path: root/Basic_Engineering_Thermodynamics_by_Rayner_Joel/Chapter7.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 7 - Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1: pg 159"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.1\n",
      " The specific entropy of water is (kJ/kg K) =  1.304\n",
      " From table The accurate value of sf in this case is (kJ/kg K) =  1.307\n",
      "There is small error in book's final value of sf\n"
     ]
    }
   ],
   "source": [
    "#pg 159\n",
    "print('Example 7.1');\n",
    "import math\n",
    "#  aim : To determine\n",
    "#  the specific enthalpy of water\n",
    "\n",
    "#  Given values\n",
    "Tf = 273.+100;#  Temperature,[K]\n",
    "\n",
    "#  solution\n",
    "#  from steam table\n",
    "cpl = 4.187;# [kJ/kg K]\n",
    "#  using equation [8]\n",
    "sf = cpl*math.log(Tf/273.16);#  [kJ/kg*K]\n",
    "print ' The specific entropy of water is (kJ/kg K) = ',round(sf,3)\n",
    "\n",
    "#  using steam table\n",
    "sf = 1.307;#  [kJ/kg K]\n",
    "print ' From table The accurate value of sf in this case is (kJ/kg K) = ',sf\n",
    "\n",
    "print \"There is small error in book's final value of sf\"\n",
    "\n",
    "#  End\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2: pg 160"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.2\n",
      " (a) The specific entropy of wet steam is (kJ/kg K) =  5.52\n",
      " (b) The specific entropy using steam table is (kJ/kg K) =  5.559\n"
     ]
    }
   ],
   "source": [
    "#pg 160\n",
    "print('Example 7.2');\n",
    "\n",
    "#  aim : To determine\n",
    "#  the specific entropy\n",
    "import math\n",
    "#  Given values\n",
    "P = 2.;#  pressure,[MN/m^2]\n",
    "x = .8;#  dryness fraction\n",
    "\n",
    "#  solution\n",
    "#  from steam table at given pressure\n",
    "Tf = 485.4;#  [K]\n",
    "cpl = 4.187;#  [kJ/kg K]\n",
    "hfg = 1888.6;#  [kJ/kg]\n",
    "\n",
    "#  (a) finding entropy by calculation\n",
    "s = cpl*math.log(Tf/273.16)+x*hfg/Tf;#  formula for entropy calculation\n",
    "\n",
    "print ' (a) The specific entropy of wet steam is (kJ/kg K) = ',round(s,2)\n",
    "\n",
    "#  (b) calculation of entropy using steam table\n",
    "#  from steam table at given pressure\n",
    "sf = 2.447;#  [kJ/kg K]\n",
    "sfg = 3.89;#  [kJ/kg K]\n",
    "#  hence\n",
    "s = sf+x*sfg;#  [kJ/kg K]\n",
    "\n",
    "print ' (b) The specific entropy using steam table is (kJ/kg K) = ',s\n",
    "\n",
    "#  End\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3: pg 161"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.3\n",
      " (a) The specific entropy of steam is (kJ/kg K) =  6.822\n",
      " (b) The accurate value of specific entropy from steam table is (kJ/kg K) =  6.919\n"
     ]
    }
   ],
   "source": [
    "#pg 161\n",
    "print('Example 7.3');\n",
    "import math\n",
    "#  aim : To determine\n",
    "#  the specific entropy of steam\n",
    "\n",
    "#  Given values\n",
    "P = 1.5;#pressure,[MN/m^2]\n",
    "T = 273.+300;#temperature,[K]\n",
    "\n",
    "#  solution\n",
    "\n",
    "#  (a)\n",
    "#  from steam table\n",
    "cpl = 4.187;#  [kJ/kg K]\n",
    "Tf = 471.3;#  [K]\n",
    "hfg = 1946.;#  [kJ/kg]\n",
    "cpv = 2.093;#  [kJ/kg K]\n",
    "\n",
    "#  usung equation [2]\n",
    "s = cpl*math.log(Tf/273.15)+hfg/Tf+cpv*math.log(T/Tf);#  [kJ/kg K]\n",
    "print ' (a) The specific entropy of steam is (kJ/kg K) = ',round(s,3)\n",
    "\n",
    "#  (b)\n",
    "#  from steam tables\n",
