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diff --git a/Chemical_Engineering_Thermodynamics_by_S_Sundaram/2-P_V_T_Relations.ipynb b/Chemical_Engineering_Thermodynamics_by_S_Sundaram/2-P_V_T_Relations.ipynb new file mode 100644 index 0000000..b4cf68c --- /dev/null +++ b/Chemical_Engineering_Thermodynamics_by_S_Sundaram/2-P_V_T_Relations.ipynb @@ -0,0 +1,596 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: P V T Relations" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.10: EX2_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.10\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"yN2 = 1/4;//mole faction of N2 in the mixture\n", +"yH2 = 3/4;//mole fraction of H2 in the mixture\n", +"V = 5.7;//V is the rate at which mixture enters in m^3 in 1 hour\n", +"P = 600;//P is in atm\n", +"T = 298;//T is in K\n", +"TcN2 = 126;//critical temp of N2 in K\n", +"TcH2 = 33.3;//critical temp of H2 in K\n", +"TcNh3 = 406.0;//critical temp of NH3 in K\n", +"PcN2 = 33.5;//critical pressure of N2 in atm\n", +"PcH2 = 12.8;//critical pressure of H2 in atm\n", +"PcNH3 = 111.0;//critical pressure of NH3 in atm\n", +"R = 0.082;//gas constant\n", +"\n", +"//To calculate the amount of ammonia leaving the reactor and the velocity of gaseous product leaving the reactor\n", +"//(i)Calculation of amount of NH3 leaving the reactor\n", +"Tcm = (TcN2*yN2)+(TcH2*yH2);//critical temperature of the mixture\n", +"Pcm = (PcN2*yN2)+(PcH2*yH2);//critical pressure of the mixture\n", +"Trm = T/Tcm;\n", +"Prm = P/Pcm;\n", +"//From figure A.2.3\n", +"Zm = 1.57;//compressibility factor of the mixture\n", +"N = (P*V)/(Zm*R*T);//Kg mole of the mixture \n", +"N1 = 0.25*N;//Kg mole of N2 in feed\n", +"//N2+3H2 - 2NH3\n", +"W = 2*0.15*N1*17;\n", +"mprintf('(i)Ammonia formed per hour is %f Kg',W);\n", +"\n", +"//(ii)Calculation of velocity\n", +"N1 = 0.25*N-(0.25*N*0.15);//Kg mole of N2 after reactor\n", +"N2 = 0.75*N-(0.75*N*0.15);//Kg mole of H2 after reactor\n", +"N3 = 0.25*N*2*0.15;//Kg mole of NH3 after reactor\n", +"Nt = N1+N2+N3;//total Kg moles after reactor\n", +"y1NH3 = N3/Nt;//mole fraction of NH3 after reactor\n", +"y1N2 = N1/Nt;//mole fraction of N2 after reactor\n", +"y1H2 = N2/Nt;//mole fraction of H2 after reactor\n", +"T1cm = (TcN2*y1N2)+(TcH2*y1H2);\n", +"P1cm = (PcN2*y1N2)+(PcH2*y1H2);\n", +"T1 = 448;//in K\n", +"P1 = 550;//in atm\n", +"T1rm = T1/T1cm;\n", +"P1rm = P1/P1cm;\n", +"//From Figure A.2.2\n", +"Zm1 = 1.38;\n", +"V1 = (Zm1*Nt*R*T1)/P1;\n", +"d = 5*(10^-2);//diameter of pipe\n", +"v = V1/((%pi/4)*(d^2)*3600);\n", +"mprintf('\n (ii)Velocity in pipe is %f m/sec',v);\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: To_determine_the_temperature_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.1\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"m = 140;//m is the mass of N2 in Kg\n", +"P = 4.052*(10^5);//P is the pressure of the system in Pa\n", +"V = 30;//V is the volume of the system in m^3\n", +"R = 8314.4;// R is the gas constant\n", +"\n", +"//To determine temperature required\n", +"T = P*V/((m/28)*R);//T is the temperature of the system in K\n", +"mprintf('Temperature of the system is %f K',T);\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2: Theoretical_problem.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.2\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"//This example is a theoretical problem and does not involve any numerical computation\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: Theoretical_problem.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.3\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"//This example is a theoretical problem and does not involve any numerical computation\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: Theoretical_problem.