path: root/Heat_And_Thermodynamics_by_A._Manna/ch8.ipynb

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8 : First law of thermodynamics"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.1 page no : 261\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "l = 80;\t\t\t#latent heat of fusion in cal\n",
      "j = 4.2*10**7;\t\t\t#joules constant in ergs/cal\n",
      "w = -0.092*10**6;\t\t\t#work done in changing phase change in ergs\n",
      "\n",
      "# Calculations\n",
      "q = l*j;\t\t\t#heat added in ergs\n",
      "du = q-w;\t\t\t#internal energy in ergs\n",
      "\n",
      "# Result\n",
      "print 'the change in internal energy is %.1e ergs'%(du)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the change in internal energy is 3.4e+09 ergs\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.2 page no : 261"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "m = 1.;\t        \t\t#mass in gm\n",
      "l = 536.;\t\t    \t#latent heat in cal/gm\n",
      "j = 4.2*10**7;\t\t\t#joules constant in ergs/cal\n",
      "v = 1649;\t\t\t    #volume of water in cc\n",
      "p = 76*13.6*981;\t\t#pressure of water in dynes/sq.cm\n",
      "\n",
      "# Calculations\n",
      "dq = m*l*j;\t\t\t#heat supplied in ergs\n",
      "dw = p*v;\t\t\t#work done in ergs\n",
      "du = dq-dw;\t\t\t#internal energy developed in ergs\n",
      "\n",
      "# Result\n",
      "print 'internal energy of water is %.2E ergs'%(du)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "internal energy of water is 2.08E+10 ergs\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.3 pageno : 261"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "dv = 10;\t\t\t#ratio of original volume to final volume\n",
      "t1 = 293;\t\t\t#inital temperature in K\n",
      "y = 1.41;\t\t\t#coefficent of expansion\n",
      "\n",
      "# Calculations\n",
      "t2 = t1*(dv)**(y-1);\t\t\t#final temperature in K\n",
      "\n",
      "# Result\n",
      "print 'the final temperature is %.f K'%(t2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the final temperature is 753 K\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.4 pageno : 261"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "t = 273;\t\t\t#temperature of earth at height h in K\n",
      "p = 760;\t\t\t#pressure in mm of hg\n",
      "dp = 1;\t\t\t#change in pressure in mm of hg\n",
      "y = 1.418;\t\t\t#coefficient of expansion\n",
      "\n",
      "# Calculations\n",
      "dt = ((y-1)/y)*dp*t/p;\t\t\t#change in temperature in deg.C\n",
      "\n",
      "# Result\n",
      "print 'the change in temperature is %3.3f deg.C'%(dt)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the change in temperature is 0.106 deg.C\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.5 pageno : 262"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "p1 = 2;\t\t\t#pressure initial in atm\n",
      "p2 = 1.;\t\t\t#pressure final in atm\n",
      "t1 = 273 + 15;\t\t\t#inital temperature in K\n",
      "y = 1.4;\t\t\t#coefficent of expansion\n",
      "\n",
      "# Calculations\n",
      "t2 = t1*(p2/p1)**((y-1)/y);\t\t\t#final temperature in K\n",
      "dt = t1-t2;\t\t\t#drop in temperature in K\n",
      "\n",
      "# Result\n",
      "print 'drop in temperature is %3.2f K'%(dt)\n",
      "print \"Note : answer is slightly different because of rounding error\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "drop in temperature is 51.74 K\n",
        "Note : answer is slightly different because of rounding error\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.6 pageno : 262"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "t1 = 288;\t\t\t#inital temperature in K\n",
      "dv = 1./2;\t\t\t#ratio of inital to final volume\n",
      "y = 1.4;\t\t\t#coefficient of expansion\n",
      "\n",
      "# Calculations\n",
      "t2 = t1*(dv)**(y-1);\t\t\t#final temperature in K\n",
      "\n",
      "# Result\n",
      "print 'the final temperature is %3.1f K'%(t2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the final temperature is 218.3 K\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.7 pageno : 262"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "y = 1.4;\t\t\t#coefficent of exapnsion\n",
      "p1 = 1;\t\t\t#standard pressure in atm\n",
      "dv = 50;\t\t\t#ratio of initial volume to final volume\n",
      "t1 = 273;\t\t\t#standard temperature in K\n",
      "\n",
      "# Calculations\n",
      "p2 = p1*dv;\t\t\t#final pressure when slowly compressed in atm\n",
      "p3 = p1*(dv)**(y);\t\t\t#final pressure when suddenly compressed in atm\n",
      "t2 = t1*(dv)**(y-1);\t\t\t#rise in temperature when it is suddenly compressed in K\n",
      "\n",
      "# Result\n",
      "print 'the final pressure when it is compressed slowly is %.f atm  \\\n",
      "\\nthe final pressure when it is compressed suddenly is %.f atm  \\\n",
