{ "metadata": { "name": "", "signature": "sha256:75cc662b83a20e10c962bb4b327ffefb7e8b88ef4b321db4fa8f1bf933a9eccf" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 4 : First Law of Thermodynamics" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.1 page no : 119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#\n", "# Variables\n", "Q = -50.; \t\t\t#kJ/kg\n", "W = -100.; \t\t\t#kJ/kg\n", "\n", "# Calculations\n", "dU = Q-W;\n", "\n", "# Results\n", "print (\"gain in internal energy = \"),(dU),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "gain in internal energy = 50.0 kJ/kg\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.2 page no : 119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "u1 = 450.; \t\t\t#kJ/kg\n", "u2 = 220; \t\t\t#kJ/kg\n", "W = 120; \t\t\t#kJ/kg\n", "\n", "# Calculations\n", "Q = (u2-u1) + W;\n", "\n", "# Results\n", "print (\"Heat rejected by air = \"),(-Q),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat rejected by air = 110.0 kJ/kg\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.3 page no : 119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "m = 0.3; \t\t\t#kg\n", "cv = 0.75; \t\t\t#kJ/kg.K\n", "T1 = 313.; \t\t\t#K\n", "T2 = 433.; \t\t\t#K\n", "W = -30.; \t\t\t#kJ\n", "\n", "# Calculations\n", "dU = m*cv*(T2-T1);\n", "Q = dU + W;\n", "\n", "# Results\n", "print (\"Heat rejected during the process = \"),(-Q),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat rejected during the process = 3.0 kJ\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.4 page no : 120" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "p1 = 105.; \t\t\t#kPa\n", "V1 = 0.4; \t\t\t#m**3\n", "p2 = p1;\n", "V2 = 0.20; \t\t\t#m**3\n", "Q = -42.5; \t\t\t#kJ\n", "\n", "# Calculations\n", "W = p1*(V2-V1);\n", "dU = Q-W;\n", "\n", "# Results\n", "print (\"change in internal energy = \"),(dU),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "change in internal energy = -21.5 kJ\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.6 Page no :121" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "# Variables\n", "p1 = 10.**5 # Pa\n", "T1 = 25 + 273 # K\n", "p2 = 5 * 10**5 # Pa\n", "T2 = T1 \n", "\n", "# Calculations and Result\n", "print \"(i) For isothermal process :\"\n", "W12 = -p1 * (1.8)* math.log(p1/p2)\n", "print \"Work done on the air = %.3e kJ/kg.\"%W12\n", "\n", "print \"(ii) Since temperature is constant,\"\n", "print \"u2 \u2013 u1 = 0\"\n", "print \"Change in internal energy = zero.\"\n", "\n", "print \"(iii) Again,\"\n", "Q12 = 0 + W12\n", "print \"Heat rejected = %.3e kJ/kg.\"%Q12\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) For isothermal process :\n", "Work done on the air = 2.897e+05 kJ/kg.\n", "(ii) Since temperature is constant,\n", "u2 \u2013 u1 = 0\n", "Change in internal energy = zero.\n", "(iii) Again,\n", "Heat rejected = 2.897e+05 kJ/kg.\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.7 page no : 122" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "# Variables\n", "W_12 = -82.; \t\t\t#kJ\n", "Q_12 = -45.; \t\t\t#kJ\n", "dU_12 = Q_12 - W_12;\n", "W_21 = 100.; \t\t\t#kJ\n", "dU_21 = -dU_12;\n", "\n", "# Calculations\n", "Q_21 = dU_21 + W_21;\n", "\n", "# Results\n", "print (\"Heat added to the system = \"),(Q_21),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat added to the system = 63.0 kJ\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.8 page no : 123" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Q2 = 9000.; \t\t\t#kJ\n", "Q1 = 3000.; \t\t\t#kJ\n", "Q = Q1-Q2; \n", "W = 0;\n", "\n", "# Calculations\n", "dU = W-Q;\n", "\n", "# Results\n", "print (\"Work done = \"),(W)\n", "\n", "print (\"Change in internal energy = \"),(dU),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = 0\n", "Change in internal energy = 6000.0 kJ\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.9 page no : 124" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "m = 20.; \t\t\t#kg\n", "g = 9.81; \t\t\t#m/s**2\n", "z2 = 0.;\n", "z1 = 15.;\n", "\n", "# Calculations and Results\n", "print (\"(i) When the stone is about to enter the water\")\n", "Q = 0\n", "W = 0\n", "dU = 0\n", "PE = m*g*(z2-z1)\n", "KE = -PE\n", "print \"\u2206 PE = %.3f\"%KE,\"J\"\n", "\n", "print (\"(ii) When the stone dips into the math.tank and comes to rest\")\n", "Q = 0\n", "W = 0\n", "KE = 0\n", "PE = m*g*(z2-z1)\n", "dU = -PE\n", "print \"\u2206U = %.3f\"%dU\n", "\n", "print (\"(iii) When the water and stone come to their initial temperature\")\n", "W = 0\n", "KE = 0\n", "Q = -dU\n", "print \"Q = %.3f\"%Q\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) When the stone is about to enter the water\n", "\u2206 PE = 2943.000 J\n", "(ii) When the stone dips into the math.tank and comes to rest\n", "\u2206U = 2943.000\n", "(iii) When the water and stone come to their initial temperature\n", "Q = -2943.000\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.10 page no : 125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "Q_lqm = 168.; \t\t\t#kJ\n", "W_lqm = 64.; \t\t\t#kJ\n", "dU_lm = Q_lqm - W_lqm;\n", "W_lnm = 21.; \t\t\t#kJ\n", "W_ml = -42.; \t\t\t#kJ\n", "\n", "# Calculations and Results\n", "Q_lnm = dU_lm + W_lnm;\n", "print (\"(i)Q_lnm = \"),(Q_lnm), (\"kJ\")\n", "\n", "Q_ml = W_ml - dU_lm;\n", "print (\"(ii)Q_ml = \"),(Q_ml),(\"kJ\")\n", "\n", "W_ln = 21.; \t\t\t#kJ\n", "dU_ln = 84.; \t\t\t#kJ\n", "Q_ln = dU_ln + W_ln;\n", "Q_nm = Q_lnm-Q_ln;\n", "print (\"(iii)Q_nm = \"), (Q_nm), (\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)Q_lnm = 125.0 kJ\n", "(ii)Q_ml = -146.0 kJ\n", "(iii)Q_nm = 20.0 kJ\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.11 page no : 126" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math \n", "from scipy.integrate import quad \n", "\n", "# Variables\n", "T1 = 55.; \t\t\t#0C\n", "T2 = 95.; \t\t\t#0C\n", "\n", "# Calculations\n", "def f1( T): \n", "\t return 200\n", "W = quad(f1, T1, T2)[0]\n", "\n", "\n", "def f2( T): \n", "\t return 160\n", "Q = quad(f2, T1, T2)[0]\n", "dU = Q-W;\n", "\n", "# Results\n", "print (\"change in internal energy = \"),(dU/10**3),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "change in internal energy = -1.6 kJ\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.12 page no : 127" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math \n", "\n", "# Variables\n", "Q = -340.; \t\t\t#kJ\n", "n = 200.; \t\t\t#cycles/min\n", "\n", "#For Process 1-2\n", "W_12 = 4340.; \t\t\t#kJ/min\n", "Q_12 = 0.;\n", "\n", "# Calculations and Results\n", "dE_12 = Q_12-W_12;\n", "print (\"dE_12 = \"),(dE_12),(\"kJ/min\")\n", "\n", "#For process 2-3\n", "Q_23 = 42000.; \t\t\t#kJ/min\n", "W_23 = 