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author | hardythe1 | 2014-08-13 11:41:01 +0530 |
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committer | hardythe1 | 2014-08-13 11:41:01 +0530 |
commit | 728bf707ac994b2cf05a32d8985d5ea27536cf34 (patch) | |
tree | 5530b1509900ca8d6d21384e33036f50734de927 /Applied_Thermodynamics/Chapter3.ipynb | |
parent | f3e94078a83634b4353ab0cd2de3b0e204a48ac7 (diff) | |
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diff --git a/Applied_Thermodynamics/Chapter3.ipynb b/Applied_Thermodynamics/Chapter3.ipynb new file mode 100755 index 00000000..c0f77975 --- /dev/null +++ b/Applied_Thermodynamics/Chapter3.ipynb @@ -0,0 +1,1090 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:8d4c3e3e1406cca57fa7a5e5be30daeeb95ae0c1a8fcd1dccf25d2f1f8ce833d" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3: First Law of Thermodynyamics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page no. 76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#Variable Declaration: \n", + "#Pressure in the gas cylinder(in kPa):\n", + "p=689\n", + "#Final volume(in m**3):\n", + "v2=0.045\n", + "#Initial volume(in m**3):\n", + "v1=0.04\n", + "#Work done by the paddle(in kJ):\n", + "Pw=-4.88\n", + "\n", + "#Calculation:\n", + "#Work done by the system on the piston(in kJ):\n", + "w=p*(v2-v1)\n", + "#Net Work of the system(in kJ):\n", + "wn=w+Pw\n", + "\n", + "#Results:\n", + "print \"Work done on the piston in kJ: \",w\n", + "print \"Work done on the system in kJ: \",-wn" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work done on the piston in kJ: 3.445\n", + "Work done on the system in kJ: 1.435\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page no. 76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#Variable Declaration: \n", + "#Mass of the gas(in kg):\n", + "m=0.5\n", + "#Initial internal energy(in kJ/kg):\n", + "u1=26.6\n", + "#Final internal energy(in kJ/kg):\n", + "u2=37.8\n", + "\n", + "#Calculation:\n", + "#Heat required(in kJ):\n", + "Q=(u2-u1)*m\n", + "\n", + "#Results: \n", + "print \"Heat required (kJ): \",Q" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat required (kJ): 5.6\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page no. 77" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#Variable Declaration: \n", + "#Mass flow rate(in kg/hr):\n", + "m=50\n", + "#Initial temp(in C):\n", + "t1=800\n", + "#Final temp(in C):\n", + "t2=50\n", + "#Heat capacity at const pressure(in kJ/kg.K):\n", + "Cp=1.08\n", + "\n", + "#Calculation:\n", + "#Heat to be removed(in kJ/hr):\n", + "Q=m*Cp*(t2-t1)\n", + "\n", + "#Results: \n", + "print \"Heat should be removed at (kJ/hr): \",-Q" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat should be removed at (kJ/hr): 40500.0\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page no. 77" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#Variable Declaration: \n", + "#Volume of the cylinnder(in m**3):\n", + "v=0.78\n", + "#Atmospheric pressure(in kPa):\n", + "p=101.325\n", + "\n", + "#Calculation:\n", + "#Work done(in kJ):\n", + "w=round(p*v,2)\n", + "\n", + "#Results: \n", + "print \"Work done by air (KJ): \",-w\n", + "print \"Work done by surroundings (KJ): \",w" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work done by air (KJ): -79.03\n", + "Work done by surroundings (KJ): 79.03\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page no. 77" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "#Mass of the gas(in kg):\n", + "m=5\n", + "#Value