path: root/Thermodynamics_Demystified_by_Merle_C_Potter/Chapter3_2.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 3:Work and Heat"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3.1:PG-45"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#initialization of variables\n",
      "m=1            # mass in kg\n",
      "x=20.0/100.0       #quality of steam\n",
      "P=200          #constant pressure in kPa\n",
      "T1=100         #temperature intitial in degree centigrade\n",
      "T2=400         #temperature final in degree centigrade\n",
      "\n",
      "\n",
      "# first we find initial volume v1 and final volume v2\n",
      "\n",
      "# using table C.2\n",
      "vf=0.001061 # specific volume of saturated liquid in m^3 per kg \n",
      "vg=0.8857   # specific volume of saturated vapour in m^3 per kg \n",
      "\n",
      "v1=vf+x*(vg-vf);\n",
      "\n",
      "v2=1.549   # specific volume of steam in m^3 per kg at T2=400*C and P2=0.2MPa\n",
      "# now calculate work\n",
      "W=m*P*(v2-v1);   # work done in constant pressure process\n",
      "#result\n",
      "print \"Work done is\",round(W,2),\" kJ\" # work is in kJ as pressure was in kPa"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Work done is 274.2  kJ\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3.2:PG-46"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#initialization of variables\n",
      "D=110.0/1000.0 # diameter of cylinder in m\n",
      "V1=100e-6 # initial volume@ state 1 in m^3\n",
      "T1=60.0 # initial temp @ state 1 in *C\n",
      "T2=200.0 # final temo @ state 2 in *C\n",
      "M=50 # weight of piston in kg\n",
      "g=9.81 # gravitational accleration in m/sec^2\n",
      "Patm=100000 # atmospheric pressure in Pa\n",
      "A=math.pi*(D**2)/4 # area of piston in m^2\n",
      "\n",
      "# BALANCING THE FORCES To GET PRESSURE P\n",
      "# M.g=P.A-Patm\n",
      "P=Patm+(M*g/A) # atm pressure is added to get absolute pressure\n",
      "\n",
      "v1=0.001017 # specific volume at 60*C and 0.15Mpa pressure\n",
      "m=V1/v1; # mass of water in kg\n",
      "\n",
      "# find volume at state 2 \n",
      "v2=1.444 # specific volume of steam at 200*C and 0.15 MPa\n",
      "V2=m*v2 # final volume in m^3\n",
      "\n",
      "W=P*(V2-V1)/1000; # work done divided by 1000 to get in kJ\n",
      "# result\n",
      "print \"The work done is\",round(W,1),\" kJ\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The work done is 21.5  kJ\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3.3:PG-47"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#initialization of variables\n",
      "P1=200      # initial pressure in kPa\n",
      "V1=2        # initial volume in m^3\n",
      "P2=100      # final pressure in kPa\n",
      "C=P1*V1 # isothermal process i.e P.V=constant\n",
      "#  find final volume \n",
      "V2=P1*V1/P2 # final volume by P1.V1=P2.V2\n",
      "\n",
      "from scipy.integrate import quad\n",
      " \n",
      "def integrand(v,C):\n",
      "    return C/v\n",
      "W, err =quad(integrand, V1, V2,C ) # itegrating over volume to get work\n",
      "# result\n",
      "print \"The Work done by gas is\",int(W),\" kJ\" # answer is approximated in textbook"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Work done by gas is 277  kJ\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3.4:PG-48"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# initialization of variables\n",
      "M=100 # mass in kg\n",
      "d=3 # depth by which mass drops in m\n",
      "V=0.002 # increased volume in m^3\n",
      "g=9.8 # gravitational accleration in m/sec^2\n",
      "Pgauge=100*1000 # gauge pressure in N/m\n",
      "Patm =100*1000 # atmospheric pressure in N/m\n",
      "P=Pgauge+Patm # to get absolute pressure\n",
      "\n",
      "# calculate work done by paddle wheel\n",
      "Wpaddlewheel=(-M*g*d) # work is negative as it is done on the system\n",
      "\n",
      "# calculate work done on piston it \n",
      "Wboundary=P*V # area mulitiplied by height is volume thus W=P.V \n",
      "\n",
      "#net work\n",
      "\n",
      "Wnet=Wpaddlewheel+Wboundary; # Work in joule as SI units are used\n",
      "print \"The Net Work done is \",round(Wnet),\" J\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Net Work done is  -2540.0  J\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3.5:PG-51"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "# initialization of variables\n",
      "T=100 # torque of shaft in N.m\n",
      "N=3000 # rotation speed in rpm\n",
      "omega=(N*2*math.pi/60) # angular velocity in rad/sec\n",
      "# calculation of power\n",
      "Wdot=(T*omega); # power is work done per unit time\n",
      "print \"Power transmitted is\",round(Wdot/746,1),\" hp\" # divided by 746 to convert W into hp\n",
      "#answer is approximated in textbook"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Power transmitted is 42.1  hp\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3.6:PG-51"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "# initialization of variables\n",
      "D=10.0/100    # diameter of cylinder in m\n",
      "d=50.0/1000   # compression in spring in m\n",
      "Patm=100000   # atmospheric pressure in Pa\n",
      "K=10.0*1000   # spring constant converted in  N/m\n",
      "w=50*9.81 # weight of piston in Newton =mass*gravitational acceleration\n",
      "\n",
      "# find the initial pressure in cylinder by force balance\n",
      "A=(math.pi*D**2)/4; # area of piston\n",
      "P1=((Patm*A)+w)/A;      # balancing forces on piston P1.A=Patm.A+W\n",
      "\n",
      "# work done by air to raise the piston for 50mm if spring not present\n",
      "Wgas=P1*A*d; # pressure*area= force and Work = Force* displacement\n",
      "\n",
      "# work done on spring to compress\n",
      "Wspring=(K*d**2)/2; # Work in j\n",
      "\n",
      "# now total work done by air is sum of two works\n",
      "Wnet=Wgas+Wspring; # Work in j\n",
      "# result\n",
      "print \"The net work done by air is\",round(Wnet,1),\" J\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The net work done by air is 76.3  J\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3.7:PG-53"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# variable initialization\n",
      "\n",
      "d=2   # distance travelled by weight in m\n",
      "m=50  # mass of weight in kg\n",
      "g=9.8  # gravitaional acceleration in m/sec^2\n",
      "\n",
      "# calculation of work in non-quasiequilibrium process\n",
      "W=m*g*d; # work in joules\n",
      "\n",
      "# the work done must be transferred as heat\n",
      "Q=W;\n",
      "\n",
      "print \"The heat that must transfer is \",int(Q),\" Joules\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The heat that must transfer is  980  Joules\n"
       ]
      }
     ],
     "prompt_number": 45
    }
   ],
   "metadata": {}
  }
 ]
}