    "s = 6.919;#  [kJ/kg K]\n",
    "print ' (b) The accurate value of specific entropy from steam table is (kJ/kg K) = ',s\n",
    "\n",
    "#  End\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 4: pg 164"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.4\n",
      " The final dryness fraction of steam is x2  =  0.989\n"
     ]
    }
   ],
   "source": [
    "#pg 164\n",
    "print('Example 7.4');\n",
    "\n",
    "#  aim : To determine\n",
    "#  the dryness fraction of steam\n",
    "\n",
    "#  Given values\n",
    "P1 = 2.;#  initial pressure, [MN/m^2]\n",
    "t = 350.;#  temperature, [C]\n",
    "P2 = .28;#  final pressure, [MN/m^2]\n",
    "\n",
    "#  solution\n",
    "#  at 2 MN/m^2 and 350 C,steam is superheated because the saturation temperature is 212.4 C\n",
    "#  From steam table\n",
    "s1 = 6.957;#  [kJ/kg K]\n",
    "\n",
    "#  for isentropic process\n",
    "s2 = s1;\n",
    "#  also\n",
    "sf2 = 1.647;#  [kJ/kg K]\n",
    "sfg2 = 5.368;#  [kJ/kg K]\n",
    "\n",
    "#  using\n",
    "#  s2 = sf2+x2*sfg2, where x2 is dryness fraction of steam\n",
    "#  hence\n",
    "x2 = (s2-sf2)/sfg2;\n",
    "print ' The final dryness fraction of steam is x2  = ',round(x2,3)\n",
    "\n",
    "#  End\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 5: pg 165"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.5\n",
      " (a) From steam table at .06 MN/m^2 steam is superheated and has temperature of 100 C with specific volume is (m^3/kg) =  2.83\n",
      " (b) The change in specific entropy during the hyperbolic process is (kJ/kg K) =  0.679\n"
     ]
    }
   ],
   "source": [
    "#pg 165\n",
    "print('Example 7.5');\n",
    "\n",
    "#  aim : To determine\n",
    "#  the  final condition of steam...\n",
    "#  the change in specific entropy during hyperbolic process\n",
    "\n",
    "#  Given values\n",
    "P1 = 2;#  pressure, [MN/m^2]\n",
    "t = 250.;#  temperature, [C]\n",
    "P2 = .36;#  pressure, [MN/m^2]\n",
    "P3 = .06;#  pressure, [MN/m^2]\n",
    "\n",
    "#  solution\n",
    "\n",
    "#  (a)\n",
    "#  from steam table\n",
    "s1 = 6.545;#  [kJ/kg K]\n",
    "#  at .36 MN/m^2\n",
    "sg = 6.930;#  [kJ/kg*K]\n",
    "\n",
    "sf2 = 1.738;#  [kJ/kg K]\n",
    "sfg2 = 5.192;#  [kJ/kg K]\n",
    "vg2 = .510;#  [m^3]\n",
    "\n",
    "#  so after isentropic expansion, steam is wet\n",
    "#  hence, s2=sf2+x2*sfg2, where x2 is dryness fraction\n",
    "#  also\n",
    "s2 = s1;\n",
    "#  so\n",
    "x2 = (s2-sf2)/sfg2;\n",
    "#  and\n",
    "v2 = x2*vg2;#  [m^3]\n",
    "\n",
    "#  for  hyperbolic process\n",
    "#  P2*v2=P3*v3\n",
    "#  hence\n",
    "v3 = P2*v2/P3;#  [m^3]\n",
    "\t\n",
    "print ' (a) From steam table at .06 MN/m^2 steam is superheated and has temperature of 100 C with specific volume is (m^3/kg) = ',round(v3,2)\n",
    "\n",
    "#  (b)\n",
    "#  at this condition\n",
    "s3 = 7.609;#  [kJ/kg*K]\n",
    "#  hence\n",
    "change_s23 = s3-sg;#  change in specific entropy during the hyperblic process[kJ/kg*K]\n",
    "print ' (b) The change in specific entropy during the hyperbolic process is (kJ/kg K) = ',change_s23\n",
    "\n",
    "# In the book they have taken sg instead of s2 for part (b), so answer is not matching\n",
    "\n",
    "#  End\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6: pg 166"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.6\n"
     ]
    },
    {
