path: root/Engineering_Thermodynamics/ch4.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 4 : First Law of Thermodynamics"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.1 Page No : 78"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "V1 = 0.3; \t\t\t# Initial volume in m3\n",
      "V2 = 0.15; \t\t\t# Final volume in m3\n",
      "P = 0.105e06; \t\t\t# Pressure in Pa\n",
      "Q = -37.6e03; \t\t\t# Heat tranferred in J\n",
      "\n",
      "# Calculation\n",
      "W = P*(V2-V1); \t\t\t# Work done\n",
      "U = Q-W; \t\t\t# Internal energy change\n",
      "\n",
      "# Results\n",
      "print \"Change in the internal energy of the system is %.2f kJ\"%(U/1000)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Change in the internal energy of the system is -21.85 kJ\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.2 Page No : 78"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "Qacb = 84e03;\n",
      "Wacb = 32e03;\n",
      "Uba = Qacb-Wacb; \t\t\t# Ub-Ua\n",
      "\n",
      "# Calculation and Results\n",
      "# Part (a)\n",
      "Wadb = 10.5e03; \n",
      "Qadb = Uba+Wadb; \n",
      "print \"The heat flow into the system along the path adb\",(Qadb/1000),\"kJ\"\n",
      "\n",
      "# Part (b)\n",
      "Wb_a = -21e03;\n",
      "Uab = - Uba;\n",
      "Qb_a = Uab+Wb_a;\n",
      "print \"The heat liberated along the path b-a is\",round(Qb_a/1000),\"kJ\"\n",
      "\n",
      "# Part (c)\n",
      "Wdb = 0.; \t\t\t# Constant volume\n",
      "Wad = 10.4e03; \n",
      "Wadb = Wdb-Wad; \n",
      "Ud = 42e03;\n",
      "Ua = 0.;\n",
      "Qad = Ud-Ua+Wad;\n",
      "Qdb = Qadb-Qad; \n",
      "print \"The heat absorbed in the path ad and db are\",round(Qdb/1000),\"kJ\",\"and\",round(Qad/1000),\"kJ\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The heat flow into the system along the path adb 62.5 kJ\n",
        "The heat liberated along the path b-a is -73.0 kJ\n",
        "The heat absorbed in the path ad and db are 10.0 kJ and 52.0 kJ\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.3 Page No : 79"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "# Process a-b\n",
      "Qab = 0;\n",
      "Wab = 2170; \t\t\t# in KJ/min\n",
      "Eab = Qab-Wab; \n",
      "\n",
      "# Process b-c\n",
      "Qbc = 21000;\n",
      "Wbc = 0; \n",
      "Ebc = Qbc-Wbc;\n",
      "\n",
      "# Process c-d\n",
      "Qcd = -2100;\n",
      "Ecd = -36600; \n",
      "Wcd = Qcd-Ecd;\n",
      "\n",
      "# Calculation\n",
      "# Process d-a\n",
      "Q = -17000; \t\t\t# Total heat transfer\n",
      "Qda = Q-Qab-Qbc-Qcd; \n",
      "Eda = -Eab-Ebc-Ecd;\n",
      "Wda = Qda-Eda;\n",
      "M = [[Qab, Wab, Eab],[Qbc, Wbc ,Ebc],[Qcd, Wcd, Ecd],[Qda, Wda, Eda]];\n",
      "process = [\"a-b\",\"b-c\",\"c-d\",\"d-a\"]\n",
      "# Results\n",
      "print \"The completed table is\"\n",
      "print \"    process        Q          W         deltaE\"\n",
      "for i in range(4):\n",
      "    print \"%10s\"%process[i],\n",
      "    for j in range(3):\n",
      "        print \"%10d\"%M[i][j],\n",
      "\n",
      "    print \"\"\n",
      "print \"\\nRate of work output : %.f kJ/min\"%(sum([M[0][0],M[1][0],M[2][0],M[3][0]]))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The completed table is\n",
        "    process        Q          W         deltaE\n",
        "       a-b          0       2170      -2170 \n",
        "       b-c      21000          0      21000 \n",
        "       c-d      -2100      34500     -36600 \n",
        "       d-a     -35900     -53670      17770 \n",
        "\n",