of n in P*(V**n)=const:\n", + "n=1.3\n", + "#Initial pressure(in MPa):\n", + "p1=1\n", + "#Initial volume(in m**3):\n", + "v1=0.5\n", + "#Final pressure(in MPa):\n", + "p2=0.5\n", + "\n", + "#Calculation:\n", + "#Final volume(in m**3):\n", + "v2=round(v1*((p1/p2)**(1/n)),3)\n", + "#Work done(in kJ):\n", + "w=(p2*v2-p1*v1)*10**3/(1-n)\n", + "#Change in internal energy(in kJ/kg):\n", + "du=1.8*(p2*v2-p1*v1)*10**3\n", + "#Heat interaction(in kJ):\n", + "Q=du+w\n", + "\n", + "#Results: \n", + "print \"Heat interaction (kJ): \",round(Q,1)\n", + "print \"Work interaction (kJ): \",round(w,1)\n", + "print \"Change in internal energy (kJ): \",round(du,1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat interaction (kJ): 113.5\n", + "Work interaction (kJ): 246.7\n", + "Change in internal energy (kJ): -133.2\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page no. 78" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "#Initial pressure(in MPa):\n", + "p1=1.0\n", + "#Final pressure(in MPa):\n", + "p2=2.0\n", + "#Initial volume(in m**3):\n", + "v1=0.05\n", + "#Value of n:\n", + "n=1.4\n", + "\n", + "#Calculation:\n", + "#Final volume(in m**3):\n", + "v2=round(v1*((p1/p2)**(1/n)),2)\n", + "\n", + "#Change in internal energy(in kJ/kg):\n", + "du=7.5*(p2*v2-p1*v1)*10**3\n", + "#Work done(in kJ):\n", + "w=(p2*v2-p1*v1)*10**3/(1-n)\n", + "#Heat interaction(in kJ):\n", + "Q=du+w\n", + "\n", + "#Results: \n", + "print \"Heat interaction (kJ): \",Q\n", + "print \"Work interaction (kJ): \",w\n", + "print \"Change in internal energy (kJ): \",du\n", + "\n", + "#If 180 kJ heat transfer takes place:\n", + "#Work done(in kJ):\n", + "w2=180-du\n", + "print \"New work (kJ): \",w2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat interaction (kJ): 50.0\n", + "Work interaction (kJ): -25.0\n", + "Change in internal energy (kJ): 75.0\n", + "New work (kJ): 105.0\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7, page no. 79" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration:\n", + "#Universal Gas Constant (in KJ.mol/Kg.K):\n", + "r=8.3143\n", + "#Molecular weight of perfect gas:\n", + "M=16\n", + "#Molar specific heat at constant pressure for perfect gas(KJ/Kg.K):\n", + "Cp=1.7\n", + "#Initial pressure (Kpa):\n", + "p1=101.3\n", + "#Final pressure (Kpa):\n", + "p2 = 600\n", + "#Initial tempreture (K):\n", + "T1 = 273+20\n", + "#Polytripic index from PV^1.3 = const\n", + "n = 1.3\n", + "\n", + "#Calculations:\n", + "#Characterstic Gas Constant (KJ/Kg.K):\n", + "R=r/M\n", + "#Molar specific heat at constant volume for perfect gas(KJ/Kg.K):\n", + "Cv=Cp-R\n", + "#Specific heat ratio:\n", + "y = Cp/Cv\n", + "#Final Tempreture (K):\n", + "T2 = T1*(p2/p1)**((n-1)/n)\n", + "#Polytropic work (KJ/Kg):\n", + "W = R*(T1-T2)/(n-1)\n", + "#Polytropic process heat (KJ/Kg):\n", + "Q = W*(y-n)/(y-1)\n", + "\n", + "#Results:\n", + "print \"Heat transfered (KJ/Kg): \",round(Q,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat transfered (KJ/Kg): -82.06\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8, page no. 80" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math as m\n", + "\n", + "#Variable Declaration: \n", + "#Initial temperature(in K):\n", + "t1=627+273\n", + "#Final temperature(in K):\n", + "t2=27+273\n", + "#Specific heat at const pressure(in kJ/kg.K):\n", + "Cp=1.005\n", + "\n", + "#Calculation\n", + "#Exit velocity(in m/s):\n", + "c2=m.sqrt(2*Cp*10**3*(t1-t2))\n", + "\n", + "#Results: \n", + "print \"Exit Velocity (m/s): \" ,round(c2,1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Exit Velocity (m/s): 1098.2\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9, page no. 80" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "#Work interaction(in kJ):\n", + "w=-200\n", + "#Increase in enthalpy(in kJ/kg):\n", + "dh=100\n", + "#Heat picked up by the cooling water(in kJ/kg):\n", + "qc=-90\n", + "\n", + "#Calculation:\n", + "#Heat flow(in kJ/kg):\n", + "Q=dh+w\n", + "#Heat transferred to atmosphere(in kJ/kg):\n", + "Qa=Q-qc\n", + "\n", + "#Results: \n", + "print \"Heat transferred to atmosphere (kJ/kg): \",Qa" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat transferred to atmosphere (kJ/kg): -10\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10, page no. 81" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#Variable Declaration: \n", + "c=500 #Seating capacity:\n", + "q=50 #Heat requirement per person(in kcal/hr):\n", + "h1=80 #Enthalpy of water entering the pipe(in kcal/kg):\n", + "h2=45 #Enthalpy of water leaving the pipe(in kcal/kg):\n", + "z=10 #Difference in elevation of inlet and exit pipe(in m):\n", + "g=9.81 #Acceleration due to gravity(in m/s**2):\n", + "\n", + "#Calculation:\n", + "Q=c*q #Heat to be supplied(in kcal/hr):\n", + "Ql=-Q #Heat lost by water(in kcal/kg):\n", + "m=(Ql*10**3*4.18)/(g*z+(h2-h1)*10**3*4.18) #Quantity of water circulated(in kg/hr):\n", + "\n", + "\n", + "#Results: \n", + "print \"Water circulation rate (kg/min):\",round(m/60,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Water circulation rate (kg/min): 11.91\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11, page no. 81" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "h1=720.0 #Enthalpy of steam entering the injector(in kcal/kg):\n", + "h2=24.6 #Enthalpy of water entering(in kcal/kg):\n", + "h3=100.0 #Enthalpy of water and steam mixture leaving the injector(in kcal/kg):\n", + "z=2.0 #Depth of water injector from steam injector(in m):\n", + "v1=50.0 #Velocity of steam entering the injector(in m/s):\n", + "v3=25.0 #Velocity of mixture leaving the injector(in m/s):\n", + "q=12.0 #Heat loss from injector to surroundings(in kcal/kg):\n", + "g=9.8 #Acceleration due to gravity (m/s^2):\n", + "\n", + "\n", + "#Calculation:\n", + "m=(((v3**2)/2+h3*10**3*4.18)-(h2*10**3*4.18+g*z))/(((v1**2)/2+h1*10**3*4.18)-((v3**2)/2+h3*10**3*4.18)-(q*10**3*4.18))\n", + "\n", + "#Results: \n", + "print \"Steam supply rate (kg/s): \",round(m,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Steam supply rate (kg/s): 0.124\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12, page no. 82" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#Variable Declaration: \n", + "p=1.013 #Atmospheric pressure(in bar):\n", + "v=0.4 #Volume to which the baloon is inflated(in m**3):\n", + "w1=0 #Work done by cylinder(in kJ):\n", + "\n", + "#Calculation:\n", + "w2=p*10**5*v #Work done by the balloon(in kJ):\n", + "w=w1+w2 #Total work(in kJ):\n", + "\n", + "\n", + "#Results: \n", + "print \"Work done by the system upon atmoshere (KJ): \",w/(10**3)\n", + "print \"Work done by the atmoshere (KJ): \",-w/(10**3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work done by the system upon atmoshere (KJ): 40.52\n", + "Work done by the atmoshere (KJ): -40.52\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13, page no. 82" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "Qa=5000 #Heat added(in J/s):\n", + "\n", + "#Calculation:\n", + "Wt=0.25*Qa #Turbine work(in J/s):\n", + "Qr=0.75*Qa #Heat rejected(in J/s):\n", + "Wp=0.002*Qa #Work by feed pump(in J/s):\n", + "C=Wt-Wp #Capacity of generator(in W):\n", + "\n", + "#Results: \n", + "print \"Capacity of generator (KW): \",C/(10**3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Capacity of generator (KW): 1.24\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14, page no. 83" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math as m\n", + "\n", + "#Variable Declaration: \n", + "T1=27+273 #Ambient temperature(in K):\n", + "T2=750+273 #Temperature of air inside heat exchanger(in K):\n", + "T3=600+273 #Temperature of air leaving turbine(in K):\n", + "T4=500+273 #Temperature of air leaving turbine(in K):\n", + "c2=50 #Velocity of air entering turbine(in m/s):\n", + "c3=60 #Velocity of air entering the nozzle(in m/s):\n", + "Cp=1.005#Specific heat at constant pressure(in kj?kg.K):\n", + "\n", + "\n", + "#Calculation:\n", + "Q12=Cp*(T2-T1) #Heat transfer to air in heat exchanger(in kJ):\n", + "Wt=Cp*(T2-T3)+(c2**2-c3**2)*10**(-3)/2 #Power output from turbine(in kJ/s):\n", + "c4=m.sqrt(2*(Cp*(T3-T4)+(c3**2)*10**(-3)/2))#Velocity at exit of the nozzle(in m/s):\n", + "\n", + "#Results: \n", + "print \"Heat transfer to air in heat exchanger (KJ): \",round(Q12,2)\n", + "print \"Power output from turbine (KJ/s): \",Wt\n", + "print \"Velocity at exit of the nozzle (m/s): \",round(c4,1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat transfer to air in heat exchanger (KJ): 726.61\n", + "Power output from turbine (KJ/s): 150.2\n", + "Velocity at exit of the nozzle (m/s): 14.3\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15, page no. 85" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math as m\n", + "\n", + "#Variable Declaration: \n", + "p1=0.5 #Initial pressure(in MPa):\n", + "T1=400 #Initial temperature(in K):\n", + "r1=2 #Ratio of v2 to v1:\n", + "r2=6 #Ratio of v3 to v1:\n", + "R=8.314 #Universal gas constant(in kJ/kg):\n", + "\n", + "#Calculation:\n", + "Wa=R*T1 #Work from state 1 to 2(in kJ):\n", + "T2=2*T1 #Temperature at point 2(in K):\n", + "Wb=R*T2*m.log(r2/r1) #Work done from state 2 to 3(in kJ):\n", + "W=Wa+Wb#Total work done by air(in kJ):\n", + "\n", + "#Results: \n", + "print \"Work done (KJ): \",round(W,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work done (KJ): 10632.69\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16, page no. 85" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "pi=0.5*10**6 #Initial pressure(in Pa):\n", + "vi=0.5 #Initial volume(in m**3):\n", + "pf=1*10**6 #Final pressure(in Pa):\n", + "patm=1.013*10**5 #Atmospheric pressure(in Pa):\n", + "\n", + "#Calculation:\n", + "vf=3*vi #Final volume(in m**3):\n", + "W=(vf-vi)*(pi+pf)/2 #Work done(in J):\n", + "\n", + "#Results: \n", + "print \"Work done (MJ): \",W/10**6" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work done (MJ): 0.75\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17, page no. 87" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "p1=0.5*10**6 #Initial pressure(in Pa):\n", + "pf=1*10**6 #Final pressure(in Pa):\n", + "v1=0.5 #Initial volume(in m**3):\n", + "v2=0.25 #Final volume(in m**3):\n", + "vN2=0.75#Final Nitrogen volume(in m**3):\n", + "T1=273+27#Initial Tempereature (K):\n", + "patm=1.013*10**5 #Atmospheric pressure(in Pa):\n", + "CpH2=14.307 #Cp of hydrogen (KJ/Kg)\n", + "CpN2=1.039 #Cp of hydrogen (KJ/Kg)\n", + "RN2=0.2968\n", + "RH2=4.1240 \n", + "\n", + "#Calculations:\n", + "rH2=CpH2/(CpH2-RH2) #Adiabatic index of compression for