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.4\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"//This example is a theoretical problem and does not involve any numerical computation\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: To_calculate_the_volume_of_Methane.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.5\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"n = 1;//n is Kg moles of methane\n", +"T = 423;//T is the temperatue of the system in kelvin\n", +"P = 100;//P is the pressure of the system in atm\n", +"Tc = 191;//Tc is the critical temperature of the system in K\n", +"Pc = 45.8;//Pc is the critical pressure of the system in atm\n", +"R = 0.08206;//R is the gas constant in (m^3 atm/Kg mole K)\n", +"\n", +"//To calculate the volume of methane\n", +"//(i)Using ideal gas equation\n", +"V1 = (n*R*T)/P;//V1 is the volume of the gas in m^3\n", +"mprintf('(i)Volume of the gas using ideal gas equation is %f cubic meter',V1);\n", +"\n", +"//(ii)Using Vander Waals' equation\n", +"a = (27*(R^2)*(Tc^2))/(64*Pc);//Vander Waais constant\n", +"b = (R*Tc)/(8*Pc);//Vander Waais constant\n", +"v = poly(0, 'v');\n", +"q = -((a*b)/P)+(a/P)*v-(((R*T)+(b*P))/P)*v^2+(v^3);//According to Vander Waals equation\n", +"r = roots(q);\n", +"mprintf('\n (ii)Volume of the gas using Vander Waals equation is %f cubic meter',r(1));\n", +"\n", +"//(iii)Using generalized Z chart\n", +"Tr = T/Tc;//Tr is the reduced temperatue\n", +"Pr = P/Pc;//Pr is the reduced pressure\n", +"//From the figure A.2.2,\n", +"Z = 0.97;//Z is the compressibility factor\n", +"V = (Z*R*T)/P;\n", +"mprintf('\n (iii)Volume of the gas using Z chart is %f cubic meter',V);\n", +"\n", +"//(iv)Using molar polarisation method\n", +"//From Table 2.2\n", +"Pmc = 6.82;//Pmc is the molar polarisation for methane\n", +"//From figure A.2.4\n", +"Z0 = .965;\n", +"Z1 = 14.8*(10^-4);\n", +"Z = Z0+(Z1*Pmc);\n", +"V = (Z*R*T)/P;\n", +"mprintf('\n (iv)Volume of the gas using molar polarisation method is %f cubic meter',V);\n", +"\n", +"//(v)From experiment\n", +"//Given\n", +"Z = 0.9848;\n", +"V = (0.9848*n*R*T)/P;\n", +"mprintf('\n (v)Volume of the gas calculated by experimental Z value is %f cubic meter',V);\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6: To_calculate_the_final_pressure_acheived.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.6\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"P1 = 266;\n", +"T1 = 473.16;//Initial temperature in Kelvin\n", +"T2 = 273.16;//Final temperature in Kelvin\n", +"V1 = 80; V2 = 80;//Initial & final volume in litres\n", +"N1 = (14.28/28); N2 = (14.28/28);//Initial and final Kg moles are equal\n", +"Tc = 126;//Critical temperature of N2 in K\n", +"Pc = 33.5;//Critical pressure of N2 in atm\n", +"\n", +"//To calculate the final pressure achieved\n", +"//(i)Using ideal gas law\n", +"p2 = (P1*V1*N2*T2)/(V2*N1*T1);\n", +"mprintf('(i)Final pressure of N2 using ideal gas law is %f atm',p2);\n", +"\n", +"//(ii)Using generalized Z chart\n", +"Tr1 = T1/Tc;//reduced initial temp in k\n", +"Pr1 = P1/Pc;//reduced initial press in K\n", +"//From the Z-chart compressibility factor coressponding to the above Tr1 &Pr1 is\n", +"Z1 = 1.07;\n", +"P2 = [125,135,150];\n", +"Z2 = [0.95, 0.96, 0.98];\n", +"F = [0,0,0];\n", +"for i = 1:3\n", +" F(i) = (P2(i)/(Z2(i)*T2))-(P1/(Z1*T1));\n", +"end\n", +"clf;\n", +"plot(P2,F);\n", +"xtitle('P2 vs F','P2','F');\n", +"P3 = interpln([F;P2],0);\n", +"mprintf('\n (ii)Final pressure of N2 from Z chart is %f atm',P3);\n", +"\n", +"//(iii)Using Pseudo reduced density chart\n", +"R = 0.082;//gas constant\n", +"v = V1/N1;//Volume per moles of