{ "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": {} } ] }