H2:\n", + "rN2=CpN2/(CpN2-RN2) #Adiabatic index of compression for N2:\n", + "p2=p1*(v1/v2)**rH2 #Final pressure of hydrogen(in Pa):\n", + "Pw=0 #Partition work:\n", + "WH2=(p1*v1-p2*v2)/(rH2-1) #Work done upon H2(in J):\n", + "WN2=-WH2 #Work done by nitrogen(in J):\n", + "mN2=round(p1*v1/(RN2*10**3*T1),1) #Mass of N2(in kg):\n", + "T2=p2*vN2*T1/(p1*v1) #Final temperature of N2(in K):\n", + "CvN2=CpN2-RN2 #Cv of N2(in kJ/kg):\n", + "QN2=mN2*CvN2*10**3*(T2-T1)+WN2 #Heat added to N2(in kJ):\n", + "\n", + "#Results: \n", + "print \"Final pressure of hydrogen (MPa): \",round(p2/(10**6),3)\n", + "print \"Partition work (KJ): \",Pw\n", + "print \"Work done by hyrogen (10^5 J): \",round(WH2/10**5)\n", + "print \"Work done by nitrogen (10^5 J): \",round(WN2/10**5)\n", + "print \"Heat added to nitrogen (kJ): \",round(QN2/(10**3),2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Final pressure of hydrogen (MPa): 1.324\n", + "Partition work (KJ): 0\n", + "Work done by hyrogen (10^5 J): -2.0\n", + "Work done by nitrogen (10^5 J): 2.0\n", + "Heat added to nitrogen (kJ): 2053.09\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18, page no. 88" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "v1=2 #Volume of the cylinder(in m**3):\n", + "p1=0.5*10**6 #Pressure in the cylinder(in Pa):\n", + "T1=375 #Temperature of the cylinder(in K):\n", + "Cp=1.003 #Specific heat at const pressure(in kJ/kg.K):\n", + "Cv=0.716 #Specific heat at const volume(in kJ/kg.K):\n", + "Ra=0.287 #Gas constant for air(in kJ/kg.K):\n", + "patm=1.013*10**5 #Atmospheric pressure(in Pa):\n", + "r=1.4 #Compression ratio:\n", + "\n", + "#Calculation:\n", + "m1=p1*v1/(Ra*T1) #Initial mass of air(in kg):\n", + "T2=T1*(patm/p1)**((r-1)/r) #Final temperature(in K):\n", + "m2=patm*v1/(Ra*T2) #Final mass of air left in tank(in kg):\n", + "KE=m1*Cv*T1-m2*Cv*T2-(m1-m2)*Cp*T2 #Kinetic energy available(in kJ):\n", + "\n", + "#Results: \n", + "print \"Amount of work available (KJ): \",round(KE/10**3,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Amount of work available (KJ): 482.67\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19, page no. 89" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "p1=0.5*10**6 #Pressure in the vessel(in Pa):\n", + "v1=0.5 #Volume of 1st chamber(in m**3):\n", + "T1=300 #Temperature in the vessel(in K):\n", + "p2=10**6 #Final pressure(in Pa):\n", + "v2=0.5 #Volume of 2nd chamber(in m**3):\n", + "T2=500 #Final temperature(in K):\n", + "R=8314 #Universal gas constant(in J/kg.K):\n", + "\n", + "#Calculation:\n", + "n1=p1*v1/(R*T1) #Moles in chamber 1:\n", + "n2=p2*v2/(R*T2) #Moles in chamber 2:\n", + "T3=(n1*T1+n2*T2)/(n1+n2) #Temperature of the mixture(in K):\n", + "p3=(n1+n2)*R*T3/(v1+v2) #Final pressure(in MPa):\n", + "\n", + "\n", + "#Results: \n", + "print \"Final pressure (MPa): \",p3/(10**6)\n", + "print \"Final temperature (K): \",round(T3,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Final pressure (MPa): 0.75\n", + "Final temperature (K): 409.09\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20, page no. 90" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "\n", + "#Variable Declaration: \n", + "v=0.5 #Volume of the bottle(in m**3):\n", + "p=1.0135 #Pressure in the bottle(in Bar):\n", + "\n", + "#Calculation:\n", + "W=p*10**5*(0-v) #Displacement work(in N-m):\n", + "Q=-W #Heat transfer(in N-m):\n", + "\n", + "#Results: \n", + "print \"Heat transferred (N-m): \",Q" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat transferred (N-m): 50675.0\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21, page no. 90" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "v1=0.3 #Volume of bottle(in m**3):\n", + "p1=35.0 #Pressure in the bottle(in bar):\n", + "T1=40.0+273.0 #Temperature in the bottle(in K):\n", + "w1=5.0 #Turbo generator's actual output(in kJ/s):\n", + "p2=1.0 #Final prssure(in bar):\n", + "v2=v1 #Final volume(in m**3):\n", + "Ra=0.287 #Gas constant for air(in kJ/kg.K):\n", + "r=1.4 #Compression ratio:\n", + "Cv=0.718 #Specific heat at const volume(in kJ/kg):\n", + "Cp=1.005 #Specific heat at const pressure(in kJ/kg):\n", + "\n", + "#Calculation:\n", + "T2=T1*(p2/p1)**((r-1)/r) #Final temperature(in K):\n", + "m1=p1*10**2*v1/(Ra*T1) #Initial mass in the bottle(in kg):\n", + "m2=p2*10**2*v2/(Ra*T2) #Final mass in the bottle(in kg):\n", + "W=(m1*Cv*T1-m2*Cv*T2)-(m1-m2)*Cp*T2 #Maximum work that can be obtained(in kJ):\n", + "i=w1/0.6 #Input to the turbo generator(in kJ/s):\n", + "t=W/round(i,2) #Time duration(in s):\n", + "\n", + "#Results: \n", + "print \"Duration (Seconds): \",round(t,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Duration (Seconds): 159.11\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 22, page no. 91" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math as M\n", + "#Variable Declaration: \n", + "p1=1.5 #Pressure at state 1(in bar):\n", + "T1=77+273 #Temperature at state 1(in K):\n", + "p2=7.5 #Pressure at state 2(in bar):\n", + "m=3 #Mass of the air(in kg):\n", + "n=1.2 #Value of n:\n", + "Ra=0.287 \n", + "\n", + "#Calculation:\n", + "T2=T1*(p2/p1)**((n-1)/n) #Temperature at state 2(in K):\n", + "v1=m*Ra*T1/(p1*10**2) #Initial volume(in m**3):\n", + "v2=(p1*(v1**n)/p2)**(1/n) #Volume at state 2(in m**3):\n", + "T3=T1 #Temperature at state 3(in K):\n", + "v3=v2*T3/T2 #Volume at state 3(in m**3):\n", + "p3=7.5 #Pressure at state 3(in bar):\n", + "W12=m*Ra*(T2-T1)/(1-n) #Compression work during process 1-2(in kJ):\n", + "W23=p2*(10**2)*(v3-v2) #Work during process 2-3(in kJ):\n", + "W31=p3*10**2*v3*M.log(v1/v3) #Work during process 3-1(in kJ):\n", + "Wn=W12+W23+W31 #Net work(in kJ):\n", + "\n", + "#Results: \n", + "print \"Heat transferred from the system (kJ): \",round(-Wn,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat transferred from the system (kJ): 71.28\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 23, page no. 93" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable Declaration: \n", + "v1=0.15 #Volume of air bottle(in m**3):\n", + "p1=40 #Initial pressure(in bar):\n", + "T1=27+273 #Initial temperature(in K):\n", + "p2=2.0 #Final presure(in bar):\n", + "Ra=0.287 #Gas constant for air(in kJ/kg):\n", + "Cp=1.005 #Specific heat at const pressure(in kJ/kg):\n", + "Cv=0.718 #Specific heat at const volume(in kJ/kg):\n", + "r=1.4 #Compression ratio:\n", + "\n", + "#Calculation:\n", + "v2=v1 #Final volume(in m**3):\n", + "m1=p1*10**2*v1/(Ra*T1) #Initial mass of air in bottle(in kg):\n", + "T2=T1*(p2/p1)**((r-1)/r) #Final temperature(in K):\n", + "m2=p2*10**2*v2/(Ra*T2) #Final mass of air in bottle(in kg):\n", + "E=m1*Cv*T1-m2*Cv*T2-(m1-m2)*Cp*T2 #Energy available for running of turbine due to emptying of bottle(in kJ):\n", + "\n", + "#Results: \n", + "print \"Work available from turbine(KJ):\",round(E,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work available from turbine(KJ): 638.33\n" + ] + } + ], + "prompt_number": 24 + } + ], + "metadata": {} + } + ] +}
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