path: root/Thermodynamics/Chapter11.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 11:THERMODYNAMIC PROPERTY RELATIONS"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.1, Page No:510"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "p1=150; p2=200; p3=250; p4=300; p5=350; p6=400; p7=450; p8=500; p9=550; p10=600; p11=650; p12=700;\n",
      "p13=750; p14=800; p15=850; p16=900; # Pressures of merect's  boiler experiment in kPa\n",
      "t1=111.4; t2=120.2; t3=127.4; t4=133.6; t5=138.9; t6=143.6; t7=147.9; t8=151.9;  t9=155.5; t10=158.9; t11=162;\n",
      "t12=165; t13=167.8; t14=170.4; t15=173; t16=175.4; # Temperatures of merect's boiler experiment in degree celcius\n",
      "n=16;# Total number of readings taken  \n",
      "\n",
      "#Calculation for constants\n",
      "# Values of constant A & B\n",
      "s_y= math.log10 (p1*p2*p3*p4*p5*p6*p7*p8*p9*p10*p11*p12*p13*p14*p15*p16);\n",
      "s_x=1/(t1+273)+1/(t2+273)+1/(t3+273)+1/(t4+273)+1/(t5+273)+1/(t6+273)+1/(t7+273)+1/(t8+273)+1/(t9+273)+1/(t10+273)+1/(t11+273)+1/(t12+273)+1/(t13+273)+1/(t14+273)+1/(t15+273)+1/(t16+273);\n",
      "s_xy=((math.log10 (p1))*1/(t1+273))+ ((math.log10 (p2))*1/(t2+273))+ ((math.log10 (p3))*1/(t3+273))+ ((math.log10 (p4))*1/(t4+273))+ ((math.log10 (p5))*1/(t5+273))+ ((math.log10 (p6))*1/(t6+273))+ ((math.log10 (p7))*1/(t7+273))+ ((math.log10 (p8))*1/(t8+273))+ ((math.log10 (p9))*1/(t9+273))+ ((math.log10 (p10))*1/(t10+273))+ ((math.log10 (p11))*1/(t11+273)) + ((math.log10 (p12))*1/(t12+273)) + ((math.log10 (p13))*1/(t13+273)) + ((math.log10 (p14))*1/(t14+273)) + ((math.log10 (p15))*1/(t15+273)) + ((math.log10 (p16))*1/(t16+273));\n",
      "s_x2=(1/(273+t1))**2+(1/(273+t2))**2+(1/(273+t3))**2+(1/(273+t4))**2+(1/(273+t5))**2+(1/(273+t6))**2+(1/(273+t7))**2+(1/(273+t8))**2+(1/(273+t9))**2+(1/(273+t10))**2+(1/(273+t11))**2+(1/(273+t12))**2+(1/(273+t13))**2+(1/(273+t14))**2+(1/(273+t15))**2+(1/(273+t16))**2;\n",
      "B= ((n*s_xy)-(s_x*s_y))/((n*s_x2)-((s_x)**2)); # Constant B\n",
      "A=((s_y)-(B*s_x))/n; # Constant A\n",
      "\n",
      "#Result for constants\n",
      "print \"Values of constant A & B\"\n",
      "print \"A =\",round(A,5)\n",
      "print \"B =\",round(B,1),\"   (roundoff error)\"\n",
      "\n",
      "#Calculation for latent heat of vapourization\n",
      "# The latent heat of vapourization\n",
      "T=150; # The latent heat of vapourization at this temperature in degree celcius\n",
      "d_T=20; d_p=258.7; # Temperature and pressure difference\n",
      "vg=0.3928; vf=0.0011; # specific volume in m^3/kg\n",
      "hfg=(T+273)*(vg-vf)*d_p/d_T; # Clapeyron equztion\n",
      "\n",
      "#Result for latent heat of vapourization\n",
      "print \"The latent heat of vapourization at 150 oC =\",round(hfg,2),\"kJ/kg\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Values of constant A & B\n",
        "A = 7.62068\n",
        "B = -2091.6    (roundoff error)\n",
        "The latent heat of vapourization at 150 oC = 2143.19 kJ/kg\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.3, Page No:517"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "p5=6000; # Pressure of superheated steam in kPa\n",
      "T5=723.15; # Temperature of superheated steam in kelvin\n",
      "p1=0.6113; # Pressure at reference state in kPa\n",