0;\n", "\n", "dE_23 = Q_23-W_23;\n", "print (\"dE_23 = \"),(dE_23),(\"kJ/min\")\n", "\n", "#For process 3-4\n", "Q_34 = -4200.; \t\t\t#kJ/min\n", "dE_34 = -73200.; \t\t\t#kJ/min\n", "\n", "W_34 = Q_34-dE_34;\n", "print (\"W_34 = \"), (W_34), (\"kJ/min\")\n", "\n", "#For process 4-1\n", "Q_41 = Q*n-Q_12-Q_23-Q_34;\n", "print (\"Q_41 = \"), (Q_41), (\"kJ/min\")\n", "\n", "dE_41 = 0-dE_12-dE_23-dE_34;\n", "print (\"dE_41 = \"), (dE_41), (\"kJ/min\")\n", "\n", "W_41 = Q_41-dE_41;\n", "print (\"W_41 = \"), (W_41), (\"kJ/min\")\n", "\n", "print \"Since sum(Q) = sum(W), \"\n", "print \"Rate of work output = -68000 KJ/min\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "dE_12 = -4340.0 kJ/min\n", "dE_23 = 42000.0 kJ/min\n", "W_34 = 69000.0 kJ/min\n", "Q_41 = -105800.0 kJ/min\n", "dE_41 = 35540.0 kJ/min\n", "W_41 = -141340.0 kJ/min\n", "Since sum(Q) = sum(W), \n", "Rate of work output = -68000 KJ/min\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.13 page no : 128" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "P = 1200.; \t\t\t#kW\n", "Qin = 3360.; \t\t\t#kJ/kg\n", "Qout = 2520.; \t\t\t#kJ/kg\n", "F = 6.; \t\t\t#kW\n", "\n", "# Calculations\n", "dQ = Qin - Qout;\n", "dW = P-F; \t\t\t#kJ/s\n", "m = dW/dQ;\n", "\n", "# Results\n", "print (\"Steam flow round the cycle %.3f\")%(m), (\"kg/s\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Steam flow round the cycle 1.421 kg/s\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.14 page no : 129" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "dT = 25.; \t\t\t#0C\n", "Q = 30.; \t\t\t#kJ\n", "cv = 1.2; \t\t\t#kJ/kg.0C\n", "m = 2.5; \t\t\t#kg\n", "\n", "# Calculations\n", "dU = m*cv*dT;\n", "\n", "# Results\n", "print (\"change in internal energy = \"),(dU), (\"kJ\")\n", "\n", "W = Q - dU;\n", "print (\"Work done = \"),(W),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "change in internal energy = 75.0 kJ\n", "Work done = -45.0 kJ\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.15 page no : 129" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Q = 50.; \t\t\t#kJ\n", "dV = 0.14; \t\t\t#m**3\n", "p = 1.2*10**5; \t\t#N/m**2\n", "m = 90.; \t\t\t#kg\n", "d = 5.5; \t\t\t#m\n", "g = 9.8; \t\t\t#m/s**2\n", "W_adb = -110.; \t#kJ\n", "Wnet = m*g*d/1000; \t#kJ\n", "\n", "# Calculations and Results\n", "W = p*dV/1000 + Wnet; \t\t\t#kJ\n", "dE = Q-W;\n", "print (\"(i)Change in internal energy %.3f kJ\")%(dE)\n", "\n", "Q = 0;\n", "dE = -W_adb;\n", "print (\"(ii) Adiabatic process %.3f kJ\")%(dE)\n", "\n", "\n", "Q = 50.; \t\t\t#kJ\n", "dE = Q - (W_adb+W);\n", "print (\"(iii)Change in internal energy %.3f kJ\")%(dE)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)Change in internal energy 28.349 kJ\n", "(ii) Adiabatic process 110.000 kJ\n", "(iii)Change in internal energy 138.349 kJ\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.16 page no : 130" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math \n", "from scipy.integrate import quad \n", "\n", "# Variables\n", "V1 = 0.15; \t\t\t#m**3\n", "V2 = 0.05; \t\t\t#m**3\n", "Q = -45.; \t\t\t#kJ\n", "p1 = (5./V1+1.5)*10**5; \t\t\t#N/m**2\n", "p2 = (5./V2+1.5)*10**5; \t\t\t#N/m**2\n", "\n", "# Calculations\n", "def f0( V): \n", "\t return (5/V+1.5)*10**2\n", "\n", "W = quad(f0, V1, V2)[0]\n", "\n", "dU = Q-W;\n", "print (\"(i)Change in internal energy = %.3f kJ\")%(dU)\n", "\n", "dH = (dU*10**3+(p2*V2-p1*V1))/10**3;\n", "print (\"(ii) Change in enthalpy = %.3f kJ\")%(dH)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)Change in internal energy = 519.306 kJ\n", "(ii) Change in enthalpy = 504.306 kJ\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.17 page no : 131" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "V1 = 0.25; \t\t\t#m**3\n", "p1 = 500.; \t\t\t#kPa\n", "p2 = 100.; \t\t\t#kPa\n", "\n", "# Calculations and Results\n", "V2 = V1*(p1/p2)**(1/1.25)\n", "n = 1.25\n", "dU = 3.64*(p2*V2 - p1*V1)\n", "\n", "print (\"(i) If the expansion is quasi-static\")\n", "W = (p1*V1-p2*V2)/(n-1);\n", "Q = dU+W\n", "print (\"Heat transfered = %.3f\")%(Q),(\"kJ\")\n", "\n", "print (\"(ii) In another process\")\n", "Q = 32; \t\t\t#kJ\n", "W = Q-dU;\n", "print (\"Work done = %.3f\")%(W),(\"kJ\")\n", "\n", "print (\"(iii)The difference\")\n", "print (\" The work in (ii) is not equal to \u222b p dV math.since the process is not quasi-static.\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) If the expansion is quasi-static\n", "Heat transfered = 12.385 kJ\n", "(ii) In another process\n", "Work done = 157.225 kJ\n", "(iii)The difference\n", " The work in (ii) is not equal to \u222b p dV math.since the process is not quasi-static.\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.18 page no : 132" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "from scipy.integrate import quad \n", "\n", "# Variables\n", "v1 = 0.3; \t\t\t#m**3/kg\n", "T1 = 20.; \t\t\t#0C\n", "v2 = 0.55; \t\t\t#m**3/kg\n", "T2 = 260; \t\t\t#0C\n", "p = 1.6*10**5; \t\t\t#Pa\n", "\n", "print (\"(i)Heat added per kg = \")\n", "\n", "# Calculations and Results\n", "def f5( T): \n", "\t return 1.5 + 75/(T+45)\n", "\n", "Q = quad(f5, T1,T2)[0]\n", "\n", "print (\"Q = %.3f\")%(Q), (\"kJ/kg\")\n", "\n", "\n", "print (\"(ii)The work done per kg of fluid\")\n", "W = p*(v2-v1)/1000; \t\t\t#kJ/kg\n", "print (\"W = %.3f\")%(W),(\"kJ/kg\")\n", "\n", "\n", "print (\"(iii)Change in internal energy\")\n", "dU = Q-W;\n", "print (\"dU = %.3f\")%(dU),(\"kJ/kg\")\n", "\n", "\n", "print (\"(iv)Change in enthalpy\")\n", "dH = Q;\n", "print (\"dH = %.3f\")%(dH),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)Heat added per kg = \n", "Q = 475.944 kJ/kg\n", "(ii)The work done per kg of fluid\n", "W = 40.000 kJ/kg\n", "(iii)Change in internal energy\n", "dU = 435.944 kJ/kg\n", "(iv)Change in enthalpy\n", "dH = 475.944 kJ/kg\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.19 page no : 133" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "m = 1.; \t\t\t#kg\n", "du = -42000.; \t\t\t#J\n", "cp = 840.; \t\t\t#J/kg.0C\n", "cv = 600.; \t\t\t#J/kg.0C\n", "\n", "# Calculations\n", "dT = du/m/cv;\n", "Q = m*cp*dT;\n", "W = (Q-du)/10**3;\n", "\n", "# Results\n", "print (\"Work done = \"),(W),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = -16.8 kJ\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Example 4.20 page no : 133" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "from numpy import *\n", "from scipy.integrate import quad \n", "\n", "# Variables\n", "p1 = 190.; \t\t\t#kPa\n", "V1 = 0.035; \t\t\t#m**3\n", "p2 = 420.; \t\t\t#kPa\n", "V2 = 0.07; \t\t\t#m**3\n", "dU = 3.6*(p2*V2-p1*V1);\n", "p = [[1,0.035],[1,0.07]]\n", "q = [190,420];\n", "#X = linalg.inv(p)*q;\n", "X = linalg.solve(p,q)\n", "a = X[0]\n", "b = X[1]\n", "\n", "# Calculations\n", "def f4( V): \n", "\t return a+b*V\n", "\n", "W = quad(f4, V1, V2)[0]\n", "\n", "# Results\n", "print (\"Work done by the system = \"),(W),(\"kJ\")\n", "\n", "\n", "Q = dU+W;\n", "print (\"Heat transfer into the system = \"),(Q),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done by the system = 10.675 kJ\n", "Heat transfer into the system = 92.575 kJ\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.21 page no : 134" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Qv = 90.; \t\t\t#kJ\n", "Qp = -95; \t\t\t#kJ\n", "W = -18; \t\t\t#kJ\n", "U_l = 105; \t\t\t#kJ\n", "W_lm = 0;\n", "Q_lm = 90;\n", "\n", "# Calculations\n", "U_m = U_l+90;\n", "dU_mn = Qp-W;\n", "U_n = U_m+dU_mn;\n", "dQ = Qv+Qp;\n", "dW = dQ;\n", "W_nl = dW-W;\n", "\n", "# Results\n", "print (\"W_nl(in kJ) = \"),(W_nl)\n", "\n", "print (\"U_l in kJ = \"),(U_l)\n", "\n", "print (\"U_m in kJ = \"),(U_m)\n", "print (\"U_n in kJ\"), (U_n)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "W_nl(in kJ) = 13.0\n", "U_l in kJ = 105\n", "U_m in kJ = 195\n", "U_n in kJ 118\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.23 page no : 136" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "V1 = 0.2; \t\t\t#m**3\n", "p1 = 4.*10**5; \t\t#N/m**2\n", "T1 = 403.; \t\t\t#K\n", "p2 = 1.02*10**5; \t#N/m**2\n", "dH = 72.5; \t\t\t#kJ\n", "Q_23 = dH;\n", "cp = 1.; \t\t\t#kJ/kg\n", "cv = 0.714; \t\t#kJ/kg\n", "y = 1.4;\n", "\n", "# Calculations\n", "V2 = round(V1*(p1/p2)**(1/y),2);\n", "T2 = round(T1*((p2/p1)**((y-1)/y)),1);\n", "R = (cp-cv)*1000; \t\t\t#J/kg.K\n", "m = round(p1*V1/R/T1,3);\n", "T3 = round(Q_23/(m*cp) +T2);\n", "V3 = 0.732 # round(V2*T3/T2,2);\n", "W_12 = (p1*V1 - p2*V2)/(y-1);\n", "W_23 = p2*(V3-V2);\n", "W_123 = W_12+W_23;\n", "\n", "# Results\n", "print (\"Total work done = %.3f\")%(W_123),(\"J\")\n", "\n", "print (\"(ii) Index of expansion, n\")\n", "p3 = p2;\n", "n = (p1*V1-p3*V3)/W_123 + 1;\n", "print (\"value of index = %.3f\")%(n)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Total work done = 85454.000 J\n", "(ii) Index of expansion, n\n", "value of index = 1.062\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.25 page no : 139" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "d = 0.15; \t\t\t#m\n", "T = 303.; \t\t\t#K\n", "p = 3.*10**5; \t\t#N/m**2\n", "l = 0.085; \t\t\t#m\n", "Q = -4000.; \t\t#J\n", "\n", "# Calculations and Results\n", "print (\"(i) Workdone by the system\")\n", "dv = math.pi/4*d**2*l;\n", "W = p*dv;\n", "print (\"W = %.3f\")%(W/10**3),(\"kJ\")\n", "\n", "print (\"(ii) Decrease in internal energy of the system\")\n", "dU = (Q-W)/10**3;\n", "print (\"Decrease in internal energy = %.3f\")%(-dU),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Workdone by the system\n", "W = 0.451 kJ\n", "(ii) Decrease in internal energy of the system\n", "Decrease in internal energy = 4.451 kJ\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.27 page no : 140" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "# Variables\n", "y = 1.4\n", "R = 294.2; \t\t\t#J/kg.0C\n", "p1 = 1.*10**5; \t\t#N/m**2\n", "T1 = 353.; \t\t\t#K\n", "V1 = 0.45; \t\t\t#m**3\n", "V2 = 0.13; \t\t\t#m**3\n", "p2 = 5.*10**5; \t\t#N/m**2\n", "\n", "# Calculations and Results\n", "cv = R/(y-1);\n", "print (\"(i) The mass of gas\")\n", "m = p1*V1/R/T1;\n", "print (\"m = %.3f\")%(m),(\"kg\")\n", "\n", "print (\"(ii) The value of index \u2018n\u2019 for compression\")\n", "n = math.log(p2/p1)/math.log(V1/V2);\n", "print (\"n = %.3f\")%(n)\n", "\n", "print (\"(iii) The increase in internal energy of the gas\")\n", "T2 = T1*(V1/V2)**(n-1);\n", "dU = m*cv*(T2-T1)/10**3;\n", "print (\"dU = %.3f\")%(dU),(\"kJ\")\n", "\n", "print (\"(iv) The heat received or rejected by the gas during compression.\")\n", "W = m*R*(T1-T2)/(n-1)/10**3;\n", "Q = dU+W;\n", "print (\"Q = %.3f\")%(Q),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) The mass of gas\n", "m = 0.433 kg\n", "(ii) The value of index \u2018n\u2019 for compression\n", "n = 1.296\n", "(iii) The increase in internal energy of the gas\n", "dU = 50.000 kJ\n", "(iv) The heat received or rejected by the gas during compression.\n", "Q = -17.535 kJ\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.28 page no : 141" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "p1 = 1.02*10**5; \t#Pa\n", "T1 = 295.; \t\t\t#K\n", "V1 = 0.015; \t\t#m**3\n", "p2 = 6.8*10**5; \t#Pa\n", "y = 1.4;\n", "\n", "# Calculations and Results\n", "print (\"(i) Final temperature\")\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "t2 = T2-273; \n", "print (\"t2 = %.3f\")%(t2),(\"\u00b0C\")\n", "\n", "\n", "print (\"(ii) Final volume :\")\n", "V2 = V1*(p1/p2)**(1/y);\n", "print (\"V2 = %.3f\")%(V2),(\"m**3\")\n", "\n", "\n", "print (\"(iii)Work done\")\n", "R = 287;\n", "m = p1*V1/R/T1;\n", "W = m*R*(T1-T2)/(y-1)/10**3;\n", "print (\"W = %.3f\")%(W),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Final temperature\n", "t2 = 234.253 \u00b0C\n", "(ii) Final volume :\n", "V2 = 0.004 m**3\n", "(iii)Work done\n", "W = -2.752 kJ\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.29 page no : 142" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "from numpy import *\n", "import math\n", "\n", "# Variables\n", "m = 0.44; \t\t\t#kg\n", "T1 = 453.; \t\t\t#K\n", "ratio = 3.; \t\t#ratio = V2/V1\n", "T2 = 288.; \t\t\t#K\n", "W_12 = 52.5; \t\t#kJ\n", "\n", "# Calculations\n", "y = math.log(T2/T1)/ math.log(1/ratio) + 1;\n", "R = W_12*(y-1)/m/(T1-T2);\n", "M = [[1,-1],[1,-y]];\n", "N = [R,0];\n", "X = linalg.inv(M)*N;\n", "cp = X[0][0];\n", "cv = X[1][0];\n", "\n", "# Results\n", "print (\"cp = %.3f\")%(cp),(\"kJ/kg.K\")\n", "\n", "print (\"cv = %.3f\")%(cv),(\"kJ/kg.K\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "cp = 1.021 kJ/kg.K\n", "cv = 0.723 kJ/kg.K\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.30 page no : 143" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "n = 1.3;\n", "m = 1; \t\t\t#kg\n", "p1 = 1.1; \t\t\t#bar\n", "T1 = 300.; \t\t\t#K\n", "p2 = 6.6; \t\t\t#bar\n", "R0 = 8314.;\n", "M = 30.;\n", "cp = 1.75; \t\t\t#kJ/kg.K\n", "\n", "\n", "# Calculations\n", "R = R0/M/1000; \t\t\t#kJ/kg.K\n", "cv = cp - R;\n", "y = cp/cv;\n", "T2 = T1 *(p2/p1)**((n-1)/n);\n", "W = R*(T1-T2)/(n-1);\n", "Q = ((y-n)/(y-1))*W;\n", "\n", "# Results\n", "print (\"Heat supplied = %.3f\")%(Q),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat supplied = 84.352 kJ/kg\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.31 page no : 144" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "# Variables\n", "cp = 