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6anEhxDPPhEWL0uyqwmmr7bdvdcVmBr0QFhHxfP73RUm/I51WWiBpq4hYIGlrYGHefT5Q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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa5a7fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) The heat transfer during the expansion is  (kJ)  (received) =  1224.986976\n",
      " (b) The work done during the expansion is (kJ) =  2705.234976\n"
     ]
    }
   ],
   "source": [
    "#pg 166\n",
    "print('Example 7.6');\n",
    "\n",
    "#  aim : To determine the\n",
    "#  (a) heat transfer during the expansion and\n",
    "#  (b) work done durind the expansion\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "from matplotlib import pyplot\n",
    "#  given values\n",
    "m = 4.5;  #  mass of steam,[kg]\n",
    "P1 = 3.;  #  initial pressure,[MN/m^2]\n",
    "T1 = 300.+273;  #  initial temperature,[K]\n",
    "\n",
    "P2 = .1;  #  final pressure,[MN/m^2]\n",
    "x2 = .96;  #  dryness fraction at final stage\n",
    "\n",
    "#  solution\n",
    "#  for state point 1,using steam table\n",
    "s1 = 6.541;#  [kJ/kg/K]\n",
    "u1 = 2751;# [kJ/kg]\n",
    "\n",
    "#  for state point 2\n",
    "sf2 = 1.303;#  [kJ/kg/K]\n",
    "sfg2 = 6.056;#  [kJ/kg/k]\n",
    "T2 = 273+99.6;#  [K]\n",
    "hf2 = 417;#  [kJ/kg]\n",
    "hfg2 = 2258;#  [kJ/kg]\n",
    "vg2 = 1.694;#   [m^3/kg]\n",
    "\n",
    "#  hence\n",
    "s2 = sf2+x2*sfg2;# [kJ/kg/k]\n",
    "h2 = hf2+x2*hfg2;# [kJ/kg]\n",
    "u2 = h2-P2*x2*vg2*10**3;# [kJ/kg]\n",
    "\n",
    "#  Diagram of example 7.6\n",
    "x = ([s1, s2]);\n",
    "y = ([T1, T2]);\n",
    "pyplot.plot(x,y);\n",
    "pyplot.title('Diagram for example 7.6(T vs s)');\n",
    "pyplot.xlabel('Entropy (kJ/kg K)');\n",
    "pyplot.ylabel('Temperature (K)');\n",
    "x = ([s1,s1]);\n",
    "y = ([0,T1]);\n",
    "pyplot.plot(x,y);\n",
    "x = ([s2,s2]);\n",
    "y = ([0,T2]);\n",
    "pyplot.plot(x,y);\n",
    "pyplot.show()\n",
    "#  (a)\n",
    "#  Q_rev is area of T-s diagram\n",
    "Q_rev = (T1+T2)/2*(s2-s1);# [kJ/kg]\n",
    "#  so total heat transfer is\n",
    "Q_rev = m*Q_rev;# [kJ]\n",
    "\n",
    "#  (b)\n",
    "del_u = u2-u1;#  change in internal energy, [kJ/kg]\n",
    "#  using 1st law of thermodynamics\n",
    "W = Q_rev-m*del_u;#  [kJ]\n",
    "\n",
    "print ' (a) The heat transfer during the expansion is  (kJ)  (received) = ',Q_rev\n",
    "\n",
    "print ' (b) The work done during the expansion is (kJ) = ',W\n",
    "\n",
    "#  End\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7: pg 176"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.7\n",
      " (a) The change of entropy is (kJ/K) =  -0.046\n",
      " (b) The approximate change of entropy obtained by dividing the heat transferred by the gas by the mean absolute temperature during the compression (kJ/K) =  -0.0448\n"
     ]
    }
   ],
   "source": [
    "#pg 176\n",
    "print('Example 7.7');\n",
    "\n",
    "#  aim : To determine the  \n",
    "#  (a) change of entropy\n",
    "#  (b)  The approximate change of entropy obtained by dividing the heat transferred by the gas by the mean absolute temperature during the compression\n",
    "import math\n",
    "#  Given values\n",
    "P1 = 140.;# initial pressure,[kN/m^2]\n",
    "V1 = .14;# initial volume, [m^3]\n",
    "T1 = 273.+25;# initial temperature,[K]\n",
    "P2 = 1400.;# final pressure [kN/m^2]\n",
    "n = 1.25; # polytropic index\n",
    "cp = 1.041;# [kJ/kg K]\n",
    "cv = .743;# [kJ/kg K]\n",
    "\n",
    "#  solution\n",
    "# (a)\n",
    "R = cp-cv;# [kJ/kg/K]\n",
    "#  using ideal gas equation \n",