      "T1=273.16; # Temperature at reference state in kelvin\n",
      "hfg1=2501.3; # Latent heat of vapourization of water at reference state in kJ/kg\n",
      "R_1=8.3143; # Universal gas constant of air in kJ/kmol K\n",
      "# The critical state properties of water\n",
      "pc=2.09; # pressure in MPa\n",
      "Tc=647.3; # Temperature in kelvin\n",
      "h1=0; # Reference state in kJ/kg\n",
      "\n",
      "#Calculation\n",
      "h2=h1+hfg1; # specific enthalpy in kJ/kg \n",
      "# At point 2\n",
      "p2=p1; T2=T1;\n",
      "z=0.9986;\n",
      "r=18.015;\n",
      "A2=(0.4278/(pc*10**4))*(Tc/T2)**2.5; # Constants\n",
      "B=(0.0867/(pc*10**4))*(Tc/T2); # Constants\n",
      "h2_h3=R_1*(T2/r)*(((-3/2)*(A2/B)*math.log (1+(B*p2/z)))+z-1); # Enthalpy difference between state 2 & 3\n",
      "# At point 5\n",
      "z1=0.9373;\n",
      "A2=(0.4278/(pc*10**4))*(Tc/T5)**2.5; # Constants\n",
      "B=(0.0867/(pc*10**4))*(Tc/T5); # Constants\n",
      "h5_h4=R_1*(T5/r)*(((-3/2)*(A2/B)*math.log (1+(B*p5/z1)))+z1-1); # Enthalpy difference between state 5 & 4\n",
      "a=1.6198;b=6.6*10**-4; # Constants\n",
      "h4_h3=a*(T5-T1)+b*(T5**2-T1**2)/2; # Enthalpy difference between state 3 & 4\n",
      "h5=h2-h2_h3+h5_h4+h4_h3; # Specific enthalpy at state 5 \n",
      "\n",
      "#Result\n",
      "print \"Specific enthalpy at state 5 = \",round(h5,1),\"kJ/kg    (roundoff error)\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Specific enthalpy at state 5 =  3308.3 kJ/kg    (roundoff error)\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.4, Page No:527"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "T2=373; # Temperature of CO2 gas in kelvin\n",
      "p2=100; # Pressure of CO2 gas in atm\n",
      "T1=0; # Reference state temperature in kelvin\n",
      "# The crictical constants for CO2 are \n",
      "Tc=304.2; # Temperature in kelvin\n",
      "Pc=72.9; # Pressure in atm\n",
      "zc=0.275;\n",
      "\n",
      "#Calculation\n",
      "# Refer figure 11.7 for state definition\n",
      "h1_0=((-3.74*T2)+((30.53/(100**0.5))*((T2**1.5)/1.5))-((4.1/100)*((T2**2)/2))+((0.024/(100**2))*((T2**3)/3)));\n",
      "Tr=T2/Tc; Pr=p2/Pc; # Reduced properties\n",
      "# From generalized chart figure 11.6\n",
      "hR_Tc=10.09;\n",
      "h1_2=hR_Tc*Tc;\n",
      "M=44; # Molecular weight\n",
      "h10=h1_0/M; h12=h1_2/M;\n",
      "h373=h10-h12; # The required enthalpy of CO2 gas at 373 K and 100 atm\n",
      "\n",
      "#Result\n",
      "print \"The required enthalpy of CO2 gas at 373 K and 100 atm = \",round(h373,0),\"kJ/kg\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The required enthalpy of CO2 gas at 373 K and 100 atm =  168.0 kJ/kg\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.5, Page No:531"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "p1=11; # Initial pressure in bar\n",
      "T1=40; # Initial temperature in degree celcius\n",
      "p2=60; #  Final pressure in bar\n",
      "R_1=8.3143; # Universal gas constant  in kJ/kmol K\n",
      "# The crictical properties for natural gas \n",
      "Tc=161; # Temperature in kelvin\n",
      "Pc=46.4; # Pressure in bar\n",
      "\n",
      "#Calculation\n",
      "# Reduced properties are\n",
      "Pr1=p1/Pc; Pr2=p2/Pc;\n",
      "Tr1=(T1+273)/Tc;\n",