14.3; \t\t\t#kJ/kg.K\n", "cv = 10.2; \t\t\t#kJ/kg.K\n", "V1 = 0.1; \t\t\t#m**3\n", "T1 = 300.; \t\t\t#K\n", "p1 = 1.; \t\t\t#bar\n", "p2 = 8.; \t\t\t#bar\n", "y = cp/cv;\n", "R = cp-cv;\n", "V2 = V1*(p1/p2)**(1/y);\n", "V3 = V2;\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "p3 = p1*V1/V3;\n", "T3 = 300.; \t\t\t#K\n", "\n", "\n", "# Calculations and Results\n", "print (\"(i) Pressure at the end of consmath.tant volume cooling = %.3f\")%(p3),(\"bar\")\n", "\n", "print (\"(ii) Change in internal energy during consmath.tant volume process\")\n", "m = p1*V1/R/T1*10**2; \t\t\t#kg\n", "\n", "dU_23 = m*cv*(T3-T2);\n", "print (\"dU_23 = %.3f\")%(dU_23),(\"kJ\")\n", "\n", "print (\"(iii) Net work done and heat transferred during the cycle\")\n", "W_12 = m*R*(T1-T2)/(y-1);\n", "W_23 = 0;\n", "W_31 = p3*V3*math.log(V1/V3)*10**2; \t\t\t#kJ\n", "Wnet = W_12+W_23+W_31;\n", "print (\"Net work done = %.3f\")%(Wnet),(\"kJ\")\n", "Qnet = Wnet;\n", "print (\"Heat transferred during the complete cycle = %.3f\")%(Qnet),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Pressure at the end of consmath.tant volume cooling = 4.407 bar\n", "(ii) Change in internal energy during consmath.tant volume process\n", "dU_23 = -20.281 kJ\n", "(iii) Net work done and heat transferred during the cycle\n", "Net work done = -5.449 kJ\n", "Heat transferred during the complete cycle = -5.449 kJ\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.32 page no : 145" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "# Variables\n", "V1 = 0.15; \t\t\t#m**3\n", "p1 = 15.; \t\t\t#bar\n", "T1 = 550.; \t\t\t#K\n", "T2 = T1;\n", "r = 4.; \t\t\t#r = V2/V1\n", "V2 = r*V1;\n", "T3 = 290.; \t\t\t#K\n", "\n", "# Calculations\n", "p2 = p1*V1/V2;\n", "W_12 = p1*V1*math.log(V2/V1)*10**2; \t\t\t#kJ\n", "V3 = V2;\n", "p3 = p2*T3/T2;\n", "W_23 = 0;\n", "n = math.log(p1/p3)/math.log(V3/V1);\n", "W_31 = (p3*V3-p1*V1)/(n-1)*10**2; \t\t\t#kJ\n", "\n", "# Results\n", "\n", "Wnet = W_12+W_23+W_31\n", "print (\"net work done = %.3f\")%Wnet , (\"kJ\")\n", "\n", "Qnet = Wnet;\n", "print (\"Heat transferred during the cycle = %.3f\")%(Qnet),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "net work done = 81.537 kJ\n", "Heat transferred during the cycle = 81.537 kJ\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.33 page no : 146" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "%matplotlib inline\n", "\n", "import math \n", "from scipy.integrate import quad \n", "from matplotlib.pyplot import *\n", "from numpy import *\n", "\n", "# Variables\n", "m = 1; \t\t\t#kg\n", "p1 = 5; \t\t\t#bar\n", "V1 = 0.02; \t\t\t#m**3\n", "V2 = 0.08; \t\t\t#m**3\n", "p2 = 1.5; \t\t\t#bar\n", "\n", "\n", "# Calculations and Results\n", "def f(V):\n", " return a+b*V;\n", "\n", "A = [[1,0.02],[1,0.08]]\n", "B = [5,1.5];\n", "#X = linalg.inv(A)*B;\n", "X = linalg.solve(A,B)\n", "a = X[0]\n", "b = X[1]\n", "\n", "print (\"(i) p-V diagram\")\n", "\n", "V = linspace(0.02,0.08,80);\n", "p = a+b*V;\n", "plot(V,p,'b')\n", "\n", "V = [0.0667 ,0.08];\n", "p = [1.5 ,1.5];\n", "plot(V,p,'g')\n", "\n", "V = linspace(0.02,0.0667,447)\n", "def fa(V):\n", " return 0.1/V;\n", "f = fa(V)\n", "plot(V,f,'r')\n", "suptitle(\"p-V diagram\")\n", "\n", "V = [0.0667, 0.0667];\n", "p = [1.5, 0];\n", "plot(V,p,'--')\n", "xlabel(\"V(m)**3\")\n", "ylabel(\"P(bar)\")\n", "text(.04,4,'Reversible Expansion')\n", "text(0.04,2.3,\"pV = C\")\n", "text(0.07,1.2,\"p = C\")\n", "\n", "print (\"(ii) Work done and heat transfer\")\n", "\n", "\n", "def f7(V): \n", "\t return (a+b*V)*10**2\n", "\n", "W_12 = quad(f7,V1,V2)[0]\n", "\n", "print (\"Work done by the system = \"),(W_12), (\"kJ\")\n", "\n", "p3 = p2;\n", "V3 = round(p1*V1/p3,4);\n", "W_23 = p2*(V3-V2)*10**2; \t\t\t#kJ\n", "\n", "W_31 = round(p3*V3*math.log(V1/V3)*10**2,2); \t\t\t#kJ\n", "print (\"Work done on the system = %.3f\")% (W_31), (\"kJ\")\n", "\n", "W_net = W_12+W_23+W_31;\n", "print (\"Net work done = %.3f\")% (W_net), (\"kJ\")\n", "\n", "Q_net = W_net;\n", "print (\"Heat transferred during the complete cycle = %.3f\")% (Q_net),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n", "(i) p-V diagram" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "(ii) Work done and heat transfer" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Work done by the system = 19.5 kJ\n", "Work done on the system = -12.050 kJ\n", "Net work done = 5.455 kJ\n", "Heat transferred during the complete cycle = 5.455 kJ\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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9S/fKsZhl2EcIgf/85z8YM2YM/vnPf+LYsWNGNUh2oGZN4O235Yrj3bsDffvK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\nLTh8+DBWr16NtLQ0pZqzSkl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"text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.34 page no : 147" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "from scipy.integrate import quad \n", "\n", "\n", "# Variables\n", "cv = 0.71; \t\t\t#kJ/kg.K\n", "R = 0.287; \t\t\t#kJ/kg.K\n", "d = 8.; \t\t\t#cm\n", "l = 3.5; \t\t\t#cm\n", "S = 150.; \t\t\t#N/cm\n", "p1 = 30.; \t\t\t#N/cm\n", "V1 = 45.; \t\t\t#cm**3\n", "T1 = 293.; \t\t\t#K\n", "cv = 0.71; \t\t\t#kJ/kg.K\n", "R = 0.287; \t\t\t#kJ/kg.K\n", "\n", "# Calculations\n", "A = math.pi/4*d**2;\n", "C = p1-S/A**2*V1;\n", "dV = l*A;\n", "V2 = V1+dV;\n", "p2 = S/A**2*V2 + C;\n", "\n", "def f3( p): \n", "\t return A**2/S*p/100\n", "\n", "W = quad(f3, p1, p2)[0]\n", "\n", "T2 = p2*V2*T1/p1/V1;\n", "m = p1*V1/R/T1/10**5; \t\t\t#kg\n", "dU = m*cv*(T2-T1);\n", "Q_12 = dU + W*10**(-3);\n", "\n", "# Results\n", "print (\"Amount of heat added to the system = %.3f\")% (Q_12), (\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Amount of heat added to the system = 0.250 kJ\n" ] } ], "prompt_number": 31 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.35 page no : 164" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "r = 10.; \t\t\t#kg/min\n", "p1 = 1.5*10**5; \t\t\t#N/m**2\n", "rho1 = 26.; \t\t\t#kg/m**3\n", "C1 = 110.; \t\t\t#m/s\n", "u1 = 910.; \t\t\t#kJ/kg\n", "p2 = 5.5*10**5; \t\t\t#N/m**2\n", "rho2 = 5.5; \t\t\t#kg/m**3\n", "C2 = 190.; \t\t\t#m/s\n", "u2 = 710.; \t\t\t#kJ/kg\n", "Q = 55.; \t\t\t#kJ/s\n", "h = 55.; \t\t\t#m\n", "g = 9.81; \t\t\t#m/s**2\n", "v2 = 1/rho2;\n", "v1 = 1/rho1;\n", "\n", "# Calculations and Results\n", "\n", "dh = u2-u1+ (p2*v2-p1*v1)/10**3;\n", "print (\"(i) Change in enthalpy %.3f\")%(dh), (\"kJ/kg\")\n", "\n", "print (\"(ii) Work done during the process (W).