    "m = P1*V1/(R*T1);# mass of gas,[kg]\n",
    "#  since gas is following law P*V^n=constant ,so \n",
    "V2 = V1*(P1/P2)**(1./n);#  [m^3]\n",
    "\n",
    "#  using eqn [9]\n",
    "del_s = m*(cp*math.log(V2/V1)+cv*math.log(P2/P1));#  [kJ/K]\n",
    "print ' (a) The change of entropy is (kJ/K) = ',round(del_s,3)\n",
    "\n",
    "#  (b)\n",
    "W = (P1*V1-P2*V2)/(n-1);# polytropic work,[kJ]\n",
    "Gamma = cp/cv;# heat capacity ratio\n",
    "Q = (Gamma-n)/(Gamma-1)*W;# heat transferred,[kJ]\n",
    "\n",
    "# Again using polytropic law\n",
    "T2 = T1*(V1/V2)**(n-1);# final temperature, [K]\n",
    "T_avg = (T1+T2)/2;# mean absolute temperature, [K]\n",
    "\n",
    "# so approximate change in entropy is\n",
    "del_s = Q/T_avg;# [kJ/K]\n",
    "\n",
    "print ' (b) The approximate change of entropy obtained by dividing the heat transferred by the gas by the mean absolute temperature during the compression (kJ/K) = ',round(del_s,4)\n",
    "\n",
    "#  End\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 8: pg 179"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.8\n",
      " The change of entropy in constant volume process is (kJ/kg K) =  0.149\n",
      " The change of entropy in constant pressure process is (kJ/kg K) =  0.332\n",
      "there is misprint in the book's result\n"
     ]
    }
   ],
   "source": [
    "#pg 179\n",
    "print('Example 7.8');\n",
    "\n",
    "#  aim : To determine\n",
    "#  the change of entropy\n",
    "import math\n",
    "#  Given values\n",
    "m = .3;#  [kg]\n",
    "P1 = 350.;#  [kN/m^2]\n",
    "T1 = 273.+35;#  [K]\n",
    "P2 = 700.;#  [kN/m^2]\n",
    "V3 = .2289;#  [m^3]\n",
    "cp = 1.006;#  [kJ/kg K]\n",
    "cv = .717;#  [kJ/kg K]\n",
    "\n",
    "#  solution\n",
    "#  for constant volume process\n",
    "R = cp-cv;#  [kJ/kg K]\n",
    "#  using PV=mRT\n",
    "V1 = m*R*T1/P1;#  [m^3]\n",
    "\n",
    "#  for constant volume process P/T=constant,so\n",
    "T2 = T1*P2/P1;#  [K]\n",
    "s21 = m*cv*math.log(P2/P1);#  formula for entropy change for constant volume process\n",
    "print ' The change of entropy in constant volume process is (kJ/kg K) = ',round(s21,3)\n",
    "\n",
    "# 'For the above part result given in the book is wrong\n",
    "\n",
    "V2 = V1;\n",
    "# for constant pressure process\n",
    "T3 = T2*V3/V2;#  [K]\n",
    "s32 = m*cp*math.log(V3/V2);#  [kJ/kg K]\n",
    "\n",
    "print ' The change of entropy in constant pressure process is (kJ/kg K) = ',round(s32,3)\n",
    "\n",
    "print \"there is misprint in the book's result\"\n",
    "\n",
    "# End\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9: pg 181"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example 7.9\n",
      " The change of entropy is (kJ/kg K) =  0.04151\n"
     ]
    }
   ],
   "source": [
    "#pg 181\n",
    "print('Example 7.9');\n",
    "import math\n",
    "#  aim : To determine\n",
    "#  the  change of entropy\n",
    "\n",
    "# Given values\n",
    "P1 = 700.;# initial pressure, [kN/m^2]\n",
    "T1 = 273.+150;#  Temperature ,[K]\n",
    "V1 = .014;# initial volume, [m^3]\n",
    "V2 = .084;#  final volume, [m^3]\n",
    "\n",
    "#  solution\n",
    "#  since process is isothermal so\n",
    "T2 = T1;\n",
    "# and using fig.7.10\n",
    "del_s = P1*V1*math.log(V2/V1)/T1 ;#  [kJ/K]\n",
    "#results\n",
    "print ' The change of entropy is (kJ/kg K) = ',round(del_s,5)\n",
    "\n",
    "#  End\n"
   ]
  }
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