nitrogen in m^3/Kg mole\n", +"Dr = (R*Tc)/(Pc*v);\n", +"Tr2 = T2/Tc;//final reduced temp in K\n", +"//From figure A.2.1, reduced pressure coressponding to this Dr and Tr2 is\n", +"Pr2 = 4.1//final reduced pressure in atm\n", +"p2_ = Pr2*Pc;\n", +"mprintf('\n (iii)Final pressure achieved using Dr chart is %f atm',p2_);\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: To_compute_the_work_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.7\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"n = 1;//n is the Kg mole of methane gas\n", +"T = 298;//T is the constant temperature in K\n", +"P1 = 1;//P1 is the initial pressure of the system\n", +"P2 = 100;//P2 is the final pressure of the system\n", +"R = 8314.4;//R is the gas constant in Nm/Kgmole deg K\n", +"\n", +"//To compute the work required\n", +"//(i)Using ideal gas law\n", +"W = R*T*log(P1/P2);\n", +"mprintf('(i)Work done by the system if the gas obeys ideal gas law is %4.2e Nm',W);\n", +"\n", +"//(ii)Using Vander Waals' equation\n", +"//Given\n", +"//For methane\n", +"a = 2.32*(10^5);//Vander Wals' constant a in N/m^2\n", +"b = 0.0428;//Vanderwaals' constant b in m^3\n", +"//V1 and V2 are evaluated by trial and error using Vanderwaals' equation as P1 and P2 are known\n", +"V1 = 11.1;//initial volume of the gas in m^3\n", +"V2 = 0.089;//final volume of the gas in m^3\n", +"W = (R*T*log((V2-b)/(V1-b)))+(a*((1/V2)-(1/V1)))\n", +"mprintf('\n (ii)Work done by the system if the gas obeys Vander Waals equation is %4.2e Nm',W);\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8: To_determine_the_vapour_pressure_of_Chlorine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.8\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"V = 27*(10^-3);//Volume of the container in m^3\n", +"n = (15/70.91);//n is the Kg moles of chlorine\n", +"T = 293;//T is the temperature in K\n", +"R = 0.08206;\n", +"P = 10^(4.39-(1045/293));//P is the vapour pressure of chlorine\n", +"Pc = 76.1;//Critical pressure of Chlorine\n", +"Tc = 417;//Critical temperature of Chlorine \n", +"Pr = P/Pc;//Reduced pressure of Chlorine\n", +"Tr = T/Tc;//Critical temperature of Chlorine\n", +"M = 70.91;//Molecular weight of the Chlorine\n", +"\n", +"//To determine the vapour pressure of chlorine, amount of liquid Cl2 and temperature required\n", +"//(i)Specific volume of liquid Chlorine\n", +"//From figure A.2.2\n", +"Zg = 0.93;\n", +"//From figure A.2.6\n", +"Zl = 0.013;\n", +"vl = ((Zl*R*T)/P);\n", +"mprintf('(i)Specific volume of liquid Chlorine from compressibility chart is %f cubic meter /Kgmole',vl);\n", +"\n", +"//From Francis relation, taking the constants from Table 2.3\n", +"D = (1.606-(216*(10^-5)*20)-(28/(200-20)))*10^3;//Density of liq Cl2 in Kg/m^3\n", +"Vl = M/D;\n", +"mprintf('\n Specific volume of liquid Chlorine from Francis relation is %f cubic meter /Kgmole',Vl);\n", +"\n", +"//(ii)Amount of liquid Cl2 present in the cylinder\n", +"vg = ((Zg*R*T)/P);\n", +"V1 = V-vg;//V1 is the volume of liquid Chlorine\n", +"Vct = 0.027;//volume of the container\n", +"Vg = (0.212-(Vct/vl))/((1/vg)-(1/vl));//By material balance\n", +"W = ((V-Vg)*70.9)/vl;\n", +"mprintf('\n\n (ii)Weight of Chlorine at 20deg cel is %f Kg',W);\n", +"\n", +"//(iii)Calculation of temperature required to evaporate all the liquid chlorine\n", +"//log P' = 4.39 - 1045/T (given)\n", +"//Assume the various temperature\n", +"Ng = 0.212;//total Kg moles of gas\n", +"Ta = [413 415 417];\n", +"N = [0,0,0];\n", +"for i = 1:3\n", +" Tr(i) = Ta(i)/Tc;//reduced temperature in K\n", +" P(i) = 10^(4.39-(1045/Ta(i)));\n", +" Pr(i) = P(i)/Pc;//reduced pressure in K\n", +"//From the compressibility factor chart,Z values coressponding to the above Tr &Pr are given as\n", +"Z = [0.4 0.328 0.208];\n", +"N(i) = (P(i)*Vct)/(Z(i)*R*Ta(i));\n", +"end\n", +"\n", +"clf;\n", +"plot(N,Ta);\n", +"xtitle('Ta vs N','N','Ta');\n", +"T1 = interpln([N;Ta],0.212);//in K\n", +"mprintf('\n (iii)The temperature required to evaporate all the liquid chlorine is %f deg celsius',T1-273);\n", +"//end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9: To_calculate_the_pressure_exerted_by_the_gas_mixture.