{ "metadata": { "name": "", "signature": "sha256:698d37f412d89d016a22fab7149569fc8652a8ce9fa170122f874fd8734f1895" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 7: Thermodynamics Processes" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.1, page no. 124" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization\n", "\n", "P1 = 160.0 #lb/in^2\n", "T1 = 100.0 #F\n", "P2 = 140.0 #lb/in^2\n", "T2 = 550.0 #F\n", "\n", "#From steam tables\n", "h1 = 67.97 #B/lbm\n", "h2 = 1299.3 #B/lbm\n", "s1 = 0.1295 #B/lbm R\n", "s2 = 1.6785 #B/lbm R\n", "\n", "#calculation\n", "dh = h2-h1\n", "ds = s2-s1\n", "\n", "#result\n", "print \"Change in enthalpy = %.1f B/lbm\" %dh\n", "print \"Change in entropy = %.4f B/lbm R\" %ds" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in enthalpy = 1231.3 B/lbm\n", "Change in entropy = 1.5490 B/lbm R\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.2, page no. 125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization\n", "P1 = 160.0 #lb/in^2\n", "T1 = 100.0 #F\n", "P2 = 140.0 #lb/in^2\n", "T2 = 550.0 #F\n", "\n", "#From steam tables\n", "h1 = 67.97 \n", "s1 = 0.1295\n", "h2 = 1300.9\n", "s2 = 1.6945\n", "\n", "#calculation\n", "dh = h2-h1\n", "ds = s2-s1\n", "\n", "#result\n", "print \"Change in enthalpy = %.1f B/lbm\" %dh\n", "print \"Change in entropy = %.4f B/lbm R\" %ds\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in enthalpy = 1232.9 B/lbm\n", "Change in entropy = 1.5650 B/lbm R\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.3, page no. 126" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import scipy.integrate\n", "\n", "#initialization\n", "P1 = 30.0 #lb/in^2\n", "T1 = 300+460.0 #R\n", "T2 = 60 +460.0 #R\n", "cp = 0.25 #B/lbm F\n", "R = 53.3 #ft-lb/lbm R\n", "\n", "#calculation\n", "Q = cp*(T2-T1)\n", "du = (cp-R/778)*(T2-T1)\n", "W = 778*(Q-du)\n", "def c(T):\n", " ds = cp/T\n", " return ds\n", "S = scipy.integrate.quadrature(c, T1, T2)[0]\n", "\n", "#result\n", "print \"Heat flow\", Q, \" B/lbm\"\n", "print \"change in internal energy\", round(du, 1), \" B/lbm\"\n", "print \"the work done is \", W, \" ft-lb/lbm\" #mistake in book for calculation of W\n", "print \"Change in entropy = %.3f B/lbm R\" %S" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat flow -60.0 B/lbm\n", "change in internal energy -43.6 B/lbm\n", "the work done is -12792.0 ft-lb/lbm\n", "Change in entropy = -0.095 B/lbm R\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.4, page no. 129" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization\n", "\n", "T1 = 300.0 #F\n", "# From steam tables\n", "\n", "h1 = 269.59 #B/lbm\n", "h2 = 1179.7 #B/lbm\n", "s1 = 0.4369 #B/lbm R\n", "s2 = 1.6350 #B/lbm R\n", "\n", "#calculation\n", "dh = h2-h1\n", "ds = s2-s1\n", "\n", "#result\n", "print \"Change in enthalpy = %.1f B/lbm\" %dh\n", "print \"Change in entropy = %.4f B/lbm R\" %ds" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in enthalpy = 910.1 B/lbm\n", "Change in entropy = 1.1981 B/lbm R\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.5, page no. 129" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#initialization\n", "v = 12.8 #ft^3\n", "T = 80+460.0 #R\n", "P = 14.0 #lb/in^2\n", "Pf = 500.0 #lb/in^2\n", "\n", "#calculation\n", "Q = -53.3*T*math.log(Pf/P)/778.0\n", "v2 = 