{ "metadata": { "name": "", "signature": "sha256:353d9311290d1e9a150d4f5b7334fda96148ffc036b68321a43e559706361c16" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 6:Power Vapor Cycles" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.1:PG-146" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "# Please refer to the given figure in question for quantities\n", "P2=2*1000 #higher pressure converted in in kPa\n", "P1=10 # lower pressure in kPa\n", "rho=1000 # density of water in Kg/m^3\n", "h1=192 # enthalpy at state 1 in kJ/kg\n", "h3=3248 # enthalpy at state 3 in kJ/kg\n", "s3=7.1279# entropy at state 3 in kJ/kg.K\n", "\n", "#calculation of pump work\n", "wp=(P2-P1)/rho # pump work given by equation 4.56 in textbook\n", "h2=h1+wp # by enrgy balance b/w state 1 and 2\n", "q=h3-h2 # Heat input from 2 to 3\n", "\n", "s4=s3 # isentropic process\n", "sf=0.6491 # entropy of saturated liquid @10 kPa from steam table\n", "sg=8.151 # entropy of saturated vapour @10 kPa from steam table\n", "x=(s4-sf)/(sg-sf)# from property of pure substance\n", "hf=191.8 #enthalpy of saturated liquid @10 kPa from steam table\n", "hg=2584 # enthalpy of saturated vapour @10 kPa from steam table\n", "h4=hf+x*(hg-hf)# enthalpy @ state 4\n", "\n", "wt=h3-h4 # turbine work\n", "\n", "efficiency=(wt-wp)/q # efficiency of power cycle\n", "print \" The Efficiency is\",round(efficiency,4),\" or\",round(efficiency*100,1),\"%\"\n", "# the answer is correct within limits\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.3238 or 32.4 %\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.2:PG-149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "# Please refer to the given figure of question 6.1 for quantities\n", "effi1=0.323 #old efficiency\n", "P2=4*1000 #higher pressure converted in in kPa\n", "P1=10 # lower pressure in kPa\n", "rho=1000 # density of water in Kg/m^3\n", "h1=192 # enthalpy at state 1 in kJ/kg\n", "h3=3214 # enthalpy at state 3 i.e @400 degree celsius and 4MPa in kJ/kg\n", "s3=6.769# entropy at state 3 i.e @400 degree celsius and 4MPa in kJ/kg.K\n", "\n", "s4=s3 # insentropic process\n", "sf=0.6491 # entropy of saturated liquid @10 kPa from steam table\n", "sg=8.151 # entropy of saturated vapour @10 kPa from steam table\n", "\n", "x=(s4-sf)/(sg-sf)# quality of steam\n", "\n", "hf=192 #enthalpy of saturated liquid @10 kPa from steam table\n", "hg=2584 # enthalpy of saturated vapour @10 kPa from steam table\n", "h4=hf+x*(hg-hf)# enthalpy @ state 4\n", "h2=h1 # isenthalpic process\n", "qb=h3-h2 # heat addition\n", "\n", "wt=h3-h4 # turbine work\n", "\n", "effi2=(wt)/qb # efficiency of power cycle\n", "\n", "print \" The Efficiency is\",round(effi2,3),\" or\",round(effi2*100),\"% \\n\"\n", "\n", "perincrease=((effi2-effi1)/effi1)*100 \n", "\n", "print \" The % increase in Efficiency is\",round(perincrease,2),\" \\n\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.354 or 35.0 % \n", "\n", " The % increase in Efficiency is 9.69 \n", "\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.3:PG-149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "# Please refer to fig of question 6.1 for quantities\n", "effi1=0.323 #old efficiency\n", "P2=2*1000 #higher pressure converted in in kPa\n", "P1=10 # lower pressure in kPa\n", "rho=1000 # density of water in Kg/m^3\n", "T2=600# max temperature of cycle in degree celsius\n", "h1=192 # enthalpy at state 1 in kJ/kg\n", "h3=3690 # enthalpy at state 3 in kJ/kg, 600*C and 2MPa pressure\n", "s3=7.702# entropy at state 3 in kJ/kg.K, 600*C and 2MPa pressure\n", " \n", "s4=s3# isentropic process\n", "sf=0.6491 # entropy of saturated liquid @10 kPa from steam table\n", "sg=8.151 # entropy of saturated vapour @10 kPa from steam table\n", "\n", "x=(s4-sf)/(sg-sf)# quality of steam\n", "\n", "hf=192 #enthalpy of saturated liquid @10 kPa from steam table\n", "hg=2584 # enthalpy of saturated vapour @10 kPa from steam table\n", "h4=hf+x*(hg-hf)# enthalpy @ state 4\n", "\n", "h2=h1 # isenthalpic process\n", "qb=h3-h2 # heat addition\n", "\n", "wt=h3-h4 # turbine work\n", "\n", "effi2=(wt)/qb # efficiency of power cycle\n", "print \" The Efficiency is\",round(effi2,3),\" or\",round(effi2*100),\"% \\n\"\n", "perincrease=((effi2-effi1)/effi1)*100 \n", "print \" The % increase in Efficiency is\",round(perincrease,2),\" \\n\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.357 or 36.0 % \n", "\n", " The % increase in Efficiency is 10.56 \n", "\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.4:PG-150" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "# Please refer to fig of question 6.1 for quantities\n", "effi1=0.323 #old efficiency\n", "P2=2*1000 #higher pressure converted in in kPa\n", "P1=4 # condenser pressure in kPa\n", "rho=1000 # density of water in Kg/m^3\n", "h1=192 # enthalpy at state 1 in kJ/kg\n", "h3=3248 # enthalpy at state 3 in kJ/kg\n", "s3=7.1279# entropy at state 3 in kJ/kg.K\n", "\n", "s4=s3 # isentropic process \n", "\n", "sf=0.4225 # entropy of saturated liquid @10 kPa from steam table\n", "sg=8.4754 # entropy of saturated vapour @10 kPa from steam table\n", "\n", "x=(s4-sf)/(sg-sf)# from property of pure substance\n", "\n", "hf=121 #enthalpy of saturated liquid @4 kPa from steam table\n", "hg=2554 # enthalpy of saturated vapour @4 kPa from steam table\n", "h4=hf+x*(hg-hf)# enthalpy @ state 4h1=h2 # isenthalpic process\n", "h2=h1 # isenthalpic process\n", "qb=h3-h2 # heat addition\n", "\n", "wt=h3-h4 # turbine work\n", "\n", "effi2=(wt)/qb # efficiency of power cycle\n", "print \" The Efficiency is\",round(effi2,4),\" or\",round(effi2*100),\"% \\n\"\n", "perincrease=((effi2-effi1)/effi1)*100 \n", "print \" The % increase in Efficiency is\",round(perincrease,2),\" \\n\"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.3603 or 36.0 % \n", "\n", " The % increase in Efficiency is 11.55 \n", "\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.5:PG-152" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "P2=2*1000 #higher pressure converted in in kPa\n", "P1=10 # lower pressure in kPa\n", "h1=192.0 # enthalpy at 10 kPa in kJ/kg\n", "h3=3248.0 # enthalpy @ state 3 in kJ/kg from table C.3\n", "s3=7.128 # entropy @ state 3 in kJ/kg.K from table C.3\n", "s4=s3 # isentropic process\n", "\n", "h2=h1 #isenthalpic process\n", "h4=((s4-7.038)/(7.233-7.038))*(3056-2950)+2950 #using adjacent values for \n", "#interpolation from table C.3 \n", "h5=3267.0 # enthalpy at 800 kPa and $00 degree celsius\n", "s5=7.572 # entropy at 800 kPa and $00 degree celsius\n", "\n", "s6=s5 # isentropic process\n", "sf=0.6491# entropy of saturated liquid @10 kPa from steam table\n", "sg=8.151 # entropy of saturated vapour @10 kPa from steam table\n", "\n", "x=(s6-sf)/(sg-sf)# quality of steam\n", "\n", "hf=192.0 #enthalpy of saturated liquid @10 kPa from steam