      "\\nthe rise in temperature when it is suddenly compressed is %.0f K'%(p2,p3,t2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the final pressure when it is compressed slowly is 50 atm  \n",
        "the final pressure when it is compressed suddenly is 239 atm  \n",
        "the rise in temperature when it is suddenly compressed is 1305 K\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.8 pageno : 263"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "y = 1.5;\t\t\t#coefficient of expansion\n",
      "dp = 1./8;\t\t\t#ratio of inital pressure to final pressure\n",
      "t1 = 300;\t\t\t#inital tempreature in K\n",
      "\n",
      "# Calculations\n",
      "t2 = t1*(dp)**((1-y)/y);\t\t\t#change in temperature in K\n",
      "t3 = t2-t1;\t\t\t#rise in temperature in K\n",
      "\n",
      "# Result\n",
      "print 'the rise in temperature is %3.2f K'%(t3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the rise in temperature is 300.00 K\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.9 pageno : 263"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "\n",
      "# Variables\n",
      "t1 = 400;\t\t\t#inital temperature in K\n",
      "dv = 2;\t\t\t#ratio of volumes final and inital\n",
      "r = 8.31*10**7;\t\t\t#universal gas constant in ergs/kg.K\n",
      "\n",
      "# Calculations\n",
      "w = r*t1*math.log(2);\t\t\t#work done in expanding isothermally in ergs\n",
      "\n",
      "# Result\n",
      "print 'the work done in expanding isothermally is %.1e ergs'%(w)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the work done in expanding isothermally is 2.3e+10 ergs\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.10 page no : 263"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "p1 = 76;\t\t\t#inital pressure in cm\n",
      "t1 = 290;\t\t\t#inital temperature in K\n",
      "y = 1.4;\t\t\t#coefficent of expansion\n",
      "dv = 2;\t\t\t#ratio of inital to fianl volume when air expands isothermally \n",
      "dv1 = 2;\t\t\t#ratio of inital to final volume when air expands adiabatically\n",
      "\n",
      "# Calculations\n",
      "p2 = p1/dv;\t\t\t#final pressure when air expands isothermally in cm of hg\n",
      "t2 = t1;\t\t\t#final temperature when air expands isothermally in K\n",
      "t3 = t2*(1./dv1)**(y-1);\t\t\t#temprature when air expands adiabatically in K\n",
      "p3 = p2*(1./dv1)**(y);\t\t\t#final pressure when air expands adiabatically in mm of hg\n",
      "\n",
      "# Result\n",
      "print 'final pressure when air expands isothermally in cm of hg %3.2f mm of hg  \\\n",
      "\\nfinal temperature when air expands isothermally is %3.2f K  \\\n",
      "\\ntemprature when air expands adiabatically is %3.1f K  \\\n",
      "\\nfinal pressure when air expands adiabatically is %3.2f cm of mercury'%(p2,t2,t3,p3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "final pressure when air expands isothermally in cm of hg 38.00 mm of hg  \n",
        "final temperature when air expands isothermally is 290.00 K  \n",
        "temprature when air expands adiabatically is 219.8 K  \n",
        "final pressure when air expands adiabatically is 14.40 cm of mercury\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.11 pageno : 264"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "p = 76*13.6*981;\t\t\t#pressure of air in dynes/sq.cm\n",
      "v = 11100.;\t\t\t#volume expanded in ml\n",
      "t1 = 273.;\t\t\t#inital temperature in K\n",
      "t2 = 274.;\t\t\t#final temperature in K\n",
      "cv = 2.411;\t\t\t#specific heat at constant volume in cal/K\n",
      "j = 4.2*10**7;\t\t\t#joules constant in ergs/cal\n",
      "\n",
      "# Calculations\n",
      "w = p*v*math.log(t2/t1);\t\t\t#work done in ergs\n",
      "h = cv*(t2-t1)+w/j;\t\t\t        #heat supplied in cal\n",
      "\n",
      "# Result\n",
      "print 'the work done is %3.3e erg  \\\n",
      "\\nthe heat supplied is %3.3f cal'%(w,h)\n",
      "print \"Note : answer is different because of rounding error\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the work done is 4.115e+07 erg  \n",
        "the heat supplied is 3.391 cal\n",
        "Note : answer is different because of rounding error\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.12 pageno : 264"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "p = 10**6;\t\t\t#pressure of air in dynes\n",
      "d = 0.0001293;\t\t\t#density of air in gm/cc\n",
      "t1 = 273;\t\t\t#inital temperature in K\n",
      "dv = 2;\t\t\t#ratio of inital volume to final volume\n",
      "y = 1.4;\t\t\t#coefficient of expansion\n",
      "\n",
      "# Calculations\n",
      "r = p/(d*t1);\t\t\t#universal gas constant in dynes.cc/gm.K\n",
      "t2 = round(t1*(dv)**(y-1));\t\t\t#final temperature in K\n",
      "w = r*(t2-t1)/(y-1);\t\t\t#work done in adiabatic compression in ergs\n",
      "\n",
      "# Result\n",
      "print 'work done in adiabatic compression is %.3e ergs'%(w)\n",
      "print \"Note : answer is different because of rounding error\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "work done in adiabatic compression is 6.162e+09 ergs\n",
        "Note : answer is different because of rounding error\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.13 pageno : 265"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "m = 5;\t\t\t#mass of air in gm\n",
      "cv = 0.172;\t\t\t#specific heat at consmath.tant volume cal/gm\n",
      "dt = 10;\t\t\t#changi in temperature in K\n",
      "\n",
      "# Calculations\n",
      "ie = m*cv*dt;\t\t\t#change in internal energy in cal\n",
      "\n",
      "# Result\n",
      "print 'change in internal energy is %3.2f cal'%(ie)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "change in internal energy is 8.60 cal\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.14 pageno : 265"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "v1 = 10**3;\t\t\t#inital volume in cc\n",
      "v2 = 2*v1;\t\t\t#final volume in cc\n",
      "p1 = 76*13.6*981;\t\t\t#pressure in dyne/sq.cm\n",
      "t1 = 273;\t\t\t#intial temperature in K\n",
      "d = 1.29;\t\t\t#density of the gas gm/lit\n",
      "cv = 0.168;\t\t\t#specific heat at constant volume in cal/gm\n",
      "\n",
      "# Calculations\n",
      "t2 = (v2/v1)*t1;\t\t\t#final temperature in K\n",
      "r = 0.068;\t\t\t#universal gas consmath.tant in cal\n",
      "cp = cv+r;\t\t\t#specific heat at constant pressure in cal\n",
      "q = d*cp*(t2-t1);\t\t\t#heat supplied in cal\n",
      "\n",
      "# Result\n",
      "print 'the heat supplied to the gas is %3.2f cal'%(q)\n",
      "print \"Note: answer is slightly different because of rounding error.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the heat supplied to the gas is 83.11 cal\n",
        "Note: answer is slightly different because of rounding error.\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.15 pageno : 165"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "t = 303;\t\t\t#temperature of the one mole of the argon in K\n",
      "v1 = 1;\t\t\t#intial volume in litres\n",
      "v2 = 10;\t\t\t#final volume in litres\n",
      "r = 8.31*10**7;\t\t\t#universal gas constant in ergs/K.mol\n",
      "\n",
      "# Calculations\n",
      "w = r*t*math.log(v2/v1);\t\t\t#work done in isothermal expansion in ergs\n",
      "\n",
      "# Result\n",
      "print 'the work done in isothermal expansion is %.1e ergs'%(w)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the work done in isothermal expansion is 5.8e+10 ergs\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.16 pageno : 266"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "dv = 4;\t\t\t#final volume of neon in lit\n",
      "t = 273;\t\t\t#temperature of the gas in K\n",
      "n = 2.6/22.4;\t\t\t#the no.of moles of neon\n",
      "r = 1.98;\t\t\t#universal gas constant in cal/K.mol\n",
      "\n",
      "# Calculations\n",
      "w = n*t*r*math.log(dv);\t\t\t#work done by gas in ergs\n",
      "\n",
      "# Result\n",
      "print 'the work done by 2.6lit of neon is %3.2f ergs'%(w)\n",
      "print \"Note: answer is slightly different because of rounding error.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the work done by 2.6lit of neon is 86.98 ergs\n",
        "Note: answer is slightly different because of rounding error.\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.18 page no : 266"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "# Variables\n",
      "dv = 10**(-3);\t\t\t#ratio of initial and final volume\n",
      "t1 = 10**5;\t\t\t#initial temperature in K\n",
      "y = 1.66;\t\t\t#coefficient of expansion\n",
      "\n",
      "# Calculations\n",
      "t2 = t1*((4./3*math.pi*10**12)/(4./3*math.pi*10**15))**(y-1);\t\t\t#final temperature in K\n",
      "\n",
      "# Result\n",
      "print 'final temperature of the gas is %3.2f K'%(t2)\n",
      "print \"Note : Answer in book is wrong. Please calculate manually.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "final temperature of the gas is 1047.13 K\n",
        "Note : Answer in book is wrong. Please calculate manually.\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.19 pageno : 267"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "p1 = 8.;\t\t\t#intial pressure in cm of hg\n",
      "p2 = 6.;\t\t\t#final pressure in cm of hg\n",
      "v1 = 1000.;\t\t\t#intial volume in cc\n",
      "v2 = 1190.;\t\t\t#final volume in cc\n",
      "\n",
      "# Calculations\n",
      "y = math.log(p1/p2)/math.log(v2/v1);\t\t\t#coefficient of expansion\n",
      "\n",
      "# Result\n",
      "print 'the coefficent of expansion is %3.2f'%(y)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the coefficent of expansion is 1.65\n"
       ]
      }
     ],
     "prompt_number": 42
    }
   ],
   "metadata": {}
  }
 ]
}