraction of each component\n",
      "m1=(M1*y1)/M;#The fraction of CO2 component\n",
      "m2=(M2*y2)/M;#The fraction of O2 component\n",
      "m3=(M3*y3)/M;#The fraction of CO component\n",
      "m4=(M4*y4)/M;#The fraction of N2 component\n",
      "print \"\\n(b).The fraction of CO2,O2,CO,N2 components are given below respectively \"\n",
      "print \"m1 =\",round(m1,3)\n",
      "print \"m2 =\",round(m2,3)\n",
      "print \"m3 =\",round(m3,3)\n",
      "print \"m4 =\",round(m4,3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).Average molecular mass and apperent gas constant of exhaust gas \n",
        "Average molecular mass =  29.84 kmol\n",
        "Apperent gas constant of exhaust gas = 0.2786 kJ/kg K\n",
        "\n",
        "(b).The fraction of CO2,O2,CO,N2 components are given below respectively \n",
        "m1 = 0.147\n",
        "m2 = 0.064\n",
        "m3 = 0.028\n",
        "m4 = 0.76\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.3, Page No:557"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "y1=0.79; # Volume of Nitrogen in 1 kg of air\n",
      "y2=0.21; # Volume of Oxygen in 1 kg of air\n",
      "R_1=8.3143; # Universal gas constant of air in kJ/kmol K\n",
      "T0=298; # temperature of Surroundings in kelvin\n",
      "\n",
      "#Calculation\n",
      "del_Sgen=-R_1*((y1*math.log (y1))+(y2*math.log (y2))); #Entropy generation\n",
      "LW=T0*del_Sgen; # Minimum work\n",
      "\n",
      "#Result\n",
      "print \"The minimum work required for separation of two gases = \",round(LW,0),\"kJ/kmmol K\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The minimum work required for separation of two gases =  1273.0 kJ/kmmol K\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.4, Page No:562"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "DPT=8; # Dew point temperature in degree celcius\n",
      "p=100; # Pressure of air in kPa\n",
      "T=25; # Temperature of air in degree celcius\n",
      "\n",
      "#Calculation for (a)\n",
      "# (a).partial pressure of water vapour in air\n",
      "pv=1.0854; # Saturation pressure of water at DBT in kPa\n",
      "\n",
      "#Result for (a)\n",
      "print \"(a).partial pressure of water vapour in air = \",pv,\"kPa\"\n",
      "\n",
      "#Calculation for (b)\n",
      "# (b).Specific humidity\n",
      "sh=0.622*pv/(p-pv);#Specific humidity\n",
      "\n",
      "#Result for (b)\n",
      "print \"\\n(b).Specific humidity =\",round(sh,4),\"kg of water vapour /kg of dry air\"\n",
      "\n",
      "#Calculation for (c)\n",
      "# (c).Relative humidity\n",
      "pg=3.169; # Saturation pressure of water at T in kPa\n",
      "RH=pv/pg; #Relative humidity\n",
      "\n",
      "#Result for (c)\n",
      "print \"\\n(c).Relative humidity =\",round(RH*100,2),\"%\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).partial pressure of water vapour in air =  1.0854 kPa\n",
        "\n",
        "(b).Specific humidity = 0.0068 kg of water vapour /kg of dry air\n",
        "\n",
        "(c).Relative humidity = 34.25 %\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.5, Page No:566"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "DBT=35; # Dry bulb temperature in degree celcius\n",
      "WBT=23; # Wet bulb temperature in degree celcius\n",
      "P=100; # Pressure of air in kPa\n",
      "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n",
      "R=0.287; # characteristic gas constant of air in kJ/kg K\n",
      "# (a).Humidity ratio\n",
      "hv=2565.3; # specific enthalpy hg at DBT in kJ/kg \n",
      "hfWBT=96.52; hfgWBT=2443; # specific enthalpy at WBT in kJ/kg \n",
      "PsatWBT=2.789;# Saturation pressure at WBT in kPa\n",
      "\n",
      "#Calculation for (a)\n",
      "shWBT=0.622*PsatWBT/(P-PsatWBT);# specific humidity\n",
      "sh=((Cpo*(WBT-DBT))+(shWBT*hfgWBT))/(hv-hfWBT); # Humidity ratio\n",
      "\n",
      "#Result for (a)\n",
      "print \"(a).Humidity ratio =\",round(sh,4),\"kg w.v /kg d.a\"\n",
      "\n",
      "#Calculation for (b)\n",
      "# (b).Relative Humidity\n",
      "pv=sh*P/(0.622+sh); # Partial pressure of water vapour\n",
      "pg=5.628; # Saturation pressure at DBT in kPa\n",
      "RH=pv/pg; #Relative Humidity\n",
      "\n",
      "#Result for (b)\n",
      "print \"\\n(b).Relative Humidity =\",round(RH*100,2),\"%\"\n",
      "\n",
      "#Calculation for (c)\n",
      "# (c).Dew point temperature\n",
      "DPT=17.5; # Saturation temperature at pg in degree celcius\n",
      "\n",
      "#Result for (c)\n",
      "print \"\\n(c).Dew point temperature =\",DPT,\"oC\"\n",
      "\n",
      "#Calculation for (d)\n",
      "# (d).Specific volume\n",
      "v=(R*(DBT+273))/(P-pv); # Specific volume\n",
      "\n",
