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| author | hardythe1 | 2015-04-07 15:58:05 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-04-07 15:58:05 +0530 |
| commit | 92cca121f959c6616e3da431c1e2d23c4fa5e886 (patch) | |
| tree | 205e68d0ce598ac5caca7de839a2934d746cce86 /Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter12.ipynb | |
| parent | b14c13fcc6bb6d01c468805d612acb353ec168ac (diff) | |
| download | Python-Textbook-Companions-92cca121f959c6616e3da431c1e2d23c4fa5e886.tar.gz Python-Textbook-Companions-92cca121f959c6616e3da431c1e2d23c4fa5e886.tar.bz2 Python-Textbook-Companions-92cca121f959c6616e3da431c1e2d23c4fa5e886.zip | |
added books
Diffstat (limited to 'Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter12.ipynb')
| -rwxr-xr-x | Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter12.ipynb | 462 |
1 files changed, 462 insertions, 0 deletions
diff --git a/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter12.ipynb b/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter12.ipynb new file mode 100755 index 00000000..c12bf202 --- /dev/null +++ b/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter12.ipynb @@ -0,0 +1,462 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:41b66ed6dbdebdc3dd934ef963f179576dd8d1497050c4ff934c3909d90dbee3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12: Probability"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.1, Page Number 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.2, Page Number 284"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from fractions import Fraction\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 52 #Total cards\n",
+ "nheart = 13 #Number of cards with hearts\n",
+ "\n",
+ "#Calculations\n",
+ "Pe = Fraction(nheart,n)\n",
+ "\n",
+ "#Results\n",
+ "print 'Probability of one (heart)card picked from a std. stack of %d cards is'%n,Pe"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probability of one (heart)card picked from a std. stack of 52 cards is 1/4\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.3, Page Number 285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.4, Page Number 285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable Declaration\n",
+ "n1 = 2 #Two spin states for 1st electron in orbit 1\n",
+ "n2 = 2 #Two spin states for 2nd electron in orbit 2\n",
+ "\n",
+ "#Calculation\n",
+ "M = n1*n1\n",
+ "\n",
+ "#Results\n",
+ "print 'Possible spin states for excited state are %2d'%M"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Possible spin states for excited state are 4\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.5, Page Number 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import factorial\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 12 #Total Number of players \n",
+ "j = 5 #Number player those can play match\n",
+ "\n",
+ "#Calculation\n",
+ "P = factorial(n)/factorial(n-j)\n",
+ "\n",
+ "#Results\n",
+ "print 'Maximum Possible permutations for 5 player to play are %8d'%P"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum Possible permutations for 5 player to play are 95040\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.6, Page Number 287"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import factorial\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 52 #Number of cards in std . pack\n",
+ "j = 5 #Number of cards in subset\n",
+ "\n",
+ "#Calculation\n",
+ "C = factorial(n)/(factorial(j)*factorial(n-j))\n",
+ "\n",
+ "#Results\n",
+ "print 'Maximum Possible 5-card combinations are %8d'%C"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum Possible 5-card combinations are 2598960\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.7, Page Number 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import factorial\n",
+ "\n",
+ "#Variable Declaration\n",
+ "x = 6 #Number of electrons\n",
+ "n = 2 #Number of states\n",
+ "\n",
+ "#Calculation\n",
+ "P = factorial(x)/(factorial(n)*factorial(x-n))\n",
+ "\n",
+ "#Results\n",
