path: root/Engineering_Physics_by_Shyam_Rajeev/Chapter15.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "15: Statistical mechanics"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 15.1, Page number 341"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#importing modules\n",
      "import math\n",
      "import fractions\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "n = 10;       #number of identical coins\n",
      "r1 = 10;       #number of heads in 1st case\n",
      "r2 = 5;        #number of heads in 2nd case\n",
      "r3 = 3;        #number of heads in 3rd case\n",
      "\n",
      "#Calculation\n",
      "P10_0 = math.factorial(n)/(math.factorial(r1)*math.factorial(n-r1)*(2**n));        #probability of getting all heads\n",
      "P10_0 = fractions.Fraction(P10_0);        #probability in fraction\n",
      "P5_5 = math.factorial(n)/(math.factorial(r2)*math.factorial(n-r2)*(2**n));         #probability of getting 5 heads and 5 tails\n",
      "P5_5 = fractions.Fraction(P5_5);          #probability in fraction\n",
      "P3_7 = math.factorial(n)/(math.factorial(r3)*math.factorial(n-r3)*(2**n));         #probability of getting 3 heads and 7 tails\n",
      "P3_7 = fractions.Fraction(P3_7);          #probability in fraction\n",
      "Pmax = math.factorial(n)/(((math.factorial(n/2))**2)*(2**n))            #most probable combination\n",
      "Pmax = fractions.Fraction(Pmax);          #probability in fraction\n",
      "Pmin = 1/(2**n);              #least probable combination\n",
      "Pmin = fractions.Fraction(Pmin);            #probability in fraction\n",
      "\n",
      "#Result\n",
      "print \"probability of getting all heads is\",P10_0\n",
      "print \"probability of getting 5 heads and 5 tails is\",P5_5\n",
      "print \"probability of getting 3 heads and 7 tails is\",P3_7\n",
      "print \"most probable combination is\",Pmax\n",
      "print \"least probable combination is\",Pmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "probability of getting all heads is 1/1024\n",
        "probability of getting 5 heads and 5 tails is 63/256\n",
        "probability of getting 3 heads and 7 tails is 15/128\n",
        "most probable combination is 63/256\n",
        "least probable combination is 1/1024\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 15.2, Page number 342"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#importing modules\n",
      "import math\n",
      "import fractions\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "n = 3;          #number of particles\n",
      "N = 2;          #number of compartments\n",
      "ms = 4;         #number of macrostates\n",
      "n1_03 = 0;        #value of n1 for (0,3)\n",
      "n2_03 = 3;        #value of n2 for (0,3)\n",
      "n1_12 = 1;        #value of n1 for (1,2)\n",
      "n2_12 = 2;        #value of n2 for (1,2)\n",
      "n1_21 = 2;        #value of n1 for (2,1)\n",
      "n2_21 = 1;        #value of n2 for (2,1)\n",
      "n1_30 = 3;        #value of n1 for (3,0)\n",
      "n2_30 = 0;        #value of n2 for (3,0)\n",
      "\n",
      "#Calculation\n",
      "#the macrostates are (n1,n2) = [(0,3),(1,2),(2,1),(3,0)]\n",
      "ms_03 = math.factorial(n)/(math.factorial(n1_03)*math.factorial(n2_03));          #number of microstates in the macrostate (0,3)\n",
      "mis_03 = \"(0,xyz)\";                   #microstates in the macrostate (0,3)\n",
      "ms_12 = math.factorial(n)/(math.factorial(n1_12)*math.factorial(n2_12));          #number of microstates in the macrostate (1,2)\n",
      "mis_12 = \"[(x,yz),(y,zx),(z,xy)]\";             #microstates in the macrostate (1,2)\n",
      "ms_21 = math.factorial(n)/(math.factorial(n1_21)*math.factorial(n2_21));          #number of microstates in the macrostate (2,1)\n",
      "mis_21 = \"[(xy,z),(yz,x),(zx,y)]\";             #microstates in the macrostate (2,1)\n",
      "ms_30 = math.factorial(n)/(math.factorial(n1_30)*math.factorial(n2_30));          #number of microstates in the macrostate (3,0)\n",
      "mis_30 = \"(xyz,0)\";                   #microstates in the macrostate (3,0)\n",
      "tms = N**n;            #total number of microstates\n",
      "mis = \"[(0,xxx),(x,xx),(xx,x),(xxx,0)]\";        #the microstates when particles are indistinguishable\n",
      "\n",
      "#Result\n",
      "print \"number of microstates in the macrostate (0,3) is\",ms_03,\"that is\",mis_03\n",
      "print \"number of microstates in the macrostate (1,2) is\",ms_12,\"that is\",mis_12\n",
      "print \"number of microstates in the macrostate (2,1) is\",ms_21,\"that is\",mis_21\n",
      "print \"number of microstates in the macrostate (3,0) is\",ms_30,\"that is\",mis_30\n",
      "print \"total number of microstates is\",tms\n",