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chemical Engineering Thermodynamics\n", +"//Chapter 2\n", +"//P-V-T Relations\n", +"\n", +"//Example 2.9\n", +"clear;\n", +"clc;\n", +"\n", +"//Given\n", +"N1 = 0.7;//Kg mole of CH4\n", +"N2 = 0.3;//Kg mole of N2\n", +"R = 0.08206;//Gas constant\n", +"T = 323;//Temperature in Kelvin\n", +"V = 0.04;//Volume in m^3\n", +"a1 = 2.280; b1 = 0.0428;//Vanderwaals constants for CH4\n", +"a2 = 1.345;b2 = 0.0386;//Vanderwaals constants for N2\n", +"Tc1 = 191; Pc1 = 45.8;//Critical temperature in K and pressure of CH4 in atm\n", +"Tc2 = 126;Pc2 = 33.5;//Critical temperature in K and pressure of N2 in atm\n", +"\n", +"//To find Approx Value\n", +"function[A]=approx(V,n)\n", +" A=round(V*10^n)/10^n;//V-Value n-To what place\n", +" funcprot(0)\n", +"endfunction \n", +"\n", +"//To calculate the pressure exerted by the gas mixture\n", +"//(i)Using ideal gas law\n", +"P = (N1+N2)*((R*T)/V);\n", +"mprintf('(i) Pressure exerted by the gas mixture using ideal gas law is %d atm',P);\n", +"\n", +"//(ii)Using Vander waal equation\n", +"P1 = ((N1*R*T)/(V-(N1*b1)))-((a1*(N1^2))/(V^2));//Partial pressure of CH4\n", +"P2 = ((N2*R*T)/(V-(N2*b2)))-((a2*(N2^2))/(V^2));//Partial pressure of N2\n", +"Pt = P1+P2;\n", +"mprintf('\n(ii) Pressure exerted by the gas mixture using Vander waal equation is %f atm', Pt);\n", +"\n", +"//(iii)Using Zchart and Dalton's law\n", +"Tra = T/Tc1;//reduced temperature of CH4\n", +"Trb = T/Tc2;//reduced temperature of N2\n", +"//Asssume the pressure\n", +"P = [660 732 793 815 831];\n", +"for i = 1:5\n", +" Pa(i) = N1*P(i);// partial pressure of CH4 for the ith total pressure\n", +" Pb(i) = N2*P(i);// partial pressure of N2 for the ith total pressure\n", +" Pra(i) = Pa(i)/Pc1;//reduced pressure of CH4 for the ith total pressure\n", +" Prb(i) = Pb(i)/Pc2;//reduced pressure of N2 for the ith total pressure\n", +"end\n", +"\n", +"//For the above Pr and Tr values compressibility factors from the figure A.2.3 are given as\n", +"Za = [1.154 1.280 1.331 1.370 1.390];//Z values of CH4 \n", +"Zb = [1 1 1 1 1];//Z values of N2\n", +"V3 = 0.0421;\n", +"for i = 1:5\n", +" Pa(i) = Za(i)*N1*((R*T)/V);//partial pressure of CH4 coressponding to the ith total presure\n", +" Pb(i) = Zb(i)*N2*((R*T)/V);//partial pressure of N2 coressponding to the ith total pressure\n", +" Pt(i) = Pa(i)+Pb(i);//total pressure of the gas mixture\n", +" if Pt(i)-P(i) < 15 \n", +" mprintf('\n(iii) pressure exerted by the gas mixture using Z chart and Dalton Law is %d atm',Pt(i));\n", +" else\n", +" end\n", +"end\n", +"\n", +"//(iv)Using Amagat's law and Z chart\n", +"P = [1000 1200 1500 1700];\n", +"for i=1:4\n", +" Pra(i) = P(i)/Pc1;\n", +" Prb(i) = P(i)/Pc2;\n", +"end\n", +"//For the above Pr and Tr values compressibility factors from the figure A.2.3 are given as\n", +"Za = [1.87 2.14 2.52 2.77];\n", +"Zb = [1.80 2.10 2.37 2.54];\n", +"for i = 1:4\n", +" Va(i) = approx((N1*Za(i)*((R*T)/P(i))),4);\n", +" Vb(i) = approx((N2*Zb(i)*((R*T)/P(i))),4);\n", +" V1(i) = approx((Va(i)+Vb(i)),4);\n", +" if V1(i)-V <= 0.003\n", +" mprintf('\n(iv) Pressure exerted by the gas mixture using Amagat law and Zchart is %d atm ',P(i));\n", +" else\n", +"end\n", +"end\n", +"//end" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |