{ "metadata": { "name": "", "signature": "sha256:abd0537a9b98c6cb49f3032d9229bd28210acff6f4a7d9f1c5434293bf15ef92" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 4:The First Law of Thermodynamics" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.1:PG-62" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#initialization of variables\n", "K=100 # spring constant in kN/m\n", "d=0.8 # dispacement of spring in m\n", " # to get total work we integrate from 0 to 0.8 displacement\n", "x1=0; # lower limit of integration\n", "x2=0.8; # upper limit of integration\n", "from scipy.integrate import quad\n", "\n", "# we find work\n", "def integrand(x,K):\n", " return K*x\n", "\n", "W12, err = quad(integrand, x1, x2, K) # integrating to get work\n", "Q12=W12; # by first law of thermodynamics\n", "print \"The Heat transfer is \",int(Q12),\" J\"\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Heat transfer is 32 J\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.2:PG-65" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "P= 5*746 # power of fan converted in watt\n", "t=1*60*60 # time converted to seconds\n", "\n", "# by first law of thermodynamics Q=delU + W\n", "# Q=0 hence -W=delU\n", "# first we find work input\n", "W=-P*t # work in J\n", "delU=-W # from 1st law\n", "print \"The internal energy increase is \",float(delU),\" J\"\n", "# The answer is approximated in textbook\n", "# our answer is precise\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The internal energy increase is 13428000.0 J\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.3:PG-65" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "P=400 # pressure in kPa\n", "T1=200 # initial temperature in degree celsius\n", "V1= 2 # initial volume in m^3\n", "Q=3500 # heat added in kJ\n", "v1=0.5342 # specific volume of steam at 200 degree celcius and 0.4 Mpa pressure from table C.3\n", "u1=2647 # specific internal energy in kJ/kg @ pressure = 0.4 MPa\n", "m=V1/v1 # mass in kg\n", "# we have a relation Between u2 and v2 from 1st law of thermodynamics\n", "v2=1.06 # specific volume at state 2 by trial and error and interpolation\n", "V2=m*v2 \n", "u2=((3500-400*(V2-V1))/m)+2647 # specific internal energy for v2=1.06 by trial and error\n", "\n", "# on interpolation from steam table at 0.4 MPa we get temperature \n", "T2=644 # temperature in degree celsius\n", "print \"The temperature for u2=\",round(u2),\" kJ and v2 =\",round(v2,3),\" kg/m^3 is \\n \",int(T2),\" degree celsius\"\n", "# this numerical is solved by trial and error thus refer to Appendix C" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The temperature for u2= 3372.0 kJ and v2 = 1.06 kg/m^3 is \n", " 644 degree celsius\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.4:PG-67" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# initialization of variables\n", "P=400 # pressure in kPa\n", "T1=200 # initial tmperature in degree celsius\n", "V=2 # initial volume in m^3\n", "Q=3500 # heat added in kJ\n", "\n", "#solution\n", "h1=2860 # initial enthalpy @ 200*C and 400 kPa from steam table\n", "v=0.5342 # specific volume from steam table C.3 \n", "m=V/v;\n", "h2=(Q/m)+h1; # final enthalpy in kJ/kg from energy equation\n", "\n", "# NOW USING THIS ENTHLAPY AND INTERPOlATING FROM STEAM TABLE\n", "\n", "T2=600+(92.6/224)*100\n", "\n", "print \"The Final temperature is \",int(T2),\" degree Celsius\"\n", "# result is obtained from interpolation on steam table\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Final temperature is 641 degree Celsius\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.5:PG-71" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "T1=300 # initial temperature in degree celsius\n", "T2=700 # final temperature in degree celsius\n", "P=150 # pressure in kPa\n", "m=3 # mass of steam in kg\n", "\n", "# solution\n", "# part (a)\n", "from scipy.integrate import quad\n", "\n", "# now we make function to integrate\n", "def integrand(T):\n", " return 2.07+(T-400)/1480\n", "\n", "I, err = quad(integrand, T1, T2) # integrating specific heat over temperature range\n", "delH=m*I #integrate('2.07+(T-400)/1480','T',T1,T2) # expressing as function of temperature and integrating\n", "\n", "print\" The change in Enthalpy is \",int(delH),\" kJ \\n\"\n", " \n", "# part(b)\n", "CPavg=delH/(m*(T2-T1)) # avg value of specific heat at constant pressure\n", "print \" The average value of Cp is \",round(CPavg,2),\" kJ/kg.*C\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The change in Enthalpy is 2565 kJ \n", "\n", " The average value of Cp is 2.14 kJ/kg.*C\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.6,PG-72" ] }, { "cell_type": "code", "collapsed": false, "input": [ "m=1 # mass of nitrogen in kg\n", "T1=300 # initial temperature in Kelvin\n", "T2=1200 # final temperature in Kelvin\n", "M=28.0 # in kg/kmol\n", "# part(a)\n", "# the enthalpy change is found from gas table in App.E\n", "delh=36777-8723 # from gas table\n", "delH=delh/M \n", "print \" The entalpy change from gas table is \",round(delH),\" kJ/kg \\n\"\n", "\n", "# part (b) \n", "Cp=1.042 # from table B.2\n", "delH=Cp*(T2-T1)\n", "print \" The entalpy change by assuming constant specific heat is \",round(delH),\" kJ/kg\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The entalpy change from gas table is 1002.0 kJ/kg \n", "\n", " The entalpy change by assuming constant specific heat is 938.0 kJ/kg\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.7:PG-76" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "x=0.7 # quality of steam\n", "P1=200 # initial pressure in kPa\n", "P2=800 # final pressure in kPa\n", "V=2 # volume in m^3\n", "# The values are taken from TABLE C.2\n", "vf1=0.0010 # specific volume of saturated liquid at 200 kPa\n", "vg1=0.8857 # specific volume of saturated gas at 200 kPa\n", "uf1=504.5 # specific internal energy of saturated liquid @ state 1\n", "ug1=2529.5 # speciific internal energy of saturated gas @ state 1\n", "\n", "v1=vf1+x*(vg1-vf1); # specific volume of vapour\n", "m=V/v1\n", "\n", "u1=uf1+x*(ug1-uf1) # specific internal energy of vapour @ state 1\n", "v2=v1 # constant volume process\n", "u2=((0.6761-0.6203)*(3661-3853)/(0.6761-0.6181))+3853 # from steam table @ 800kPa by interpolating\n", "Q=m*(u2-u1) # heat transfer\n", "print \"The heat transfer is \",round(Q,3),\" kJ\"\n", "# The answer in the textbook is approximated" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The heat transfer is 5630.537 kJ\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.8:PG-76" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "V=0.02 # volume in m^3\n", "P=400 # pressure in kPa\n", "T1=50+273 # initial temperature in kelvin\n", "T2=700+273 # final temperature in kelvin\n", "Q=50 # heat added in kJ\n", "R=287 # constant for air\n", "Cp=1 # constant for specific heat of air\n", "\n", "# using the ideal gas equation\n", "\n", "m=P*1000*V/(R*T1) # mass of air in kg\n", "W=Q-(m*Cp*(T2-T1)) # work done from first law\n", "# result\n", "print \"The Paddle work is \",round(W,2),\" kJ\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Paddle work is -6.09 kJ\n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.9,PG-77" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "V1=2 # initial volume in m^3\n", "V2=0.2 # final volume in m^3\n", "T1=20+273 # temperature in kelvin\n", "P=200 # pressure in kPa\n", "R=0.287 # constant for air\n", "gama=1.4 # polytropic index for air\n", "Cv=0.717 # specific heat at constant volume for air\n", "\n", "#solution\n", "\n", "#using the ideal gas equation\n", "m=(P*V1)/(R*T1) # mass in kg\n", "# process is adiabatic thus\n", "T2=T1*((V1/V2)**(gama-1)) # final temperature\n", "\n", "W=-m*Cv*(T2-T1) # work from first law\n", "print \"The Work is \",int(W),\" kJ\"\n", "# solution is approximated in textbook" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Work is -1510 kJ\n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.10:PG-79" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# initialization of variables\n", "P1=2000.0 # initial pressure in kPa\n", "T1=600.0 # initial temperature in degree celsius\n", "p2=600.0 # final pressure in kPa\n", "T2=200.0 # final temperature in degree celsius\n", "d1=0.06 # diameter of inlet pipe in metre\n", "d2=0.120 # diameter of outlet pipe in metre\n", "V1=20.0 # velocity at inlet in m/s\n", "\n", "# solution\n", "# from superheat table C.3 values are noted\n", "v1=0.1996 # specific volume of superheated steam @ 600*C and 2000 kPa\n", "v2=0.3520 # specific volume of superheated steam @ 200*C and 2000 kPa\n", "rho1=1/v1 # initial density\n", "rho2=1/v2 # final density\n", "A1=(math.pi*d1**2)/4 # inlet area\n", "A2=(math.pi*d2**2)/4 # exit area\n", "\n", "V2=(rho1*A1*V1)/(rho2*A2) # from continuity equation\n", "print \" The Exit velocity is \",round(V2,2),\" m/s \\n\"\n", "\n", "mdot=rho1*A1*V1 # mass flow rate\n", "print\" The mass flow rate is \",round(mdot,3),\" kg/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The Exit velocity is 8.82 m/s \n", "\n", " The mass flow rate is 0.283 kg/s\n" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.11:PG-82" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "P1=8000 # initial pressure in kPa\n", "T1=300 # temperature in degree celsius\n", "P2=2000 # final pressure in kPa\n", "\n", "# solution\n", "h1=2785 # specific enthalpy of steam in kJ/kg @ 8000 kPa and 300 degree celsius from steam table\n", "h2=h1 # throttling process thus enthalpy is constant\n", "T2=212.4 # from steam table as we know enthalpy and pressure\n", "hf2=909 # specific enthalpy of saturated liquid @ 2000 kPa and 300 degree celsius\n", "hg2=2799.5 # specific enthalpy of saturated gas @ 2000 kPa and 300 degree celsius\n", "x2=(h2-hf2)/(hg2-hf2) # quality of steam\n", "\n", "vg2=0.0992 # specific volume of saturated gas @ 2000 kPa and 212.4*c\n", "vf2=0.0012 # specific volume of saturated liquid @ 2000 kPa and 212.4*c\n", "v2=vf2+x2*(vg2-vf2) # from properties of pure substance\n", "\n", "print \"The Final Temperature and Specific volume is \",round(T2,1),\"*C and \",round(v2,3),\" m^3/kg\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Final Temperature and Specific volume is 212.4 *C and 0.098 m^3/kg\n" ] } ], "prompt_number": 50 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.12:PG-84" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# initialization of variables\n", "P1=4000 # inlet pressure in kPa\n", "T1=500 # inlet temperature in degree celsius\n", "V1=200 # inlet steam velocity in m/s\n", "d1=0.05 # inlet diameter in 'm'\n", "P2=80 # exit pressure in kPa\n", "d2=0.250 # exit diameter in 'm'\n", "\n", "# solution\n", "v1=0.08643 # specific volume from steam table @ 4000 kPa and 500*C\n", "v2=2.087 # specific volume from steam table @ 80 kPa and 500*C\n", "rho1=1/v1 # density at inlet\n", "rho2=1/v2 # density at outlet\n", "A1=(math.pi*d1**2)/4 # inlet area\n", "A2=(math.pi*d2**2)/4\n", "mdot=rho1*A1*V1 # mass flow rate\n", "mdot=round(mdot,3) # rounding to 3 significant digits\n", "\n", "#now using table C.3\n", "h1=3445 # initial specific enthalpy @ 4000 kPa and 500 *C \n", "h2=2666 # final specific enthalpy @ 80 kPa and 500 *C\n", "WT=-mdot*(h2-h1) # maximum power from