      "print \"the microstates when particles are indistinguishable are\",mis"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "number of microstates in the macrostate (0,3) is 1.0 that is (0,xyz)\n",
        "number of microstates in the macrostate (1,2) is 3.0 that is [(x,yz),(y,zx),(z,xy)]\n",
        "number of microstates in the macrostate (2,1) is 3.0 that is [(xy,z),(yz,x),(zx,y)]\n",
        "number of microstates in the macrostate (3,0) is 1.0 that is (xyz,0)\n",
        "total number of microstates is 8\n",
        "the microstates when particles are indistinguishable are [(0,xxx),(x,xx),(xx,x),(xxx,0)]\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 15.3, Page number 343"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#importing modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "n1 = 4;       #1st group of particles\n",
      "n2 = 2;       #2nd group of particles  \n",
      "n3 = 8;       #3rd group of particles\n",
      "n4 = 6;       #4th group of particles \n",
      "n5 = 5;       #5th group of particles\n",
      "v1 = 1;       #speed of 1st group of particles\n",
      "v2 = 2;       #speed of 2nd group of particles\n",
      "v3 = 3;       #speed of 3rd group of particles\n",
      "v4 = 4;       #speed of 4th group of particles  \n",
      "v5 = 5;       #speed of 5th group of particles\n",
      "\n",
      "#Calculation\n",
      "vbar = ((n1*v1)+(n2*v2)+(n3*v3)+(n4*v4)+(n5*v5))/(n1+n2+n3+n4+n5);         #average speed(m/sec)\n",
      "vsquarebar = ((v1*(n1**2))+(v2*(n2**2))+(v3*(n3**2))+(v4*(n4**2))+(v5*(n5**2)))/(n1+n2+n3+n4+n5);        #mean square speed\n",
      "rms = math.sqrt(vsquarebar);                #root mean square speed(m/sec)\n",
      "rms = math.ceil(rms*10**3)/10**3;   #rounding off to 3 decimals\n",
      "\n",
      "#Result\n",
      "print \"average speed is\",vbar,\"m/sec\"\n",
      "print \"root mean square speed is\",rms,\"m/sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "average speed is 3.24 m/sec\n",
        "root mean square speed is 4.405 m/sec\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 15.4, Page number 344"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#importing modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "t = 27;         #temperature(C)\n",
      "M = 14;         #mass of nitrogen(gm)\n",
      "kb = 1.38*10**-23;     #boltzmann constant\n",
      "a = 6.02*10**23;       #avagadro number  \n",
      "\n",
      "#Calculation\n",
      "T = t+273;      #temperature(K) \n",
      "M = M*10**-3;       #mass of nitrogen(kg)\n",
      "vmp = math.sqrt(2*kb*T*a/M);             #most probable speed of nitrogen(m/sec)\n",
      "vmp = math.ceil(vmp*10)/10;   #rounding off to 1 decimal\n",
      "\n",
      "#Result\n",
      "print \"most probable speed of nitrogen is\",vmp,\"m/sec\"\n",
      "print \"answer given in the book is wrong\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "most probable speed of nitrogen is 596.7 m/sec\n",
        "answer given in the book is wrong\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 15.5, Page number 344"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#importing modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "t = 37;       #normal temperature of human body(C)\n",
      "b = 2.898*10**-3;      #constant of proportionality(mK)\n",
      "\n",
      "#Calculation\n",
      "T = t+273;         #normal temperature of human body(K)\n",
      "lamda_m = b/T;      #wavelength for maximum energy radiation(m)\n",
      "lamda_m = lamda_m*10**10;         #wavelength for maximum energy radiation(angstrom)\n",
      "\n",
      "#Result\n",
      "print \"wavelength for maximum energy radiation is\",int(lamda_m),\"angstrom\"\n",
      "print \"answer given in the book is wrong\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "wavelength for maximum energy radiation is 93483 angstrom\n",
        "answer given in the book is wrong\n"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 15.6, Page number 344"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#importing modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#Variable declaration\n",
      "kb = 1.38*10**-23;     #boltzmann constant\n",
      "thetaE = 230;        #einstein's temperature(K)\n",
      "h = 6.63*10**-34;          #planck's constant(m**2 kg/s)\n",
      "\n",
      "#Calculation\n",
      "newE = kb*thetaE/h;         #einstein's frequency(per sec)\n",
      "\n",
      "#Result\n",
      "print \"einstein's frequency is\",round(newE/1e+12,2),\"*10**12 per sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "einstein's frequency is 4.79 *10**12 per sec\n"
       ]
      }
     ],
     "prompt_number": 47
    }
   ],
   "metadata": {}
  }
 ]
}