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diff --git a/Fundamental_of_Thermodynamics_by_Moran_and_Shapiro/6-Using_Entropy.ipynb b/Fundamental_of_Thermodynamics_by_Moran_and_Shapiro/6-Using_Entropy.ipynb new file mode 100644 index 0000000..d7eef21 --- /dev/null +++ b/Fundamental_of_Thermodynamics_by_Moran_and_Shapiro/6-Using_Entropy.ipynb @@ -0,0 +1,569 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Using Entropy" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.10: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"m1 = 5.00 // initial mass in kg\n", +"P1 = 5.00 // initial pressure in bar\n", +"T1 = 500.00 // initial temperature in kelvin\n", +"P2 = 1.00 // final pressure in bar\n", +"// From table A-22\n", +"pr1 = 8.411\n", +"// Using this value of pr2 and interpolation in table A-22\n", +"T2 = 317.00 // in kelvin\n", +"// Calculations \n", +"pr2 = (P2/P1)*pr1\n", +"m2 = (P2/P1)*(T1/T2)*m1\n", +"// Results\n", +"printf('The amount of mass remaining in the tank is %f kg',m2)\n", +"printf('and its temperature is %f kelvin.',T2);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.11: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"P1 = 1.00 // inlet pressure in bar\n", +"T1 = 593.00 // inlet temperature in kelvin\n", +"P2 = 1.00 // exit pressure in bar\n", +"eta =0.75 // turbine efficiency\n", +"// From table A-4\n", +"h1 = 3105.6 // in Kj/kg\n", +"s1 = 7.5308 // in kj/kg.k\n", +"// From table A-4 at 1 bar\n", +"h2s = 2743.00 // in kj/kg\n", +"// Calculations\n", +"w = eta*(h1 - h2s)\n", +"// Result\n", +"printf( ' The work developed per unit mass of steam flowing through is %f kJ/kg.',w);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.12: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"P1 = 3.00 // pressure of air entering in bar\n", +"T1 = 390.00 // temperature of air entering in kelvin\n", +"P2 = 1.00 // pressure of exit air\n", +"Wcvdot = 74.00 // work developed in kj/kg\n", +"// From table A-22,at 390k\n", +"h1 = 390.88 // in kj/kg\n", +"pr1 = 3.481\n", +"// From interpolation table A-22\n", +"h2s = 285.27 // in kj/kg\n", +"// calculations\n", +"pr2 = (P2/P1)*pr1\n", +"Wcvdots = h1 - h2s\n", +"eta = Wcvdot/Wcvdots\n", +"// Result\n", +"printf( ' The turbine efficiency is %.4f ',eta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.13: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"P1 = 1.00 // pressure of entering steam in Mpa\n", +"T1 = 593.00 // temperature of entering steam in kelvin\n", +"V1 = 30.00 // velocity of entering steam in m/s\n", +"P2 = 0.3 // pressure of exit steam in Mpa\n", +"T2 = 453.00 // temperature of exit steam in kelvin\n", +"// From table A-4, at T1 = 593 kelvin and P1 = 1 Mpa;\n", +"// and at T2 = 453 kelvin and P2 = .3 Mpa\n", +"h1 = 3093.9 // in kj/kg\n", +"s1 = 7.1962 // in kj/kg.k\n", +"h2 = 2823.9 // in kj/kg\n", +"// Interpolating in table A-4\n", +"h2s = 2813.3 // in kj/kg\n", +"// Calculations\n", +"V2squareby2 = h1 - h2 + (V1**2)/2000\n", +"V2squareby2s = h1 - h2s + (V1**2)/2000\n", +"eta = V2squareby2/V2squareby2s\n", +"// Results\n", +"printf( ' The nozzle efficiency is %.4f',eta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.14: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"// From table A-9\n", +"h1 = 249.75 // in kj/kg\n", +"h2 = 294.17 // in kj/kg\n", +"mdot = 0.07 // in kg/s\n", +"// From table A-9\n", +"s1 = 0.9572 // in Kj/Kg.k\n", +"h2s = 285.58 // in kj/kg\n", +"// Calculations\n", +"wcvdot = -(mdot*(h2-h1))\n", +"eta = (h2s-h1)/(h2-h1) \n", +"// Results\n", +"printf( ' The power in is %f kw',wcvdot);\n", +"printf( ' The isentropic efficiency is %.3f',eta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.15: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"P1 = 1.00 // pressure of entering air in bar\n", +"T1 = 293.00 // temperature of entering air in kelvin\n", +"P2 = 5.00 // pressure of exit air in bar\n", +"n = 1.3\n", +"R = 8.314/28.97\n", +"// From table A-22\n", +"h1 = 293.17 // in kj/kg\n", +"h2 = 426.35 // in kj/kg\n", +"// Calculations\n", +"T2 = T1*((P2/P1)**((n-1)/n)) // in kelvin\n", +"wcvdot=((n*R)/(n-1))*(T1-T2) // in kj/kg\n", +"Qcvdot= wcvdot + (h2-h1) // in kj/kg\n", +"// Results\n", +"printf( ' The work per unit mass passing through the device is %.2f kJ/kg',wcvdot)\n", +"printf( ' The heat transfer per unit mass is %.2f kJ/kg. ',Qcvdot)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"T = 373.15 // temperature in kelvin\n", +"// From table A-2\n", +"p = 1.014*(10**5) // pressure in pascal\n", +"vg = 1.673\n", +"vf = 1.0435e-3\n", +"sg = 7.3549\n", +"sf = 1.3069\n", +"// Calculations\n", +"w = p*(vg-vf)*(10**(-3))\n", +"Q = T*(sg-sf)\n", +"// Results \n", +"printf( ' The work per unit mass is %.3f KJ/Kg',w)\n", +"printf( ' The heat transfer per unit mass is %.2f kj/kg',Q)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"// Assumptions:\n", +"// From table A-2 at 100 degree celcius\n", +"ug = 2506.5 // in kj/kg\n", +"uf = 418.94 // in kj/kg\n", +"sg = 7.3549\n", +"sf = 1.3069\n", +"// Calculations:-\n", +"// From energy balance\n", +"W = -(ug-uf)\n", +"// From entropy balance\n", +"sigmabym = (sg-sf)\n", +"// Results\n", +"printf( ' The net work per unit mass is %.2f KJ/kg. ',W)\n", +"printf( ' The amount of entropy produced per unit mass is %.2f KJ/kg.',sigmabym)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"T1 = 273.0 // initial temperature of saturated vapor in kelvin\n", +"P2 = 0.7*(10**6) // final pressure in pascal\n", +"// From table A-10,\n", +"u1 = 227.06 // in kj/kg\n", +"// minimum theoretical work corresponds to state of isentropic compression\n", +"// From table A-12,\n", +"u2s = 244.32 // in kj/kg\n", +" \n", +"// Calculations \n", +"Wmin = u2s-u1\n", +"// Results\n", +"printf( ' The minimum theoretical work input required per unit mass of refrigerant is: %.2f kJ/kg',Wmin)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given :-\n", +"Qdot = -1.2 // in kilo watt\n", +"Tb = 300.0 // in kelvin\n", +"Tf = 293.0 // in kelvin\n", +"// Calculations\n", +"// Part (a)\n", +"// From entropy balance \n", +"sigmadot = -Qdot/Tb\n", +"// Part(b)\n", +"// From entropy balance \n", +"sigmadt = -Qdot/Tf\n", +"// Results\n", +"printf( ' The rate of entropy production with gearbox as system is %f kw/k',sigmadot)\n", +"printf( ' The rate of entropy production with gearbox + sorrounding as system is %f kw/k',sigmadt)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// GIven:-\n", +"Tmi = 1200.0 // initial temperature of metal in kelvin\n", +"cm = 0.42 // specific heat of metal in KJ/kg.k\n", +"mm = 0.3 // mass of metal in kg\n", +"Twi = 300.0 // initial temperature of water in kelvin\n", +"cw = 4.2 // specific heat of water in KJ/Kg.k\n", +"mw = 9.0 // mass of water in kg\n", +"// Calculations\n", +"// Part(a)\n", +"// Solving energy balance equation yields\n", +"Tf = (mw*(cw/cm)*Twi+mm*Tmi)/(mw*(cw/cm)+mm)\n", +"// Part (b)\n", +"// Solving entropy balance equation yields\n", +"sigma = mw*cw*log(Tf/Twi)+mm*cm*log(Tf/Tmi)\n", +"// Results\n", +"printf( ' The final equilibrium temperature of the metal bar and the water is %.2f kelvin.',Tf)\n", +"printf( ' The amount of entropy produced is: %.2f kJ/k.',sigma)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"P1 = 30.0 // pressure of steam entering the turbine in bar\n", +"T1 = 400.0 // temperature of steam entering the turbine in degree celcius\n", +"V1 = 160.0 // velocity of steam entering the turbine in m/s\n", +"T2 = 100.0 // temperature of steam exiting in degree celcius\n", +"V2 = 100.0 // velocity of steam exiting in m/s\n", +"Wcvdot = 540.0 // work produced by turbine in kJ/kg of steam\n", +"Tb = 350.0 // temperature of the boundary in kelvin\n", +"// From table A-4 and table A-2\n", +"h1 = 3230.9 // specific enthalpy at entry in Kj/kg\n", +"h2 = 2676.1 // specific enthalpy at exit in kj/kg\n", +"// Calculations\n", +"// Reduction in mass and energy balance equations results in \n", +"Qcvdot = Wcvdot + (h2 - h1)+ (V2**2-V1**2)/(2*(10**3)) // heat transfer rate\n", +"// From table A-2\n", +"s2 = 7.3549 // in kj/kg.k\n", +"// From table A-4\n", +"s1 = 6.9212 // in kj/kg.k\n", +"// From entropy and mass balance equations\n", +"sigmadot = -(Qcvdot/Tb) + (s2-s1)\n", +"// Results\n", +"printf( 'The rate at which entropy is produced within the turbine per kg of steam flowing is %.2f kJ/kg.k',sigmadot)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"T1 = 294.0 // entry temperature of air in kelvin\n", +"P1 = 5.1 // entry pressure of air in bars\n", +"T2 = 352.0 // exit temperature of hot stream in kelvin\n", +"P2 = 1.0 // exit pressure of hot stream in bars\n", +"T3 = 255.0 // exit temperature of cold stream in kelvin\n", +"P3 = 1.0 // exit pressure of cold stream in bars\n", +"cp = 1.0 // in kj/kg.k\n", +"// Calculations\n", +"R = 8.314/28.97\n", +"se = 0.4*(cp*log((T2)/(T1))-R*log(P2/P1)) + 0.6*(cp*log((T3)/(T1))-R*log(P3/P1))\n", +" // specific entropy in kj/kg.k\n", +"// Results\n", +"printf( ' Specific entropy in kj/kg.k = %.3f KJ/kg.',se)\n", +"printf( ' Since se > 0, the claim of the writer is true');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.8: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"P1 = 3.5 // pressure of refrigerant entering the compressor in bars\n", +"T1 = 268.0 // temperature of refrigerant entering the compressor in kelvin\n", +"P2 = 14.0 // pressure of refrigerant entering the condenser in bars\n", +"T2 = 348.0 // temperature of refrigerant entering the condenser in kelvin\n", +"P3 = 14.0 // pressure of refrigerant exiting the condenser in bars\n", +"T3 = 301.0 // temperature of refrigerant exiting the condenser in kelvin\n", +"P4 = 3.5 // pressure of refrigerant after passing through expansion valve in bars\n", +"P5 = 1.0 // pressure of indoor return air entering the condenser in bars\n", +"T5 = 293.0 // temperature of indoor return air entering the condenser in kelvin\n", +"AV5 = 0.42 // volumetric flow rate of indoor return air entering the condenser in m^3/s\n", +"P6 = 1.0 // pressure of return air exiting the condenser in bar\n", +"T6 = 323.0 // temperature of return air exiting the condenser in kelvin\n", +"// Part(a)\n", +"// From table A-9\n", +"s1 = 0.9572 // in kj/kg.k\n", +"// Interpolating in table A-9\n", +"s2 = 0.98225 // in kj/kg.k\n", +"h2 = 294.17 // in kj/kg\n", +"// From table A-7\n", +"s3 = 0.2936 // in kj/kg.k\n", +"h3 = 79.05 // in kj/kg\n", +"h4 = h3 // since expansion through valve is throttling process\n", +"// From table A-8\n", +"hf4 = 33.09 // in kj/kg\n", +"hg4 = 246.00 // in kj/kg\n", +"sf4 = 0.1328 // in kj/kg.k\n", +"sg4 = 0.9431 // in kj/kg.k\n", +"cp = 1.005 // in kj/kg.k\n", +"// Calculations\n", +"x4 = (h4-hf4)/(hg4-hf4) // quality at state 4\n", +"s4 = sf4 + x4*(sg4-sf4) // specific entropy at state 4\n", +"// CONDENSER!!\n", +"v5 = ((8314/28.97)*T5)/(P5*(10**5)) // specific volume at state 5\n", +"mairdot = AV5/v5 \n", +"h6 = cp*T6\n", +"h5 = cp*T5\n", +"mrefdot = mairdot*(h6-h5)/(h2-h3)\n", +"deltaS65 = cp*log(T6/T5)-(8.314/28.97)*log(P6/P5) // change in specific entropy\n", +"sigmacond = (mrefdot*(s3-s2)) + (mairdot*(deltaS65))\n", +"// COMPRESSOR!!\n", +"sigmacomp = mrefdot*(s2-s1)\n", +"// VALVE!!\n", +"sigmavalve = mrefdot *(s4-s3)\n", +"// Results\n", +"printf( ' The rates of entropy production for control volume enclosing the condenser is %f kw/k',sigmacond);\n", +"printf( ' The rates of entropy production for control volume enclosing the compressor is %f kW/K.',sigmacomp);\n", +"printf( ' The rates of entropy production for control volume enclosing the expansion valve is %f kW/K ',sigmavalve)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.9: Example.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Given:-\n", +"P1 = 1.00 // initial pressure in bar\n", +"T1 = 300.00 // initial temperature in kelvin\n", +"T2 = 650.00 // final temperature in kelvin\n", +"// Part(a)\n", +"// From table A-22\n", +"pr2 = 21.86 \n", +"pr1 = 1.3860\n", +"k = 1.39 // From table A-20\n", +"// Calculations\n", +"p2 = P1*(pr2/pr1)\n", +"p2a = P1*((T2/T1)**(k/(k-1)))\n", +"// Results\n", +"printf( ' P2 = %f bar.',p2)\n", +"printf( ' Part(b) IT software problem');\n", +"printf( ' P2a = %f bar',p2a);" + ] + } +], +"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 +} |