table\n", "hg=2585.0 # enthalpy of saturated vapour @10 kPa from steam table\n", "\n", "h6=hf+x*(hg-hf)# enthalpy @ state 6\n", "\n", "# we now calculate energy input\n", "qb=(h5-h4)+(h3-h2)# heat interaction\n", "\n", "# we now calculate work output\n", "wt=(h5-h6)+(h3-h4)# turbine work\n", "\n", "eff=(wt)/qb # efficiency of power cycle\n", "print\" The Efficiency is\",round(eff,3),\" or\",round(eff*100,2),\"%\"\n", "\n", "# // The anwer is different in textbook as there the intermediate values are approximated while in python the calculations are precise \n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.336 or 33.57 %\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.6:PG-155" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# initialization of variables\n", "\n", "# Please refer to fig of question 6.1 for quantities\n", "\n", "effi1=0.357 #efficiency from example 6.3\n", "P2=2*1000.0 #higher pressure converted in in kPa\n", "P1=10.0 # lower pressure in kPa\n", "rho=1000.0 # density of water in Kg/m^3\n", "T2=600.0 # max temperature of cycle in degree celsius\n", "h1=192.0 # enthalpy at state 1 in kJ/kg\n", "h3=3690.0 # enthalpy at state 3 in kJ/kg, 600*C and 2MPa pressure\n", "h4=2442.0 # enthalpy from example 6.3\n", "h6=505.0 # specific enthalpy @ 200 kPa from steam table\n", "h7=h6 # isenthalpic process\n", "s3=7.702# entropy at state 3 in kJ/kg.K, 600*C and 2MPa pressure\n", "\n", "h2=h1 # isenthalpic process\n", "s5=s3 # isentropic process\n", "h5=(s3-7.509)*(2971-2870)/(7.709-7.509)+2870 # interpolationg from steam table 2 200 kPa using s5=s3= 7.702 kJ/kg.\n", "\n", "m6=1.0 # let mass of steam =1 Kg\n", "m5=(h6-h2)*(m6)/(h5-h2) \n", "m2=m6-m5 # conservation of mass\n", "\n", "wt=h3-h5+(h5-h4)*m2 # work done by turbine\n", "qb=h3-h7 # heat given to bolier\n", "effi2=(wt)/qb # efficiency of power cycle\n", "print \" The Efficiency is\",round(effi2,4),\" or\",round(effi2*100),\"% \\n\"\n", "perincrease=((effi2-effi1)/effi1)*100 \n", "print \" The % increase in Efficiency is\",round(perincrease,2),\" \\n\"\n", "\n", "# The anwer is different in textbook as there the intermediate values are approximated while in python the calculations are precise \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.3732 or 37.0 % \n", "\n", " The % increase in Efficiency is 4.55 \n", "\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.7:PG-156" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "P2=2*1000 #higher pressure converted in kPa\n", "P1=10 # lower pressure in kPa\n", "h1=192 # enthalpy at 10 kPa in kJ/kg\n", "h3=3248 # enthalpy @ state 3 in kJ/kg from table C.3\n", "s3=7.128 # entropy @ state 3 in kJ/kg.K from table C.3\n", "\n", "s4=s3 # isentropic process\n", "\n", "h4=((s4-7.038)/(7.233-7.038))*(3056-2950)+2950 #using adjacent values for \n", "#interpolation from table C.3 \n", "h5=3267 # enthalpy at 800 kPa and $00 degree celsius\n", "s5=7.572 # entropy at 800 kPa and $00 degree celsius\n", "\n", "s6=s5 # isentropic process\n", "sf=0.6491# entropy of saturated liquid @10 kPa from steam table\n", "sg=8.151 # entropy of saturated vapour @10 kPa from steam table\n", "\n", "x=(s6-sf)/(sg-sf)# quality of steam\n", "\n", "hf=192 #enthalpy of saturated liquid @10 kPa from steam table\n", "hg=2585 # enthalpy of saturated vapour @10 kPa from steam table\n", "\n", "h6=hf+x*(hg-hf)# enthalpy @ state 6\n", "h7=721 # enthalpy of saturated liquid @800 