53.3*T/(144*Pf)\n", "w = v/v2\n", "Qdot = w*Q\n", "Wdot = w*W\n", "ds = Q/T\n", "dsbar = ds*w\n", "\n", "#result\n", "print \"Work required = %d ft-lb\" %Wdot\n", "print \"Heat transfer = %d B\" %Qdot\n", "print \"Change in entropy = %.3f B/lbm \" %dsbar\n", "print \"Change in internal energy is 0 cause this is a constant temperature process\"\n", "\n", "#answers will differ due to roundin offs" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work required = -3295227 ft-lb\n", "Heat transfer = -4235 B\n", "Change in entropy = -7.844 B/lbm \n", "Change in internal energy is 0 cause this is a constant temperature process\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.6, page no. 131" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization\n", "P1 = 14.7 #lb/in^2\n", "P2 = 20.0 #lb/in^2\n", "w = 1.0 #lbm\n", "\n", "#calculation\n", "# From table 3 of appendix\n", "v1 = 26.8\n", "h1 = 1150.4\n", "s1 = 1.7566\n", "u1 = h1- 144*P1*v1/778\n", "print \"Internal energy 1 = %.1f B/lbm\" %u1\n", "\n", "\n", "# For pressure of 20 lb/in^2 , from table 2\n", "v2 = 26.8\n", "h2 = 1260.9\n", "s2 = 1.8637\n", "u2 = h2-144*P2*v2/778\n", "du = u2-u1\n", "ds = s2-s1\n", "\n", "#result\n", "print \"Change in internal energy = %.1f B/lbm\" %du\n", "print \"CHange in entropy = %.4f B/lbm R\" %ds" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Internal energy 1 = 1077.5 B/lbm\n", "Change in internal energy = 84.2 B/lbm\n", "CHange in entropy = 0.1071 B/lbm R\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.7, page no. 133" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import scipy.integrate\n", "import math\n", "\n", "#initialization\n", "P1 = 100.0 #lb/in^2\n", "T1 = 240+460.0 #R\n", "T2 = 740+460.0 #R\n", "cp = 0.171 #B?lbm F\n", "\n", "#calculation\n", "dq = cp*(T2-T1)\n", "def s(T):\n", " ds = cp/T\n", " return ds\n", "ds = scipy.integrate.quadrature(s, T1, T2)[0]\n", "cpm = 0.247\n", "cv = cpm-53.3/778\n", "Q = cv*(T2-T1)\n", "ds2 = cv*math.log(T2/T1)\n", "v1 = 53.3*T1/(144*P1)\n", "P2 = P1*(T2/T1)\n", "\n", "# from table 6\n", "h1 = 167.56\n", "phi1 = 0.66321\n", "u1 = h1-144*P1*v1/778.0\n", "h2 = 291.30\n", "phi2 = 0.79628\n", "u2 = h2-144*P2*v1/778.0\n", "Q3 = u2-u1\n", "ds3 = phi2-phi1-53.3*math.log(P2/P1)/778.0\n", "\n", "print \"Part a\"\n", "print \"work is zero\"\n", "print \"Heat = %.1f B/lbm\" %dq\n", "print \"Change in entropy = %.4f B/lbm R\" %ds\n", "\n", "print \"part b\"\n", "print \"Heat = %.1f B/lbm\" %Q\n", "print \"Change in entropy = %.4f B/lbm R\" %ds2\n", "\n", "print \"Part c\"\n", "print \"Heat low = %.1f B/lbm\" %Q3\n", "print \"Change in entropy = %.5f B/lbm R\" %ds3" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part a\n", "work is zero\n", "Heat = 85.5 B/lbm\n", "Change in entropy = 0.0922 B/lbm R\n", "part b\n", "Heat = 89.2 B/lbm\n", "Change in entropy = 0.0962 B/lbm R\n", "Part c\n", "Heat low = 89.5 B/lbm\n", "Change in entropy = 0.09614 B/lbm R\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.8, page no. 136" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization\n", "P1 = 100.0 #lb/in^2\n", "T1 = 500+460.0 #R\n", "P2 = 16.0 #lb/in^2\n", "\n", "#calculation\n", "# From table 4 of appendix, initial conditions are\n", "ht1 = 1279.1\n", "st1 = 1.7085\n", "hg = 1152.0\n", "sg = 