\")\n", "\n", "Q = 330.; \t\t\t#kJ/kg\n", "KE = (C2**2-C1**2)/2/10**3; \t\t\t#kJ\n", "PE = g*h/10**3; \t\t\t#kJ\n", "W = -Q-KE-PE-dh;\n", "print (\"Work done = %.3f\")%(W),(\"kJ\")\n", "\n", "\n", "P = W*10/60.;\n", "print (\"Work done per second = %.3f\")%(P),(\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Change in enthalpy -105.769 kJ/kg\n", "(ii) Work done during the process (W).\n", "Work done = -236.770 kJ\n", "Work done per second = -39.462 kW\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.36 page no : 166" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "\n", "import math \n", "\n", "m = 15.; \t\t\t#kg/s\n", "v = 0.45; \t\t\t#m**3/kg\n", "P = 12000.; \t\t#kW\n", "W = P/m; \t\t\t#kJ/kg\n", "h1 = 1260.; \t\t#kJ/kg\n", "h2 = 400.; \t\t\t#kJ/kg\n", "C1 = 50.; \t\t\t#m/s\n", "C2 = 110.; \t\t\t#m/s\n", "\n", "# Calculations and Results\n", "print (\"(i) Heat rejected = \"),\n", "Q = h2-h1+(C2**2-C1**2)/2/10**3 +W;\n", "Qnet = m*Q;\n", "print (\"Qnet = %.3f\")%(-Qnet),(\"kW\")\n", "\n", "print (\"(ii) Inlet area\")\n", "A = v*m/C1;\n", "print (\"A = %.3f\")%(A),(\"m**2\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Heat rejected = Qnet = 828.000 kW\n", "(ii) Inlet area\n", "A = 0.135 m**2\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.37 page no : 167" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "m = 0.5; \t\t\t#kg/s\n", "C1 = 6.; \t\t\t#m/s\n", "C2 = 5.; \t\t\t#m/s\n", "p1 = 1.; \t\t\t#bar\n", "p2 = 7.; \t\t\t#bar\n", "v1 = 0.85; \t\t\t#m**3/kg\n", "v2 = 0.16; \t\t\t#m**3/kg\n", "du = 90.; \t\t\t#kJ/kg\n", "Q = -120.; \t\t\t#kJ/kg\n", "\n", "# Calculations and Results\n", "print (\"(i) Power required to drive the compressor\")\n", "W = -du+(C1**2-C2**2)/2/1000 + (p1*v1 - p2*v2)*10**2 + Q;\n", "Power = m*W; \n", "print (\"Power = %.3f\")%(-Power),(\"kW\")\n", "\n", "\n", "print (\"(ii) Inlet and outlet pipe cross-sectional areas\")\n", "A1 = m*v1/C1;\n", "A2 = m*v2/C2;\n", "print (\"Inlet crosssectional area = %.3f\")% (A1), (\"m**2\")\n", "\n", "print (\"Outlet crossectional area = %.3f\")%(A2), (\"m**2\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Power required to drive the compressor\n", "Power = 118.497 kW\n", "(ii) Inlet and outlet pipe cross-sectional areas\n", "Inlet crosssectional area = 0.071 m**2\n", "Outlet crossectional area = 0.016 m**2\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.38 page no : 168" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "h1 = 800.; \t\t\t#kJ/kg\n", "C1 = 5.; \t\t\t#m/s\n", "h2 = 2520.; \t\t\t#kJ/kg\n", "C2 = 50.; \t\t\t#m/s\n", "dZ = 4.; \t\t\t#m\n", "g = 9.81; \t\t\t#m/s**2\n", "Q = 2180.; \t\t\t#kJ/kg\n", "\n", "# Calculations\n", "W = h1-h2+(C1**2 - C2**2)/2/1000 +dZ*g/1000+Q;\n", "\n", "# Results\n", "print (\"Power developed = %.3f\")%(W), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Power developed = 458.802 kW\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.39 page no : 169" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "g = 9.8; \t\t\t#m/s**2\n", "m = 4500./3600; \t#kg/s\n", "C1 = 2800./60; \t\t#m/s\n", "Z1 = 5.5; \t\t\t#m\n", "h1 = 2800.; \t\t#kJ/g\n", "C2 = 5600./60; \t\t#m/s\n", "Z2 = 1.5; \t\t\t#m\n", "h2 = 2300.; \t\t#kJ/kg\n", "Q = -16000./3600; \t#kJ/s\n", "\n", "# Calculations\n", "W = Q-m*((h1-h2) + (C2**2 - C1**2)/2/1000 + (Z2-Z1)*g/1000);\n", "\n", "# Results\n", "print (\"Power output of the turbine = %.3f\")% (-W),(\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Power output of the turbine = 633.479 kW\n" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.40 page no : 170" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "p1 = 6.87; \t\t\t#bar\n", "C1 = 50.; \t\t\t#m/s\n", "p2 = 1.37; \t\t\t#bar\n", "C2 = 500.; \t\t\t#m/s\n", "print (\"From steam table corresponding to p1\")\n", "h1 = 2850.; \t\t\t#kJ/kg\n", "\n", "# Calculations\n", "h2 = h1 - (C2**2-C1**2)/2/1000;\n", "\n", "# Results\n", "print (\"Final enthalpy of steam = \"), (h2),(\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "From steam table corresponding to p1\n", "Final enthalpy of steam = 2726.25 kJ\n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.41 page no : 171" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "m = 220./60; \t\t\t#kg/s\n", "C1 = 320.; \t\t\t#m/s\n", "p1 = 6*10.**5; \t\t\t#N/m**2\n", "u1 = 2000.*10**3; \t\t\t#J/kg\n", "v1 = 0.36; \t\t\t#m**3/kg\n", "C2 = 140.; \t\t\t#m/s\n", "p2 = 1.2*10**5; \t\t\t#N/m**2\n", "u2 = 1400.*10**3; \t\t\t#J/kg\n", "v2 = 1.3; \t\t\t#m**3/kg\n", "Q = 100*10.**3; \t\t\t#J/s\n", "\n", "# Calculations\n", "W = (m*((u1-u2)+ (p1*v1 - p2*v2) + (C1**2-C2**2)/2) -Q)/10**6;\n", "\n", "# Results\n", "print (\"power capacity of the system = %.3f\")% (W),(\"MW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "power capacity of the system = 2.472 MW\n" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.42 page no : 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "p1 = 7.5*10**5; \t\t\t#N/m**2\n", "C1 = 140.; \t\t\t#m/s\n", "h1 = 950.*10**3; \t\t\t#J/kg\n", "p2 = 2*10.**5; \t\t\t#N/m**2\n", "C2 = 280.; \t\t\t#m/s\n", "h2 = 650.*10**3; \t\t\t#J/kg\n", "m = 5.; \t\t\t#kg/s\n", "\n", "# Calculations\n", "W = (h1-h2)+(C1**2-C2**2)/2\n", "Power = m*W/1000;\n", "\n", "# Results\n", "print (\"Power capacity of turbine = \"), (Power), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Power capacity of turbine = 1353.0 kW\n" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.43 page no : 173" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "C1 = 12.; \t\t\t#m/s\n", "p1 = 1.*10**5; \t\t\t#N/m**2\n", "v1 = 0.5; \t\t\t#m**3/kg\n", "C2 = 90.; \t\t\t#m/s\n", "p2 = 8.*10**5; \t\t\t#N/m**2\n", "v2 = 0.14; \t\t\t#m**3/kg\n", "dh = 150.; \t\t\t#kJ/kg\n", "Q = -11.67; \t\t\t#kJ/s\n", "m = 0.2; \t\t\t#kg/s\n", "\n", "# Calculations and Results\n", "print (\"(i) Motor power required to drive the compressor\")\n", "W = m*(-dh + (C1**2-C2**2)/2/1000) +Q;\n", "print (\"Power = %.3f\")% (-W), (\"kW\")\n", "\n", "\n", "print (\"(ii)Ratio of inlet to outlet pipi diameter\")\n", "ratio = math.sqrt(C2/C1*v1/v2);\n", "print (\"ratio = %.3f\")% (ratio)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Motor power required to drive the compressor\n", "Power = 42.466 kW\n", "(ii)Ratio of inlet to outlet pipi diameter\n", "ratio = 5.175\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.44 page no : 175" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "W = -175.; \t\t\t #kJ/kg\n", "dh = 70.; \t\t \t#kJ/kg\n", "Q_water = -92.; \t\t\t#kJ/kg\n", "\n", "# Calculations\n", "Q = dh+W;\n", "Q_atm = Q-Q_water;\n", "\n", "# Results\n", "print (\"Heat transferred to the atmosphere = \"),(-Q_atm), (\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat transferred to the atmosphere = 13.0 kJ/kg\n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.45 page no : 176" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "# Variables\n", "h1 = 2800.*10**3; \t\t\t#J/kg\n", "C1 = 50.; \t\t\t#m/s\n", "A1 = 900.*10**(-4); \t\t\t#m**2\n", "v1 = 0.187; \t\t\t#m**3/kg\n", "h2 = 2600.*10**3; \t\t\t#J/kg\n", "v2 = 0.498; \t\t\t#m**3/kJ\n", "\n", "# Calculations and Results\n", "print (\"(i) Velocity at exit of the nozzle\")\n", "C2 = math.sqrt(2*((h1-h2) + C1**2/2));\n", "\n", "print (\"C2 = %.3f\")% (C2),(\"m/s\")\n", "\n", "\n", "print (\"(ii) Mass flow rate\")\n", "m = A1*C1/v1;\n", "print (\"m = %.3f\")% (m), (\"kg/s\")\n", "\n", "\n", "print (\"(iii) Area at the exit\")\n", "A2 = m*v2/C2*10**4;\n", "print (\"A2 = %.3f\")%(A2), (\"cm**2\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Velocity at exit of the nozzle\n", "C2 = 634.429 m/s\n", "(ii) Mass flow rate\n", "m = 24.064 kg/s\n", "(iii) Area at the exit\n", "A2 = 188.894 cm**2\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.46 page no : 177" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "h1 = 240.; \t\t\t#kJ/kg\n", "h2 = 192.; \t\t\t#kJ/kg\n", "dZ = 20.; \t\t\t#m\n", "g = 9.81; \t\t\t#m/s**2\n", "\n", "# Calculations\n", "Q = (h2-h1)+dZ*g/1000;\n", "\n", "# Results\n", "print (\"heat transfer = %.3f\")% (-Q), (\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "heat transfer = 47.804 kJ/kg\n" ] } ], "prompt_number": 43 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.47 page no : 178" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math \n", "\n", "# Variables\n", "p1 = 2.; \t\t\t#bar\n", "C1 = 300.; \t\t\t#m/s\n", "Q = 0.;\n", "h1 = 915.*10**3; \t\t\t#J/kg\n", "h2 = 800.*10**3; \t\t\t#J/kg\n", "\n", "# Calculations\n", "C2 = math.sqrt(2*(h1-h2 + C1**2/2));\n", "\n", "# Results\n", "print (\"Relative velocity of gas leaving the pipe = %.3f\")% (C2), (\"m/s\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Relative velocity of gas leaving the pipe = 565.685 m/s\n" ] } ], "prompt_number": 44 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.48 page no : 179" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math \n", "\n", "# Variables\n", "mw = 50; \t\t\t#kg/s\n", "p1 = 10.**5; \t\t\t#N/m**2\n", "p2 = 4.2*10**5; \t\t\t#N/m**2\n", "h = 10.7; \t\t\t#m\n", "d1 = 0.2; \t\t\t#m\n", "d2 = 0.1; \t\t\t#m\n", "v1 = 1./1000;\n", "v2 = 1./1000;\n", "g = 9.81; \t\t\t#m/s**2\n", "\n", "# Calculations\n", "C1 = mw*4/math.pi/d1**2*v1;\n", "C2 = mw*4/math.pi/d2**2*v2;\n", "W = mw*((p1*v1-p2*v2) + (g*(0-h))+(C1**2-C2**2)/2)/10**3;\n", "\n", "# Results\n", "print (\"Capacity of electric motor %.3f\")%(-W), (\"kW\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Capacity of electric motor 22.198 kW\n" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Example 4.49 page no : 180" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math \n", "\n", "# Variables\n", "Ca = 250.; \t\t\t#m/s\n", "t = -14.; \t\t\t#0C\n", "ha = 250.; \t\t\t#kJ/kg\n", "hg = 900.; \t\t\t#kJ/kg\n", "ratio = 0.0180;\n", "Ef = 45.*10**3; \t\t\t#kJ/kg\n", "Q = -21.; \t\t\t#kJ/kg\n", "ma = 1.; \t\t\t#kg\n", "mg = 1.018; \t\t\t#kg\n", "mf = 0.018; \t\t\t#kg\n", "\n", "#Calculations\n", "Eg = 0.06*mf/mg*Ef;\n", "Cg = math.sqrt(2000*((ma*(ha+Ca**2/2/1000) + mf*Ef + Q)/mg -hg-Eg));\n", "\n", "# Results\n", "print (\"velocity of exhaust gas jet = %.3f\")%(Cg),(\"m/s\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "velocity of exhaust gas jet = 455.160 m/s\n" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.50 page no : 181" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "t1 = 20.; \t\t\t#0C\n", "C1 = 40.; \t\t\t#m/s\n", "t2 = 820.; \t\t\t#0C\n", "C2 = 40.; \t\t\t#m/s\n", "t3 = 620.; \t\t\t#0C\n", "C3 = 55.; \t\t\t#m/s\n", "t4 = 510.; \t\t\t#0C\n", "m = 2.5; \t\t\t#kg/s\n", "cp = 1.005; \t\t\t#kJ/kg.0C\n", "\n", "# Calculations and Results\n", "print (\"(i) Heat exchanger\")\n", "Q_12 = m*cp*(t2-t1);\n", "print (\"rate of heat transfer = \"),(Q_12), (\"kJ/s\")\n", "\n", "print (\"(ii) Turbine\")\n", "W_23 = m*((cp*(t2-t3))+(C2**2-C3**2)/2/1000);\n", "print (\"Power output of turbine = %.3f\")%(W_23), (\"kW\")\n", "\n", "print (\"(iii) Nozzle\")\n", "C4 = math.sqrt(2*1000*(cp*(t3-t4)+C3**2/2/1000));\n", "print (\"Velocity at exit from the nozzle = %.3f\")%(C4), (\"m/s\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Heat exchanger\n", "rate of heat transfer = 2010.0 kJ/s\n", "(ii) Turbine\n", "Power output of turbine = 500.719 kW\n", "(iii) Nozzle\n", "Velocity at exit from the nozzle = 473.418 m/s\n" ] } ], "prompt_number": 47 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.51 page no : 185" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "V = 0.028; \t\t\t#m**3\n", "p1 = 80.; \t\t\t#bar\n", "t = 350.; \t\t\t#0C\n", "p2 = 50.; \t\t\t#bar\n", "v1 = 0.02995; \t\t\t#m**3/kg\n", "h1 = 2987.3; \t\t\t#kJ/kg\n", "v2 = 0.02995; \t\t\t#m**3/kg\n", "vg2 = 0.0394; \t\t\t#m**3/kg\n", "uf2 = 1149.; \t\t\t#kJ/kg\n", "ug2 = 2597.; \t\t\t#kJ/kg\n", "\n", "# Calculations and Results\n", "m = V/v1;\n", "u1 = h1 - (p1*v1*10**2); \t\t\t#kJ/kg\n", "\n", "print (\"(i) State of steam after cooling\")\n", "x2 = v2/vg2;\n", "print (\"dryness fraction = %.3f\")%(x2)\n", "\n", "\n", "print (\"(ii) Heat rejected by the steam\")\n", "u2 = (1-x2)*uf2 + x2*ug2;\n", "Q = m*(u2-u1);\n", "print (\"Heat rejected = %.3f\")% (-Q), (\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) State of steam after cooling\n", "dryness fraction = 0.760\n", "(ii) Heat rejected by the steam\n", "Heat rejected = 465.575 kJ\n" ] } ], "prompt_number": 48 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.52 page no : 188" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "m = 0.08; \t\t\t#kg\n", "p = 2.*10**5; \t\t\t#Pa\n", "V = 0.10528; \t\t\t#m**3\n", "h1 = 2706.3; \t\t\t#kJ/kg\n", "h2 = 3071.8; \t\t\t#kJ/kg\n", "v1 = 0.885; \t\t\t#m**3/kg\n", "\n", "# Calculations and Results\n", "v2 = V/m; \t\t\t#m**3/kg\n", "\n", "print (\"(i) Heat supplied\")\n", "Q = m*(h2-h1);\n", "print (\"Q = \"),(Q), (\"kJ\")\n", "\n", "\n", "W = p*(v2-v1);\n", "W_total = m*W/10**3;\n", "print (\"(ii)Total work done = \"), (W_total), (\"kJ\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Heat supplied\n", "Q = 29.24 kJ\n", "(ii)Total work done = 6.896 kJ\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.53 page no : 189" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from numpy import *\n", "from matplotlib.pyplot import *\n", "\n", "# Variables\n", "m = 1.; \t\t\t#kg\n", "p = 8.; \t\t\t#bar\n", "s1 = 6.55; \t\t\t#kJ/kg.K\n", "T = 200.; \t\t\t#0C\n", "s_f1 = 2.0457; \t\t\t#kJ/kg.K\n", "s_fg1 = 4.6139; \t\t\t#kJ/kg.K\n", "h_f1 = 720.9; \t\t\t#kJ/kg\n", "h_fg1 = 2046.5; \t\t\t#kJ/kg\n", "h2 = 2839.3; \t\t\t#kJ/kg\n", "\n", "# Calculations and Results\n", "x1 = (s1-s_f1)/s_fg1;\n", "h1 = h_f1+x1*h_fg1;\n", "Q = h2-h1;\n", "print (\"Heat supplied = %.3f\")%(Q), (\"kJ/kg\")\n", "\n", "# For T-s diagram\n", "\n", "s = linspace(0,.10,10);\n", "T = (-(s-5)**2+298);\n", "plot(s,T)\n", "\n", "T = [295.44 ,295.44];\n", "s = [6.6 ,3.45];\n", "plot(s,T,'g')\n", "\n", "s = [6.6 ,7];\n", "T = [295.44, 300];\n", "plot(s,T,'g')\n", "\n", "s = [6.55 ,6.55];\n", "T = [270 ,295.44];\n", "plot(s,T,'r')\n", "\n", "s = [6.6, 6.6];\n", "T = [270 ,295.44];\n", "plot(s,T,'--r')\n", "\n", "s = [6.66, 6.66];\n", "T = [270, 295.44];\n", "plot(s,T,'r')\n", "\n", "\t\t\t#The area in red represents the heat flow and it goes upto x-axis\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat supplied = 120.513 kJ/kg\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 50, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.54 page no : 192" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "p1 = 7.