      "#Result for (d)\n",
      "print \"\\n(d).Specific volume = \",round(v,1),\"m^3/kg\"\n",
      "\n",
      "#Calculation for (e)\n",
      "# (e).Enthalpy of air\n",
      "h=(Cpo*DBT)+(sh*hv); #Enthalpy of air\n",
      "\n",
      "#Result for (e)\n",
      "print \"\\n(e).Enthalpy of air =\",round(h,0),\"kJ/kg d.a\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).Humidity ratio = 0.0128 kg w.v /kg d.a\n",
        "\n",
        "(b).Relative Humidity = 35.78 %\n",
        "\n",
        "(c).Dew point temperature = 17.5 oC\n",
        "\n",
        "(d).Specific volume =  0.9 m^3/kg\n",
        "\n",
        "(e).Enthalpy of air = 68.0 kJ/kg d.a\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.6, Page No:570"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "DPT1=30; # Dew point temperature at inlet in degree celcius\n",
      "DPT2=15; # Dew point temperature at outlet in degree celcius\n",
      "RH1=0.50; # Relative humidity  at inlet\n",
      "RH2=0.80; # Relative humidity  at outlet\n",
      "p=101.325; # Atmospheric pressure in kPa\n",
      "Cpo=1.0035; # Specific heat at constant pressure in kJ/kg K\n",
      "pg1=4.246; # saturation pressure of water at DBT1 in kPa\n",
      "pg2=1.7051;  # saturation pressure of water at DBT2 in kPa\n",
      "pv1=RH1*pg1; pv2=RH2*pg2; # Partial pressure of water vapour in air at inlet and outlet\n",
      "hv1=2556.3;# specific enthalpy hg at DBT1 in kJ/kg\n",
      "hv2=2528.9;# specific enthalpy hg at DBT2 in kJ/kg\n",
      "hv3=63;# specific enthalpy hf at DBT 2in kJ/kg\n",
      "\n",
      "#Calculation\n",
      "sh1=0.622*pv1/(p-pv1); sh2=0.622*pv2/(p-pv2); # Specific humidities at inlet and outlet\n",
      "q=(Cpo*(DPT2-DPT1))+(sh2*hv2)-(sh1*hv1)+((sh1-sh2)*hv3); # Heat transfer\n",
      "\n",
      "#Result\n",
      "print \"Heat removed from the air =\",round(q,1),\"kJ/kg of dry air\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat removed from the air = -27.3 kJ/kg of dry air\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.7, Page No:572"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "y1=0.5; # Molecular mass of CH4 in kmol\n",
      "y2=0.5; # Molecular mass of C3H8 in kmol\n",
      "T=363; # Temperature of gas in kelvin\n",
      "p=5.06; # Pressure of gas in MPa\n",
      "v=0.48; # volume of cylinder in m^3\n",
      "R_1=8.3143; # Universal gas constant of air in kJ/kmol K\n",
      "# (a).Using kay\u2019s rule\n",
      "# let component 1 refer to methane and component 2 to propane\n",
      "# the critical properties\n",
      "Tc1=190.7; Tc2=370; # temperature in kelvin\n",
      "Pc1=46.4; Pc2=42.7; # Pressure in bar\n",
      "\n",
      "#Calculation for (a)\n",
      "# using kay\u2019s rule for the mixture\n",
      "Tcmix=y1*Tc1+y2*Tc2;\n",
      "Pcmix=y1*Pc1+y2*Pc2;\n",
      "# reduced properties\n",
      "Tr=T/Tcmix; Pr=p/Pcmix;\n",
      "# From generalized chart\n",
      "z=0.832;\n",
      "v_1=z*R_1*T/(p*10**3); # molar volume of the mixture\n",
      "d=(v-v_1)/v; # Percentage deviation from actual value\n",
      "\n",
      "#Result for (a)\n",
      "print \"(a).Using kay\u2019s rule\",\"\\nPercentage deviation from actual value = \",round(d*100,1),\"%\"\n",
      "\n",
      "#Calculation for (b)\n",
      "# (b).Using Redlich-Kwong equation of state\n",
      "a1=0.42748*R_1*Tc1**2.5/Pc1;\n",
      "a2=0.42748*R_1*Tc2**2.5/Pc2;\n",
      "b1=0.08664*R_1*Tc1/Pc1;\n",
      "b2=0.08664*R_1*Tc2/Pc2;\n",
      "# Substituting these values in the equation 12.16\n",
      "# And solving these equation by iteration method we get\n",
      "v_1=0.47864;# molar volume of the mixture\n",
      "d=(v-v_1)/v; # Percentage deviation from actual value\n",
      "\n",
      "#Result for (b)\n",
      "print \"\\n(b).Using Redlich-Kwong equation of state\",\"\\nPercentage deviation from actual value = \",round(d*100,1),\"%\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).Using kay\u2019s rule \n",
        "Percentage deviation from actual value =  -3.4 %\n",
        "\n",
        "(b).Using Redlich-Kwong equation of state \n",
        "Percentage deviation from actual value =  0.3 %\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12.8, Page No:586"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "ln_piCH4=-0.0323;\n",
      "pi_CH4=0.9683;\n",
      "p=6895; # Pressure in kPa\n",
      "T=104.4; # Temperature in degree celcius\n",
      "a=0.784;\n",
      "\n",
      "#Calculation \n",
      "f_CH4=pi_CH4*a*p; # Faguacity\n",
      "\n",
      "#Result\n",
      "print \"The Required Faguacity = \",round(f_CH4,0),\"kPa\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Required Faguacity =  5234.0 kPa\n"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}