first law\n", "print \" The power output is \",round(WT),\" kJ/s \\n \"\n", "\n", "V2=(A1*V1*rho1)/(A2*rho2) \n", "V2=round(V2) # rounding of digits\n", "delKE=mdot*((V2**2)-(V1**2))/2 # the change in kinetic energy\n", "print \" The change in K.E is \",round(delKE),\" J/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The power output is 3540.0 kJ/s \n", " \n", " The change in K.E is -6250.0 J/s\n" ] } ], "prompt_number": 78 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.13:PG-85" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# initialization of variables\n", "Wdot=10 # pump power in hp\n", "g=9.81 # acceleration due to gravity\n", "rho=1000 # density of water in kg/m^3\n", "d1=0.06 # inlet dimeter in 'm'\n", "d2=0.10 # oulet diamter in 'm'\n", "V1=10 # velocity of water at inlet in m/s\n", "\n", "#solution\n", "A1=math.pi*(d1**2)/4 # area of inlet\n", "A2=math.pi*(d2**2)/4 # area of outlet\n", "V2=A1*V1/A2 # oulet velocity from continuity equation\n", "\n", "mdot=rho*A1*V1 # mass flow rate\n", "delP=((((Wdot*746)/mdot)-((V2**2)-V1**2)/(2*g))*rho)/1000 # change in pressure in kPa\n", "print \"The rise in pressure is \",round(delP),\" kPa\"\n", "# The answer is approximated in textbook , our answer is precise \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The rise in pressure is 268.0 kPa\n" ] } ], "prompt_number": 80 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.14:PG-85" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "# initialization of variables\n", "P1=7000.0 # inlet pressure in Pa\n", "T1=420.0 # inlet temperature in degree celsius\n", "V1=400.0 # inlet velocity in m/s\n", "d1=0.200 # inlet diameter in 'm'\n", "V2=700.0 # exit velocity in m/s\n", "k=1.4 # polytopic index for air\n", "Cp=1000 # specific heat at constant pressure for air in j/kg.K\n", "R=287 # specific gas constant for air\n", "\n", "#solution\n", "\n", "#part (a)\n", "T2=(((V1**2)-V2**2)/(2*Cp))+T1 # outlet temperature in degree celsius\n", "print \" The exit temperature is \",round(T2),\" *C \\n\"\n", "\n", "#part (b)\n", "\n", "rho1=P1/(R*(T1+273)) # density at entrance\n", "A1=(math.pi*d1**2)/4\n", "mdot=rho1*A1*V1 # \n", "print \" The mass flow rate is \",round(mdot,3),\" kg/s \\n\"\n", "\n", "# part (c)\n", "\n", "rho2=rho1*(((T2+273)/(T1+273))**(1/(k-1))) # density at exit\n", "# now we find the exit diameter\n", "d2=math.sqrt((rho1*V1*(d1)**2)/(rho2*V2))\n", "print \" The outlet diameter is \",round(d2,3),\" m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The exit temperature is 255.0 *C \n", "\n", " The mass flow rate is 0.442 kg/s \n", "\n", " The outlet diameter is 0.212 m\n" ] } ], "prompt_number": 87 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4.15:PG-89" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initialization of variables\n", "mdots=100 # mass flow rate of sodium in kg/s\n", "Ts1=450 # inlet temperature of sodium in degree celsius\n", "Ts2=350 # exit temperature of sodium in degree celsius\n", "Cp=1.25 # specific heat of sodium in KJ/kg.*C\n", "Tw1=20 # inlet temperature of water in degree celsius\n", "Pw=5000 # inlet pressure of water in kPa \n", "\n", "# solution\n", "hw1=88.65 # enthalpy from table C.4\n", "hw2=2794 # enthalpy from table C.3\n", "mdotw=(mdots*Cp*(Ts1-Ts2))/(hw2-hw1) # mass flow rate of water\n", "print \" The mass flow rate of water is \",round(mdotw,2),\" kg/s \\n\"\n", "Qdot=mdotw*(hw2-hw1) # heat transfer in kW using energy equation\n", "# result\n", "print \" The rate of heat transfer is \",round(Qdot),\" kW\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " The mass flow rate of water is 4.62 kg/s \n", "\n", " The rate of heat transfer is 12500.0 kW\n" ] } ], "prompt_number": 90 } ], "metadata": {} } ] }