+ "print 'Total number of quantum states are %3d'%P"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total number of quantum states are 15\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.8, Page Number 289"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import factorial\n",
+ "from fractions import Fraction\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 50 #Number of separate experiments\n",
+ "j1 = 25 #Number of sucessful expt with heads up\n",
+ "j2 = 10 #Number of sucessful expt with heads up\n",
+ "\n",
+ "#Calculation\n",
+ "C25 = factorial(n)/(factorial(j1)*factorial(n-j1))\n",
+ "PE25 = Fraction(1,2)**j1\n",
+ "PEC25 = (1-Fraction(1,2))**(n-j1)\n",
+ "P25 = C25*PE25*PEC25\n",
+ "\n",
+ "C10 = factorial(n)/(factorial(j2)*factorial(n-j2))\n",
+ "PE10 = Fraction(1,2)**j2\n",
+ "PEC10 = (1-Fraction(1,2))**(n-j2)\n",
+ "P10 = C10*PE10*PEC10\n",
+ "\n",
+ "#Results\n",
+ "print 'Probability of getting 25 head out of 50 tossing is %4.3f'%(float(P25))\n",
+ "print 'Probability of getting 10 head out of 50 tossing is %4.3e'%(float(P10))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probability of getting 25 head out of 50 tossing is 0.112\n",
+ "Probability of getting 10 head out of 50 tossing is 9.124e-06\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.9, Page Number 290"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import factorial, log\n",
+ "#Variable Declaration\n",
+ "N = [10,50,100] #Valures for N\n",
+ "\n",
+ "#Calculations\n",
+ "print ' N ln(N!) ln(N!)sterling Error'\n",
+ "for i in N:\n",
+ " lnN = log(factorial(i))\n",
+ " lnNs = i*log(i)-i\n",
+ " err = abs(lnN-lnNs)\n",
+ " print '%3d %5.2f %5.2f %4.2f'%(i,lnN,lnNs, err)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " N ln(N!) ln(N!)sterling Error\n",
+ " 10 15.10 13.03 2.08\n",
+ " 50 148.48 145.60 2.88\n",
+ "100 363.74 360.52 3.22\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.10, Page Number 293"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from fractions import Fraction\n",
+ "\n",
+ "#Variable Declaration\n",
+ "fi = 1 #Probability of receiving any card\n",
+ "n = 52 #Number od Cards\n",
+ "\n",
+ "#Calculations\n",
+ "sum = 0\n",
+ "for i in range(52):\n",
+ " sum = sum + fi\n",
+ "\n",
+ "Pxi = Fraction(fi,sum)\n",
+ "\n",
+ "#Results\n",
+ "print 'Probability of receiving any card', Pxi"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probability of receiving any card 1/52\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.11, Page Number 295"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import exp\n",
+ "from scipy import integrate\n",
+ "#Variable Declaration\n",
+ "\n",
+ "#Calculations\n",
+ "fun = lambda x: exp(-0.05*x)\n",
+ "Pt = 0\n",
+ "for i in range(0,101):\n",
+ " Pt = Pt + fun(i)\n",
+ " \n",
+ "Ptot = integrate.quad(fun, 0.0, 100.)\n",
+ "\n",
+ "#Results\n",
+ "print 'Sum of Px considering it as discrete function %4.1f'%Pt\n",
+ "print 'Sum of Px considering it as contineous function %4.1f'%Ptot[0]"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(19.865241060018292, 2.205484801456136e-13)\n",
+ "Sum of Px considering it as discrete function 20.4\n",
+ "Sum of Px considering it as contineous function 19.9\n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 12.12, Page Number 296"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from sympy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "r = Symbol('r') #Radius of inner circle\n",
+ "C = [5,2,0]\n",
+ "#Calculations\n",
+ "A1 = pi*r**2\n",
+ "A2 = pi*(2*r)**2 - A1\n",
+ "A3 = pi*(3*r)**2 - (A1 + A2)\n",
+ "At = A1 + A2 + A3\n",
+ "f1 = A1/At\n",
+ "f2 = A2/At\n",
+ "f3 = A3/At\n",
+ "sf = f1 + f2 + f3\n",
+ "\n",
+ "ns = (f1*C[0]+f2*C[1]+f3*C[2])/sf\n",
+ "\n",
+ "#Results\n",
+ "print 'A1, A2, A3: ', A1, A2, A3\n",
+ "print 'f1, f2, f3: ', f1,f2,f3\n",
+ "print 'Average payout $', round(float(ns),2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "A1, A2, A3: pi*r**2 3*pi*r**2 5*pi*r**2\n",
+ "f1, f2, f3: 1/9 1/3 5/9\n",
+ "Average payout $ 1.22\n"
+ ]
+ }
+ ],
+ "prompt_number": 60
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |