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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/Chapter05.ipynb | |
| parent | b14c13fcc6bb6d01c468805d612acb353ec168ac (diff) | |
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Diffstat (limited to 'Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter05.ipynb')
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diff --git a/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter05.ipynb b/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter05.ipynb new file mode 100755 index 00000000..ce8818c7 --- /dev/null +++ b/Thermodynamics,_Statistical_Thermodynamics,_&_Kinetics/Chapter05.ipynb @@ -0,0 +1,425 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:2c9e6fedd22fa6b2ae65a19697803d5aa951ae2982e5a733c3ba66fccdc2f728"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 5: Enthalpy and the Second and Third Laws of Thermodynamics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.1, Page Number 84"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable Declaration\n",
+ "Th, Tc = 500.,200. #Temeperatures IN Which reversible heat engine works, K\n",
+ "q = 1000. #Heat absorbed by heat engine, J\n",
+ "\n",
+ "#Calcualtions\n",
+ "eps = 1.-Tc/Th\n",
+ "w = eps*q\n",
+ "\n",
+ "#Results\n",
+ "print 'Efficiency of heat engine is %4.3f'%eps\n",
+ "print 'Work done by heat engine is %4.1f J'%w"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Efficiency of heat engine is 0.600\n",
+ "Work done by heat engine is 600.0 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.4, Page Number 87"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from sympy import integrate, symbols\n",
+ "from math import log\n",
+ "#Variable Declaration\n",
+ "n = 1.0 #Number of moles of CO2\n",
+ "Ti, Tf = 320.,650. #Initial and final state Temeperatures of CO2, K\n",
+ "vi, vf = 80.,120. #Initial and final state volume of CO2, K\n",
+ "A, B, C, D = 31.08,-0.01452,3.1415e-5,-1.4973e-8\n",
+ " #Constants in constant volume Heat capacity equation in J, mol, K units\n",
+ "R = 8.314 #Ideal Gas Constant, J/(mol.K) \n",
+ "#Calcualtions\n",
+ "T = symbols('T')\n",
+ "dS1 = n*integrate( (A + B*T + C*T**2 + D*T**3)/T, (T,Ti,Tf)) \n",
+ "dS2 = n*R*log(vf/vi)\n",
+ "dS = dS1 + dS2\n",
+ "#Results\n",
+ "print 'Entropy change of process is %4.2f J/(mol.K)'%dS"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change of process is 24.43 J/(mol.K)\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.5, Page Number 88"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from sympy import integrate, symbols\n",
+ "from math import log\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 2.5 #Number of moles of CO2\n",
+ "Ti, Tf = 450.,800. #Initial and final state Temeperatures of CO2, K\n",
+ "pi, pf = 1.35,3.45 #Initial and final state pressure of CO2, K\n",
+ "A, B, C, D = 18.86,7.937e-2,-6.7834e-5,2.4426e-8\n",
+ " #Constants in constant pressure Heat capacity equation in J, mol, K units\n",
+ "R = 8.314 #Ideal Gas Constant, J/(mol.K) \n",
+ "#Calcualtions\n",
+ "T = symbols('T')\n",
+ "dS1 = n*integrate( (A + B*T + C*T**2 + D*T**3)/T, (T,Ti,Tf)) \n",
+ "dS2 = n*R*log(pf/pi)\n",
+ "dS = dS1 - dS2\n",
+ "#Results\n",
+ "print 'Entropy change of process is %4.2f J/(mol.K)'%dS"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change of process is 48.55 J/(mol.K)\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.6, Page Number 89"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import log\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 3.0 #Number of moles of CO2\n",
+ "Ti, Tf = 300.,600. #Initial and final state Temeperatures of CO2, K\n",
+ "pi, pf = 1.00,3.00 #Initial and final state pressure of CO2, K\n",
+ "cpm = 27.98 #Specific heat of mercury, J/(mol.K)\n",
+ "M = 200.59 #Molecualr wt of mercury, g/(mol)\n",
+ "beta = 1.81e-4 #per K\n",
+ "rho = 13.54 #Density of mercury, g/cm3\n",
+ "R = 8.314 #Ideal Gas Constant, J/(mol.K) \n",
+ "\n",
+ "#Calcualtions\n",
+ "dS1 = n*cpm*log(Tf/Ti)\n",
+ "dS2 = n*(M/(rho*1e6))*beta*(pf-pi)*1e5\n",
+ "dS = dS1 - dS2\n",
+ "\n",
+ "#Results\n",
+ "print 'Entropy change of process is %4.1f J/(mol.K)'%dS\n",
+ "print 'Ratio of pressure to temperature dependent term %3.1e\\nhence effect of pressure dependent term isvery less'%(dS2/dS1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change of process is 58.2 J/(mol.K)\n",
+ "Ratio of pressure to temperature dependent term 2.8e-05\n",
+ "hence effect of pressure dependent term isvery less\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.7, Page Number 93"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import log\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 1.0 #Number of moles of CO2\n",
+ "T = 300.0 #Temeperatures of Water bath, K\n",
+ "vi, vf = 25.0,10.0 #Initial and final state Volume of Ideal Gas, L\n",
+ "R = 8.314 #Ideal Gas Constant, J/(mol.K) \n",
+ "\n",
+ "#Calcualtions\n",
+ "qrev = n*R*T*log(vf/vi)\n",
+ "w = -qrev\n",
+ "dSsys = qrev/T\n",
+ "dSsur = -dSsys\n",
+ "dS = dSsys + dSsur\n",
+ "\n",
+ "#Results\n",
+ "print 'Entropy change of surrounding is %4.1f J/(mol.K)'%dSsur\n",
+ "print 'Entropy change of system is %4.1f J/(mol.K)'%dSsys\n",
+ "print 'Total Entropy changeis %4.1f J/(mol.K)'%dS"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change of surrounding is 7.6 J/(mol.K)\n",
+ "Entropy change of system is -7.6 J/(mol.K)\n",
+ "Total Entropy changeis 0.0 J/(mol.K)\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.8, Page Number 93"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import log\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 1.0 #Number of moles of CO2\n",
+ "T = 300.0 #Temeperatures of Water bath, K\n",
+ "vi, vf = 25.0,10.0 #Initial and final state Volume of Ideal Gas, L\n",
+ "R = 8.314 #Ideal Gas Constant, J/(mol.K) \n",
+ "\n",
+ "#Calcualtions\n",
+ "pext = n*R*T/(vf/1e3)\n",
+ "pi = n*R*T/(vi/1e3)\n",
+ "q = pext*(vf-vi)/1e3\n",
+ "qrev = n*R*T*log(vf/vi)\n",
+ "w = -q\n",
+ "dSsur = -q/T\n",
+ "dSsys = qrev/T\n",
+ "dS = dSsys + dSsur\n",
+ "\n",
+ "#Results\n",
+ "print 'Constant external pressure and initial pressure are %4.3e J,and %4.3e J respectively'%(pext,pi)\n",
+ "print 'Heat in reverssible and irreversible processes are %4.1f J,and %4.1f J respectively'%(qrev,q)\n",
+ "print 'Entropy change of system is %4.1f J/(mol.K)'%dSsys\n",
+ "print 'Entropy change of surrounding is %4.2f J/(mol.K)'%dSsur\n",
+ "print 'Total Entropy changeis %4.2f J/(mol.K)'%dS"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Constant external pressure and initial pressure are 2.494e+05 J,and 9.977e+04 J respectively\n",
+ "Heat in reverssible and irreversible processes are -2285.4 J,and -3741.3 J respectively\n",
+ "Entropy change of system is -7.6 J/(mol.K)\n",
+ "Entropy change of surrounding is 12.47 J/(mol.K)\n",
+ "Total Entropy changeis 4.85 J/(mol.K)\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.9, Page Number 96"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from sympy import integrate, symbols\n",
+ "from math import log\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 1.0 #Number of moles of CO2\n",
+ "pi, pf = 1.35,3.45 #Initial and final state pressure of CO2, K\n",
+ "D1 = 2.11e-3 #Constants in constant pressure Heat capacity equation for K<T<12.97K, in J, mol, K units\n",
+ "A2, B2, C2, D2 = -5.666,0.6927,-5.191e-3,9.943e-4\n",
+ " #Constants in constant pressure Heat capacity equation for 12.97<T<23.66, J, mol, K units\n",