kPa from steam table\n", "h8=h7 # isenthalpic process\n", "h2=h1 # isenthalpic process\n", "\n", "m8=1 # let mass of steam =1 Kg\n", "m4=(h8-h2)*(m8)/(h4-h2)\n", "m2=m8-m4 # conservation of mass\n", "\n", "wt=h3-h4+(h5-h6)*m2 # work done by turbine\n", "qb=h3-h8+(h5-h4)*m2 # heat given to bolier\n", "\n", "effi=(wt)/qb # efficiency of power cycle\n", "# result\n", "print \" The Efficiency is\",round(effi,3),\" or\",round(effi*100,2),\"%\"\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.347 or 34.7 %\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.8:PG-159" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "\n", "# for rankine cycle refer to fig 6.9\n", "\n", "effiT=0.8 # turbine efficiency\n", "P2=2*1000 # higher pressure converted in kPa\n", "P1=10 # lower pressure in kPa\n", "h1=192 # enthalpy at 10 kPa in kJ/kg\n", "h3=3690 # enthalpy of superheated steam @ 2 MPa from steam table in kJ/kg\n", "s3=7.702 #entropy of superheated steam @ 2 MPa from steam table in kJ/kg.K\n", "# state 4' is repsresented by '41'\n", "h2=h1 #isenthalpic process\n", "s41=s3 # entropy is constant\n", "sf=0.6491 # entropy of saturated liquid @10 kPa from steam table\n", "sg=8.151 # entropy of saturated vapour @10 kPa from steam table\n", "x=(s41-sf)/(sg-sf)# from property of pure substance\n", "\n", "hf=191.8 #enthalpy of saturated liquid @10 kPa from steam table\n", "hg=2584 # enthalpy of saturated vapour @10 kPa from steam table\n", "h41=hf+x*(hg-hf)# enthalpy @ state 41\n", "\n", "wa=effiT*(h3-h41)# turbine efficiency =(actual work)/(isentropic work)\n", "\n", "qb=h3-h2 # heat supplied\n", "\n", "effi=(wa)/qb # efficiency of power cycle\n", "print\" The Efficiency is\",round(effi,3),\" or\",round(effi*100,1),\"%\"\n", "\n", "h4=h3-wa # adiabatic process\n", "\n", "# now using interpolation for superheated steam @ 10 kPa\n", "T4=(h4-2688)*(150-100)/(2783-2688)+100\n", "\n", "print \"\\n The Temperature from interpolation comes out to be\",int(T4),\" degree celsius\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Efficiency is 0.286 or 28.6 %\n", "\n", " The Temperature from interpolation comes out to be 101 degree celsius\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.9:PG-162" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization of variables\n", "\n", "# refer to fig 6.10c\n", "\n", "mdot=0.6 # mass flow rate of refrigerant in kg/sec\n", "T1=-24 # evaporator temperature in degree celsius\n", "T2=39.39 # condenser temperature in degree celsius\n", "h1=232.8 # enthalpy of saturated R134a vapour @ -24 degree celsius from table D.1\n", "s1=0.9370 # entropy of saturated R134a vapour @ -24 degree celsius from table D.1\n", "h3=105.3 # enthalpy of saturated R134a liquid @ -24 degree celsius from table D.2\n", "h4=h3 # isenthalpic process\n", "\n", "# interpolating enthalpy from table D.3 @ 39.39 degree celsius\n", "h2=(s1-0.9066)*(280.19-268.68)/(0.9428-0.9066)+268.68\n", "QdotE=mdot*(h1-h4) # heat transfer rate\n", "WdotC=mdot*(h2-h1)# power given to compressor\n", "\n", "COP=QdotE/WdotC # coefficient of performance\n", "\n", "Hp=(WdotC/0.746)/(QdotE/3.52) #calculating Horsepower required per Ton\n", "\n", "print \"The rate of refrigeration is\",round(QdotE,2),\"kJ/s \\n \"\n", "print \"The coefficient of performance is\",round(COP,2),\"\\n \"\n", "print \"The rating in horsepower per ton is\",round(Hp,3),\" hp\\n \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The rate of refrigeration is 76.5 kJ/s \n", " \n", "The coefficient of performance is 2.8 \n", " \n", "The rating in horsepower per ton is 1.686 hp\n", " \n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.10:PG-163" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization of variables\n", "# refer to fig 6.10c\n", "effi=0.8 # compressor efficiency\n", "mdot=0.6 # mass flow rate of refrigerant in Kg/sec\n", "T4=-24 # temperature of evaporator\n", "T2=39.39 # temperature of condensor\n", "T1=-20.0 # supeheating temperature\n", "T3=40 # subcooling temperature\n", "h3=106.2 # enthalpy of liquid R-134a @ 40 degree celsius from table D.1\n", "h4=h3 # isenthalpic process\n", "h1=236.5 # enthalpy of superheated R-134a @ 0.10 MPa and -20 degree celsius from table D.3\n", "s1=0.960 #entropy of superheated R-134a @ 0.10 MPa and -20 degree celsius from table D.3 \n", "\n", "s2dash=s1 # isentropic process\n", "\n", "# using interpolation from table D.3 @ 1.0 MPa for s2dash=0.960 \n", "h2dash=(s2dash-0.9428)*(291.36-280.19)/(0.9768-0.9428)+280.19\n", "\n", "h2=(h2dash-h1)/(effi)+h1 # by definition of compressor efficiency\n", "\n", "QdotE=mdot*(h1-h4)#heat transfer rate power given to compressor\n", " \n", "wdotc=mdot*(h2-h1)# power given to compressor\n", "\n", "COP=QdotE/wdotc # coefficient of performance\n", "\n", "print \"The rate of refrigeration is\",round(QdotE,1),\"kJ/s \\n \"\n", "\n", "print \"The coefficient of performance is\",round(COP,2),\"\\n \"\n", "# The value of Wdotc is shown wrong in the textbook. It should be multiplied by mass flow rate\n", " " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The rate of refrigeration is 78.2 kJ/s \n", " \n", "The coefficient of performance is 2.11 \n", " \n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.11:PG-165" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# solution\n", "#initialization of variables\n", "# refer to fig 6.10c\n", "\n", "QdotC=300 #heating Load in KWh or heat rejected by condensor\n", "T1=-12 # evaporator temperature in degree celsius\n", "P2=800 # condensor pressure in kPa \n", "h1=240 # specific enthalpy of saturated R-134a vapour @ -12 degree celsius from table D.1\n", "s1=0.927 # specific entropy of saturated R-134a vapour @ -12 degree celsius from table D.1\n", "s2=s1 # isentropic process\n", "h3=93.4 #specific enthalpy of saturated R-134a liquid @ 800 kPa from tableD.2\n", "\n", "# extrapolating enthalpy from table D.2 @ 0.8 MPa for s=0.927\n", "h2=273.7-(0.9374-s2)*(284.4-273.7)/(0.9711-0.9374)\n", "\n", "# QdotE=mdot*(h1-h4) is heat transfer rate\n", "mdot=QdotC/(h2-h3)# mass flow rate\n", "\n", "WdotC=mdot*(h2-h1)# power given to compressor\n", "\n", "#part(a)\n", "COP=QdotC/WdotC # coefficient of performance\n", "print \"The coefficient of performance is\",round(COP,2),\"\\n \"\n", "\n", "#part(b)\n", "Cost=WdotC*0.07 # cost of electricity\n", "print \"The cost of electricity is $\",round(Cost,3),\"/hr \\n\"\n", "\n", "#part(c)\n", "costgas=(300*3600*0.50)/100000 # cost of gas\n", "print \"The cost of gas is $\",round(costgas,2),\"/hr \\nThus heat pump is better \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The coefficient of performance is 5.82 \n", " \n", "The cost of electricity is $ 3.607 /hr \n", "\n", "The cost of gas is $ 5.4 /hr \n", "Thus heat pump is better \n" ] } ], "prompt_number": 66 } ], "metadata": {} } ] }