1.7549\n", "hfg = 969.7\n", "sfg = 1.4415\n", "st1 = 1.7085\n", "Xdash = (sg-st1)/sfg\n", "ht2 = hg-(Xdash)*hfg\n", "hdiff = ht1-ht2\n", "W = hdiff*778\n", "\n", "#result\n", "print \"Change in entropy is zero\"\n", "print \"heat trasnfer is zero since adiabatic\"\n", "print \"Work done = %d ft-lb/lbm\" %W\n", "print \"Change in enthalpy = %.1f B/lbm\" %hdiff" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in entropy is zero\n", "heat trasnfer is zero since adiabatic\n", "Work done = 123167 ft-lb/lbm\n", "Change in enthalpy = 158.3 B/lbm\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.9, page no. 137" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization\n", "g = 1.4\n", "cv = 0.171 #B/lbm \n", "P1 = 14.7 #lb/in^2\n", "P2 = 100 #lb/in^2\n", "T1 = 60+460 #R\n", "w = 1 #lbm\n", "\n", "#calculation\n", "Tratio = (P2/P1)**((g-1)/g)\n", "T2 = T1*Tratio\n", "WbyJ = cv*(T1-T2)\n", "W = WbyJ*778.0\n", "\n", "#result\n", "print \"Work done = %.1f B/lbm\" %W\n", "print \"CHange in internal energy = %d ft-lb/lbm\" %WbyJ\n", "\n", "#difference in answers due to rounding offs" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = -50463.5 B/lbm\n", "CHange in internal energy = -64 ft-lb/lbm\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.10, page no. 137" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#initialization\n", "P1 = 25.0 #lb/in^2\n", "T1 = 840+460.0 #R\n", "P2 = 14.7 #lb/in^2\n", "\n", "#calculation\n", "# from table 6 of appendix\n", "ht1 = 316.94\n", "Prt1 = 32.39\n", "Pratio = P1/P2\n", "Pr2 = Prt1/Pratio\n", "h2 = 272.4\n", "V2 = math.sqrt(2*32.2*778.0*(ht1-h2))\n", "\n", "#result\n", "print \"Nozzle exit velocity = %d ft/sec\" %V2\n", "\n", "#difference in the answers is due to internal rounding off in Python." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Nozzle exit velocity = 1493 ft/sec\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.11, page no. 139" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#initialization\n", "P1 = 100.0 #lb/in^2\n", "P2 = 16.0 #lb/in^2\n", "T1 = 500+460.0 #R\n", "eta = 0.996\n", "\n", "#calculation\n", "# from appendix table 4\n", "ht1 = 1279.1\n", "st1 = 1.7085\n", "hg = 1152\n", "sg = 1.7549\n", "hfg = 969.7\n", "sfg = 1.4415\n", "ht2 = hg-(1-eta)*hfg\n", "st2 = sg-(1-eta)*sfg\n", "WbyJ = ht1-ht2\n", "W = WbyJ*778\n", "ds = st2-st1\n", "\n", "#result\n", "print \"Work done = %d ft-lb/lbm\" %W #difference due to rounding off\n", "print \"Change in enrtropy = %.4f B/lbm R\" %ds" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = 101901 ft-lb/lbm\n", "Change in enrtropy = 0.0406 B/lbm R\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7.12, page no. 140" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#initialization\n", "P1 = 14.7 #lb/in^2\n", "T1 = 60+460.0 #R\n", "P2 = 100.0 #lb/in^2\n", "T2 = 470+460.0 #R\n", "cv = 0.171 #B/lbm F\n", "cp = 0.24 #B/lbm F\n", "\n", "#calculation\n", "WbyJ=cv*(T1-T2)\n", "W=778*WbyJ\n", "ds=cp*math.log(T2/T1) - 53.3*math.log(P2/P1)/778.0\n", "\n", "#result\n", "print \"Work done = %d ft-lb/lbm\" %W\n", "print \"Change in entropy = %.4f B/lbm R\" %ds" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = -54545 ft-lb/lbm\n", "Change in entropy = 0.0082 B/lbm R\n" ] } ], "prompt_number": 12 } ], "metadata": {} } ] }