*10**5; \t\t\t#Pa\n", "p2 = 1.5*10**5; \t\t\t#Pa\n", "Q = 420.; \t\t\t#kJ/kg\n", "uf = 696.; \t\t\t#kJ/kg\n", "x = 0.95;\n", "ug = 2573.; \t\t\t#kJ/kg\n", "u_f2 = 2580.; \t\t\t#kJ/kg\n", "u_g2 = 2856.; \t\t\t#kJ/kg\n", "x2 = 15./50;\n", "h_f1 = 697.1; \t\t\t#kJ/kg\n", "h_fg1 = 2064.9; \t\t\t#kJ.kg\n", "h_f2 = 2772.6; \t\t\t#kJ/kg\n", "h_g2 = 2872.9; \t\t\t#kJ/kg\n", "\n", "# Calculations and Results\n", "print (\"(i) Change of internal energy\")\n", "u1 = (1-x)*uf + x*ug;\n", "u2 = 2602.8; \t\t\t#kJ/kg\n", "du = u2-u1;\n", "print (\"du = \"),(du), (\"kJ/kg\")\n", "\n", "print (\"(ii) Change in enthalpy\")\n", "h1 = h_f1+x*h_fg1;\n", "h2 = h_f2+x2*(h_g2-h_f2);\n", "dh = h2-h1;\n", "print (\"dh = \"), (dh), (\"kJ/kg\")\n", "\n", "print (\"(iii) Work done \")\n", "W = Q-du;\n", "print (\"W = \"), (W), (\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Change of internal energy\n", "du = 123.65 kJ/kg\n", "(ii) Change in enthalpy\n", "dh = 143.935 kJ/kg\n", "(iii) Work done \n", "W = 296.35 kJ/kg\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.55 page no : 194" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math \n", "from scipy.integrate import quad \n", "\n", "\n", "p1 = 5.5*10**5; \t\t\t#Pa\n", "x1 = 1.;\n", "p2 = 0.75*10**5; \t\t\t#Pa\n", "v1 = 0.3427; \t\t\t#m**3/kg\n", "v2 = p1*v1/p2;\n", "\n", "# Since v2 > vg (at 0.75 bar), therefore, the steam is superheated at state 2.\n", "u2 = 2567.25; \t\t\t#kJ/kg\n", "u1 = 2565.; \t\t\t#kJ/kg\n", "\n", "# Calculations and Results\n", "du = u2-u1; \t\t\t#kJ/kg\n", "C = p1*v1;\n", "\n", "print (\"Work done \"),\n", "\n", "def f6( v): \n", "\t return C/v\n", "\n", "W = quad(f6, v1,v2)[0]\n", "\n", "print (\"W =\"),(W), (\"N-m/kg\")\n", "\n", "\n", "\n", "Q = du+W/10**3;\n", "\n", "print (\"Heat supplied = %.3f\")%(Q),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done W = 375543.199592 N-m/kg\n", "Heat supplied = 377.793 kJ/kg\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.56 page no : 195" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "p1 = 100.; \t\t\t#bar\n", "p2 = 10.; \t\t\t#bar\n", "s1 = 5.619; \t\t\t#kJ/kg.K\n", "T = 584.; \t\t\t#K\n", "s2 = 7.163; \t\t\t#kJ/kg.K\n", "u1 = 2545.; \t\t\t#kJ/kg\n", "u2 = 2811.8; \t\t\t#kJ/kg\n", "\n", "# Calculations and Results\n", "print (\"(i)Heat supplied \")\n", "Q = T*(s2-s1);\n", "print (\"Q = \"),(Q),(\"kJ/kg\")\n", "\n", "print (\"(ii) Work done\")\n", "W = Q-(u2-u1);\n", "print (\"W = \"), (W), (\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)Heat supplied \n", "Q = 901.696 kJ/kg\n", "(ii) Work done\n", "W = 634.896 kJ/kg\n" ] } ], "prompt_number": 53 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.57 page no : 198" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "m = 1.; \t\t\t#kg\n", "p1 = 120.*10**5; \t#N/m**2\n", "t1 = 400.; \t\t\t#0C\n", "p2 = 38.; \t\t\t#bar\n", "h1 = 3051.3; \t\t#kJ/kg\n", "v1 = 0.02108; \t\t#m**3/kg\n", "\n", "# Calculations\n", "u1 = h1-p1*v1/10**3; \t#kJ/kg\n", "u2 = 2602; \t\t\t #kJ/kg\n", "\n", "# Results\n", "W = u1-u2; \n", "print (\"Work done = %.3f\")%(W),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = 196.340 kJ/kg\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.58 page no : 201 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "p1 = 7.*10**5; \t\t\t#N/m**2\n", "x1 = 0.98;\n", "p2 = 0.34*10**5; \t\t#N/m**2\n", "vg = 0.273; \t\t\t#m**3/kg\n", "n = 1.1;\n", "v_g2 = 4.65; \t\t\t#m**3/kg\n", "u_f1 = 696.; \t\t\t#kJ/kg\n", "u_g1 = 2573.; \t\t\t#kJ/kg\n", "u_f2 = 302.; \t\t\t#kJ/kg\n", "u_g2 = 2472.; \t\t\t#kJ/kg\n", "\n", "# Calculations and Results\n", "v1 = x1*vg;\n", "v2 = v1*(p1/p2)**(1/n);\n", "x2 = v2/v_g2;\n", "\n", "\n", "print (\"(i) Work done by the steam during the process\")\n", "W = (p1*v1-p2*v2)/(n-1)/10**3; \t\t\t#kJ/kg\n", "print (\"W = %.3f\")%(W), (\"kJ/kg\")\n", "\n", "\n", "print (\"(ii) Heat transferred\")\n", "u1 = (1-x1)*u_f1+x1*u_g1;\n", "u2 = (1-x2)*u_f2+x2*u_g2;\n", "Q = u2-u1 + W;\n", "print (\"Q = %.3f\")%(Q), (\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Work done by the steam during the process\n", "W = 450.232 kJ/kg\n", "(ii) Heat transferred\n", "Q = 169.289 kJ/kg\n" ] } ], "prompt_number": 55 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.59 page no : 203" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "p1 = 15.; \t\t\t#bar\n", "t1 = 350.; \t\t\t#0C\n", "C1 = 60.; \t\t\t#m/s\n", "p2 = 1.2; \t\t\t#bar\n", "C2 = 180.; \t\t\t#m/s\n", "s1 = 7.102; \t\t\t#kJ/kg\n", "s_f2 = 1.3609; \t\t\t#kJ/kg\n", "s_g2 = 7.2884; \t\t\t#kJ/kg\n", "h_f2 = 439.4; \t\t\t#kJ/kg\n", "h_fg2 = 2241.1; \t\t\t#kJ/kg\n", "h1 = 3147.5; \t\t\t#kJ/kg\n", "\n", "# Calculations\n", "x2 = (s1 - s_f2)/(s_g2-s_f2);\n", "h2 = h_f2+x2*h_fg2;\n", "W = (h1-h2) + (C1**2 - C2**2)/2/1000;\n", "\n", "# Results\n", "print (\"Work done = %.3f\")%(W),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = 523.075 kJ/kg\n" ] } ], "prompt_number": 56 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.60 page no : 204" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "p1 = 10.; \t\t\t#bar\n", "t1 = 200.; \t\t\t#0C\n", "C1 = 60.; \t\t\t#m/s**2\n", "c2 = 650.; \t\t\t#m/s\n", "p2 = 1.5; \t\t\t#bar\n", "h1 = 2827.9; \t\t\t#kJ/kg\n", "h_f2 = 467.1; \t\t\t#kJ/kg\n", "h2 = 2618.45; \t\t\t#kJ/kg\n", "h_g2 = 2693.4; \t\t\t#kJ/kg\n", "\n", "# Calculations\n", "x2 = (h2-h_f2)/(h_g2-h_f2);\n", "\n", "# Results\n", "print (\"quality of steam leaving the nozzle = %.3f\")%(x2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "quality of steam leaving the nozzle = 0.966\n" ] } ], "prompt_number": 57 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.61 page no : 206" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "h1 = 2776.4; \t\t\t#kJ/kg\n", "h2 = h1;\n", "h_f1 = 884.6; \t\t\t#kJ/kg\n", "h_fg1 = 1910.3; \t\t#kJ/kg\n", "\n", "# Calculations\n", "x1 = (h1-h_f1)/h_fg1;\n", "\n", "# Results\n", "print (\"Initial dryness fraction = %.3f\")%(x1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Initial dryness fraction = 0.990\n" ] } ], "prompt_number": 58 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.62 page no : 207" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "p1 = 10.; \t\t\t#bar\n", "x1 = 0.9; \t\t\t#bar\n", "p2 = 2.; \t\t\t#bar\n", "\n", "# Calculations\n", "# Umath.sing Mollier chart, we get\n", "x2 = 0.94;\n", "\n", "# Results\n", "print (\"x2 = \"),(x2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "x2 = 0.94\n" ] } ], "prompt_number": 59 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.63 Page no :208" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "import math \n", "print (\"(a)From steam tables\")\n", "\n", "# Variables\n", "p1 = 15*10**5; \t\t\t#Pa\n", "p2 = 7.5*10**5; \t\t\t#Pa\n", "h_f1 = 844.7; \t\t\t#kJ/kg\n", "ts1 = 198.3; \t\t\t#0C\n", "s_f1 = 2.3145; \t\t\t#kJ/kg.K\n", "s_g1 = 6.4406; \t\t\t#kJ/kg.K\n", "v_g1 = 0.132; \t\t\t#m**3/kg\n", "h_fg1 = 1945.2; \t\t\t#kJ/kg\n", "x1 = 0.95;\n", "h_f2 = 709.3; \t\t\t#kJ/kg\n", "h_fg2 = 2055.55; \t\t\t#kJ/kg\n", "s_f2 = 2.0195; \t\t\t#kJ/kg\n", "s_g2 = 6.6816; \t\t\t#kJ/kg.K\n", "v_g2 = 0.255; \t\t\t#m**3/kg\n", "x2 = 0.9;\n", "x3 = 1;\n", "s_f3 = 0.521; \t\t\t#kJ/kg K\n", "s_g3 = 8.330; \t\t\t#kJ/kg K\n", "\n", "# Calculations\n", "h2 = h_f2+x2*h_fg2;\n", "h1 = h_f1 + x1*h_fg1;\n", "s1 = s_f1 + x1*(s_g1-s_f1);\n", "s2 = s1;\n", "ds_12 = s2-s1;\n", "\n", "s3 = s_f3+x3*(s_g3-s_f3);\n", "ds_23 = s3-s2;\n", "\n", "ds = 709.3 + 0.9 * 2055.55\n", "\n", "# Results\n", "print (\"(i) Change in entropy = %.3f\")% (ds), (\"kJ/kg K\")\n", "\n", "h3 = h2;\n", "\n", "dh = h2-h1;\n", "print (\"(ii) Change in enthalpy %.2f\")%(dh), (\"kJ/kg\")\n", "\n", "\n", "print (\"(iii) Change in internal energy\"),\n", "u1 = h1-p1*x1*v_g1/10**3;\n", "u2 = h2-p2*x2*v_g2/10**3;\n", "du = u2-u1;\n", "print (\"du = %.3f\")% (du), (\"kJ/kg\")\n", "\n", "\n", "\t\t\t# Only the expansion of steam from point 1 to 2 (i.e., isentropic expansion) is reversible because of unresisted flow whereas the expansion from point 2 to point 3 (i.e., throttling expansion) is irreversible because of frictional resismath.tance to flow. Increase of entropy also shows that expansion from point 2 to point 3 is irreversible.\n", "\n", "\n", "print (\"(b) Using Mollier chart\")\n", "h1 = 2692; \t\t\t#kJ/kg\n", "h2 = 2560; \t\t\t#kJ/kg\n", "s1 = 6.23; \t\t\t#kJ/kg K\n", "s2 = s1;\n", "s3 = 8.3; \t\t\t#kJ/kg K\n", "\n", "ds = s3-s1;\n", "print (\"(i) Change in entropy = %.3f\")%(ds), (\"kJ/kg K\")\n", "\n", "\n", "dh = h2-h1;\n", "print (\"(ii) Change in enthalpy = %.3f\")%(dh),(\"kJ/kg\")\n", "\n", "u3=u2-u1\n", "print (\"(iii) Change in internal energy =%.3f\")%(u3),(\"kJ/kg\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)From steam tables\n", "(i) Change in entropy = 2559.295 kJ/kg K\n", "(ii) Change in enthalpy -133.35 kJ/kg\n", "(iii) Change in internal energy du = -117.370 kJ/kg\n", "(b) Using Mollier chart\n", "(i) Change in entropy = 2.070 kJ/kg K\n", "(ii) Change in enthalpy = -132.000 kJ/kg\n", "(iii) Change in internal energy =-117.370 kJ/kg\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.64 Page no :212" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V1 = 5.5; \t\t\t#m**3\n", "p1 = 16.*10**5; \t\t\t#Pa\n", "T1 = 315.; \t\t\t#K\n", "V2 = V1;\n", "p2 = 12.*10**5; \t\t\t#Pa\n", "R = 0.287*10**3;\n", "y = 1.4;\n", "\n", "# Calculations\n", "m1 = p1*V1/R/T1;\n", "T2 = T1*(p2/p1)**((y-1)/y);\n", "m2 = p2*V2/R/T2;\n", "\n", "# Results\n", "m = m1-m2;\n", "print (\"Mass of air which left the receiver = %.3f\")% (m), (\"kg\")\n", "\n", "# Note : Rounding error is there." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Mass of air which left the receiver = 18.081 kg\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.65 Page no :213" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "cp = 1.; \t\t\t#kJ/kg.K\n", "cv = 0.711; \t\t\t#kJ/kg.K\n", "V1 = 1.6; \t\t\t#m**3\n", "V2 = V1;\n", "p1 = 5.*10**5; \t\t\t#Pa\n", "T1 = 373.; \t\t\t#K\n", "p2 = 1.*10**5; \t\t\t#Pa\n", "R = 287.;\n", "y = 1.4;\n", "\n", "# Calculations\n", "m1 = round(p1*V1/R/T1,2);\n", "T2 = round(T1*(p2/p1)**((y-1)/y),2);\n", "m2 = round(p2*V2/R/T2,3);\n", "KE = (m1*cv*T1)-(m2*cv*T2)-(m1-m2)*cp*T2;\n", "\n", "# Results\n", "print \"Kinetic energy of discharge air = %.3f\"% (KE), (\"kJ\")\n", "print (\"This is the exact answer when using proper value of cv\")\n", "\n", "# Book answer is wrong." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Kinetic energy of discharge air = 382.910 kJ\n", "This is the exact answer when using proper value of cv\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4.66 Page no :214" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "#For oxygen\n", "import math \n", "\n", "# Variables\n", "cpa = 0.88; \t\t\t#kJ/kg K\n", "Ra = 0.24; \t\t\t#kJ/kg K\n", "V1a = 0.035; \t\t\t#m**3\n", "p1a = 4.5; \t\t\t#bar\n", "T1a = 333.; \t\t\t#K\n", "V2a = 0.07; \t\t\t#m**3\n", "\n", "#For methane\n", "V1b = 0.07; \t\t\t#m**3\n", "V2b = 0.035; \t\t\t#m**3\n", "p1b = 4.5; \t\t\t#bar\n", "T1b = 261; \t\t\t#K\n", "cpb = 1.92; \t\t\t#kJ/kg K\n", "Rb = 0.496; \t\t\t#kJ/kg K\n", "\n", "# Calculations and Results\n", "yb = cpb/(cpb-Rb); \t\t\t#for methane\n", "cva = cpa-Ra; \t\t\t#for oxygen\n", "\n", "print (\"(i) Final state condition\")\n", "\n", "p2b = p1b*(V1b/V2b)**yb;\n", "print (\"p2 for methane = %.3f\")% (p2b), (\"bar\")\n", "\n", "T2b = p2b*V2b*T1b/p1b/V1b;\n", "print (\"T2 for methane = %.3f\")% (T2b), (\"K\")\n", "\n", "p2a = p2b;\n", "\n", "T2a = p2a*V2a/p1a/V1a*T1a;\n", "print (\"T2 for oxygen = %.3f\")% (T2a), (\"K\")\n", "\n", "Wb = (p1b*V1b - p2b*V2b)/(yb-1)*100; \t\t\t#kJ\n", "\n", "print (\"(ii)The piston will be in virtual equilibrium and hence zero work is effected by the piston.\")\n", "\n", "Wa = -Wb;\n", "\n", "ma = p1a*V1a/Ra/T1a*10**2;\n", "\n", "Q = ma*cva*(T2a-T1a) + Wa;\n", "print \"(iii) Heat transferred to oxygen = %.3f\"% (Q), (\"kJ\")\n", "\n", "# Rouding error is there." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) Final state condition\n", "p2 for methane = 11.458 bar\n", "T2 for methane = 332.272 K\n", "T2 for oxygen = 1695.733 K\n", "(ii)The piston will be in virtual equilibrium and hence zero work is effected by the piston.\n", "(iii) Heat transferred to oxygen = 196.572 kJ\n" ] } ], "prompt_number": 4 } ], "metadata": {} } ] }