      "# T2=T1, The ideal gas enthalpy h2*=h1*=h1\n",
      "h21=-47.5; # From generalized enthalpy departure chart\n",
      "M=16; # Molecular weight\n",
      "Sp2_1=(R_1/M)*math.log (p2/p1)# for the difference in ideal gas entropies\n",
      "Sp2_Sp_2=-0.1125; Sp_2_Sp_1=-2.1276; # Entropies in kJ/kg K\n",
      "s2_s1=(Sp2_Sp_2)+(Sp_2_Sp_1);\n",
      "q=(T1+273)*s2_s1; # Heat transfer\n",
      "w=q-h21; # Work of compression\n",
      "\n",
      "#Result\n",
      "print \"Heat transfer = \",round(q,1),\"kJ/kg\",\"\\nWork of compression = \",round(w,0),\"kJ/kg\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat transfer =  -701.2 kJ/kg \n",
        "Work of compression =  -654.0 kJ/kg\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.8, Page No:538"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "p1=10; # Initial pressure in MPa\n",
      "T1=263; # Initial temperature in Kelvin\n",
      "p2=1.5; #  Final pressure in MPa\n",
      "R_1=8.3143; # Universal gas constant  in kJ/kmol K\n",
      "M=28; # Molecular mass\n",
      "# The crictical properties for nitrogen gas \n",
      "Tc=126.2; # Temperature in kelvin\n",
      "Pc=3.39; # Pressure in MPa\n",
      "\n",
      "#Calculation\n",
      "# Reduced properties are\n",
      "Pr1=p1/Pc; Pr2=p2/Pc;\n",
      "Tr1=T1/Tc;\n",
      "# From the generalized chart for enthalpy departure at Pr1 & Tr1\n",
      "h_11=8.7*Tc/M;\n",
      "# The solution involves iteration procedure. Assume T2 and check if h2_h1=0\n",
      "# First approximation T2=200 K\n",
      "T2=200; # In K\n",
      "Tr2=T2/Tc;\n",
      "Cpr=1.046;\n",
      "h_21=Cpr*(T2-T1);\n",
      "# From the generalized chart for enthalpy departure at Pr1 & Tr1\n",
      "h_22=1*Tc/M;\n",
      "h2_h1=h_11-T2+T1-h_22;\n",
      "# Second approximation \n",
      "T2=190; # In K\n",
      "Tr2=T2/Tc;\n",
      "Cpr=1.046;\n",
      "h_21=Cpr*(T2-T1);\n",
      "# From the generalized chart for enthalpy departure at Pr1 & Tr1\n",
      "h_22=1.5*Tc/M;\n",
      "h2_h1=h_11-T2+T1-h_22;\n",
      "\n",
      "#Result\n",
      "print \"Here also h2-h1 != 0. Therefore the temperature is dropping. Thus Joule-Thomson coefficient is positive.\"\n",
      "print \"There is cooling in this process\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Here also h2-h1 != 0. Therefore the temperature is dropping. Thus Joule-Thomson coefficient is positive.\n",
        "There is cooling in this process\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.9, Page No:544"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "Tcammonia=405.9;\n",
      "Tcwater=647.3;\n",
      "Tr=0.576; # Condition of similarity\n",
      "\n",
      "#Calculation\n",
      "Twater=Tcwater*Tr; # At reduced temperature Temperature of water\n",
      "Tammonia=Tcammonia*Tr;#At reduced temperature Temperature of  ammonia\n",
      "# From steam table at Twater\n",
      "hfgwater=2257;# specific enthalpy in kJ/kg \n",
      "hfgammonia=Tcammonia/Tcwater *hfgwater; # Latent heat of vaporization of ammonia\n",
      "\n",
      "#Result\n",
      "print \"Latent heat of vaporization of ammonia =\",round(hfgammonia,0),\"kJ/kg\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Latent heat of vaporization of ammonia = 1415.0 kJ/kg\n"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}