        "Rate of work output : -17000 kJ/min\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.4 Page No : 80"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Part (a)\n",
      "import math \n",
      "\n",
      "# Variables\n",
      "m = 3.;\n",
      "V1 = 0.22;     #volume m^3\n",
      "P1 = 500.e03;  #initial pressure Pa\n",
      "P2 = 100.e03;  #final pressure Pa\n",
      "\n",
      "# Calculation\n",
      "V2 = V1*(P1/P2)**(1./1.2);\n",
      "dU = 3.56*(P2*V2-P1*V1);\n",
      "gama = 1.2;\n",
      "W = (P2*V2-P1*V1)/(1-gama);\n",
      "Q = dU+W;\n",
      "\n",
      "# Results\n",
      "print \"Q,W and dU of the quasi static process are\",int(dU/1000),round(W/1000),round(Q/1000),\"kJ respectively\"\n",
      "\n",
      "# Part (b)\n",
      "Qb = 30e03;\n",
      "Wb = Qb-dU; \n",
      "print \"Work transfer for the process is\",round(Wb/1000),\"kJ\"\n",
      "\n",
      "# Part (c)\n",
      "print \"Wb is not equal to integral(p*dv) .since the process is not quasi static\"\n",
      "\n",
      "# rounding off error. please check"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Q,W and dU of the quasi static process are -92 129.0 37.0 kJ respectively\n",
        "Work transfer for the process is 122.0 kJ\n",
        "Wb is not equal to integral(p*dv) .since the process is not quasi static\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.5 Page No : 81"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.linalg import inv\n",
      "from numpy import *\n",
      "from scipy.integrate import *\n",
      "\n",
      "# Variables\n",
      "V1 = 0.03;    #initial volume m^3\n",
      "P1 = 170e03;  #initial pressure Pa\n",
      "P2 = 400e03;  #final pressure Pa\n",
      "V2 = 0.06;    #final volume m^3\n",
      "U = 3.15*(P2*V2-P1*V1);\n",
      "B = array([P1, P2]);\n",
      "B= B.transpose()\n",
      "\n",
      "A = [[1, V1],[1, V2]];\n",
      "A = array(A)\n",
      "x =  inv(A)*B;\n",
      "\n",
      "a = -60000\n",
      "b = 7666666.7;\n",
      "\n",
      "# Calculation\n",
      "def pressure(V):\n",
      "    return a+b*V;\n",
      "\n",
      "W = quad(pressure,V1,V2)[0]\n",
      "Q = U+W;\n",
      "\n",
      "# Results\n",
      "print \"The work done by the system is\",round(W/1000,2),\"kJ\"\n",
      "print \"The internal energy change of the system is\",round(U/1000,1),\"J\"\n",
      "print \"The heat flow into the system is\",round(Q/1000,2),\"kJ\"\n",
      "\n",
      "# rounding off error. please check."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The work done by the system is 8.55 kJ\n",
        "The internal energy change of the system is 59.5 J\n",
        "The heat flow into the system is 68.09 kJ\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.6 Page No : 82"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Process 1-2\n",
      "import math \n",
      "\n",
      "# Variables\n",
      "Q12 = 235; \t\t\t# in KJ/Kg\n",
      "W12 = 0 ;\n",
      "\n",
      "# Calculation\n",
      "U12 = Q12-W12;\n",
      "# Process 2-3\n",
      "Q23 = 0; \n",
      "U23 = -70 ;\n",
      "W23 = Q23-U23;\n",
      "\n",
      "# Process 3-1\n",
      "Q31 = - 200; \n",
      "U31 = -U12-U23;\n",
      "W31 = Q31-U31;\n",
      "W = W12 + W23 + W31;\n",
      "Q = Q12 + Q23 + Q31;\n",
      "\n",
      "# Results\n",
      "print \"Heat trasfer in the cycle is\",Q,\"KJ/Kg\"\n",
      "print \"Work done during the the cycle is\",W,\"KJ/Kg\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat trasfer in the cycle is 35 KJ/Kg\n",
        "Work done during the the cycle is 35 KJ/Kg\n"
       ]
      }
     ],
     "prompt_number": 39
    }
   ],
   "metadata": {}
  }
 ]
}