+ "A3, B3, C3, D3 = 31.70,-2.038,0.08384,-6.685e-4\n",
+ " #Constants in constant pressure Heat capacity equation for 23.66<T<43.76, J, mol, K units\n",
+ "A4 = 46.094 #Constants in constant pressure Heat capacity equation for 43.76<T<54.39, J/(mol.K)\n",
+ "A5, B5, C5, D5 = 81.268,-1.1467,0.01516,-6.407e-5\n",
+ " #Constants in constant pressure Heat capacity equation for 54.39<T<90.20K, J, mol, K units\n",
+ "A6, B6, C6, D6 = 32.71,-0.04093,1.545e-4,-1.819e-7\n",
+ " #Constants in constant pressure Heat capacity equation for 90.20<T<298.15 KJ, mol, K units\n",
+ "R = 8.314 #Ideal Gas Constant, J/(mol.K) \n",
+ "Ltrans1 = 93.80 #Entalpy of transition at 23.66K, J/mol\n",
+ "Ltrans2 = 743.0 #Entalpy of transition at 43.76K, J/mol\n",
+ "Ltrans3 = 445.0 #Entalpy of transition at 54.39K, J/mol\n",
+ "Ltrans4 = 6815. #Entalpy of transition at 90.20K, J/mol\n",
+ "T1 = 12.97 #Maximum applicabliltiy temeprature for first heat capacity equation, K\n",
+ "T12 = 23.66 #Phase Change temperature from Solid III--II, K\n",
+ "T23 = 43.76 #Phase Change temperature from Solid II--I, K\n",
+ "T34 = 54.39 #Phase Change temperature from Solid I--liquid, K\n",
+ "T45 = 90.20 #Phase Change temperature from liquid--gas, K\n",
+ "Ts = 298.15 #Std. Temeprature, K\n",
+ "#Calcualtions\n",
+ "T = symbols('T')\n",
+ "dS1 = n*integrate( (D1*T**3)/T, (T,0,T1)) \n",
+ "dS2 = n*integrate( (A2 + B2*T + C2*T**2 + D2*T**3)/T, (T,T1,T12)) \n",
+ "dS21 = Ltrans1/T12\n",
+ "dS3 = n*integrate( (A3 + B3*T + C3*T**2 + D3*T**3)/T, (T,T12,T23)) \n",
+ "dS31 = Ltrans2/T23\n",
+ "dS4 = n*integrate( (A4)/T, (T,T23,T34)) \n",
+ "dS41 = Ltrans3/T34\n",
+ "dS5 = n*integrate( (A5 + B5*T + C5*T**2 + D5*T**3)/T, (T,T34,T45)) \n",
+ "dS51 = Ltrans4/T45\n",
+ "dS6 = n*integrate( (A6 + B6*T + C6*T**2 + D6*T**3)/T, (T,T45,Ts))\n",
+ "#print dS1+dS2,dS21\n",
+ "#print dS3, dS31\n",
+ "#print dS4, dS41\n",
+ "#print dS5, dS51\n",
+ "#print dS6\n",
+ "dS = dS1+dS2+dS21+dS3+dS31+dS4+dS41+dS5+dS51+dS6\n",
+ "\n",
+ "#Results\n",
+ "print 'Entropy change Sm0 for O2 is %4.1f J/(mol.K)'%dS"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change Sm0 for O2 is 204.8 J/(mol.K)\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example Problem 5.10, Page Number 99"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from sympy import integrate, symbols\n",
+ "from math import log\n",
+ "\n",
+ "#Variable Declaration\n",
+ "n = 1.0 #Number of moles of CO2 formed, mol\n",
+ "p = 1. #Pressure of CO2, K\n",
+ "\n",
+ "A1, B1, C1, D1 = 18.86,7.937e-2,-6.7834e-5,2.4426e-8\n",
+ " #Constants in constant pressure Heat capacity equation for CO2, J/(mol.K)\n",
+ "A2, B2, C2, D2 = 30.81,-1.187e-2,2.3968e-5, 0.0\n",
+ " #Constants in constant pressure Heat capacity equation for O2, J/(mol.K)\n",
+ "A3, B3, C3, D3 = 31.08,-1.452e-2,3.1415e-5 ,-1.4793e-8 \n",
+ " #Constants in constant pressure Heat capacity equation for CO, J/(mol.K)\n",
+ "DSr298CO = 197.67 #Std. Entropy change for CO, J/(mol.K)\n",
+ "DSr298CO2 = 213.74 #Std. Entropy change for CO, J/(mol.K)\n",
+ "DSr298O2 = 205.138 #Std. Entropy change for CO, J/(mol.K)\n",
+ "Tr = 475. #Reaction temperature, K\n",
+ "Ts = 298.15 #Std. temperature, K\n",
+ "#Calcualtions\n",
+ "T = symbols('T')\n",
+ "v1,v2,v3 = 1.,1./2,1.\n",
+ "DSr = DSr298CO2*v1 - DSr298CO*v1 - DSr298O2*v2\n",
+ "DA = v1*A1-v2*A2-v3*A3\n",
+ "DB = v1*B1-v2*B2-v3*B3\n",
+ "DC = v1*C1-v2*C2-v3*C3\n",
+ "DD = v1*D1-v2*D2-v3*D3\n",
+ "dS = DSr + n*integrate( (DA + DB*T + DC*T**2 + DD*T**3)/T, (T,Ts,Tr)) \n",
+ "\n",
+ "#Results\n",
+ "print 'Entropy change for reaction at %4d K is %4.2f J/(mol.K)'%(Tr,dS)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change Sm0 for O2 is 204.83 J/(mol.K)\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |