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diff --git a/Thermodynamics_by_C_P_Arora/ch3.ipynb b/Thermodynamics_by_C_P_Arora/ch3.ipynb new file mode 100755 index 00000000..2ad5904d --- /dev/null +++ b/Thermodynamics_by_C_P_Arora/ch3.ipynb @@ -0,0 +1,1047 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:24bb4e51d6023f981d52e0e5400d7429d32a87d104b38eab26a2fc0c3b02030a" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3 : Second Law of Thermodynamics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.1 Page No : 6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "Q2 = 1800.;\t\t\t#KJ/hr\n", + "Q2 = Q2/3600;\t\t\t#KJ/sec or KW\n", + "W = 0.35;\t\t\t#KW\n", + "\n", + "# Calculations\n", + "COP = Q2/W;\n", + "\n", + "# Results\n", + "print \"COP is : %.4f\"%COP\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "COP is : 1.4286\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.2 Page No : 21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "Q2 = 1;\t\t\t#KJ/sec or KW\n", + "W = 0.4;\t\t\t#KW\n", + "T2 = -30+273;\t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "COP = Q2/W;\n", + "print \"COP of refrigerator is : \",COP\n", + "\n", + "T1 = T2*(1+COP)/COP;\t\t\t#K\n", + "print \"Temperature at which heat is rejected in K : \",T1\n", + "\n", + "Q1 = Q2*(1+COP)/COP;\t\t\t#KW\n", + "print \"Heat rejected per KW of cooling(KW) : \",Q1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "COP of refrigerator is : 2.5\n", + "Temperature at which heat is rejected in K : 340.2\n", + "Heat rejected per KW of cooling(KW) : 1.4\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.3 Page No : 22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "Q2 = 100.;\t\t\t#KJ/sec or KW\n", + "T2 = -20.+273;\t\t\t#K\n", + "T1 = 35.+273;\t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "COP = T2/(T1-T2);\n", + "print \"COP is : \",COP\n", + "\n", + "W = Q2/COP;\t\t\t#KW\n", + "print \"Power input in KJ/s or KW : %.2f\"%W\n", + "\n", + "COPheatpump = T1/(T1-T2);\t\t\t#\n", + "print \"COP as heat pump : \",COPheatpump\n", + "\n", + "Eta_engine = (1-T2/T1)*100;\n", + "print \"Efficiency as an engine in : %.3f\"%(Eta_engine)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "COP is : 4.6\n", + "Power input in KJ/s or KW : 21.74\n", + "COP as heat pump : 5.6\n", + "Efficiency as an engine in : 17.857\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.4 Page No : 22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "Q2dot = 12000.;\t\t\t#KJ/hr\n", + "Wdot = 0.75;\t\t\t#KW\n", + "Wdot = Wdot*3600.;\t\t\t#KJ/hr\n", + "\n", + "# Calculations and Results\n", + "COP = Q2dot/Wdot;\n", + "print \"Coefficient of Performance is : %.3f\"%COP\n", + "\n", + "Q1dot = Q2dot+Wdot;\t\t\t#KJ/hr\n", + "print \"Heat transfer rate in condenser in KJ/hr : %.0f\"%Q1dot\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coefficient of Performance is : 4.444\n", + "Heat transfer rate in condenser in KJ/hr : 14700\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.5 Page No : 23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import *\t\t\n", + " \t\n", + "# Variables :\n", + "Eta1 = 25./100;\t\t\t#efficiency\n", + "deltaT = 20.;\t\t\t#degree centigrade\n", + "\n", + "# Calculations\n", + "#T2dash = T2-20;\t\t\t#K\n", + "#T1dash = T1;\t\t\t#K\n", + "deltaEta1 = 30./100;\n", + "Eta_dash = 30./100;\t\t\t#efficiency\n", + "#Eta1/Eta_dash = (1-T2dash/T1dash)/(1-T2/T1)\n", + "#T1-T2 = 100;\n", + "#0.75*T1-T2 = 0;\n", + "A = array([[1, -1],[0.75, -1]])\n", + "B = array([100,0])\n", + "X = linalg.solve(A,B);\n", + "#Solution for T1 and T2 by matrix\n", + "T1 = X[0];\t\t\t#K\n", + "T2 = X[1];\t\t\t#K\n", + "\n", + "# Results\n", + "print \"Source temperature in K : %.0f\"%T1\n", + "print \"Sink temperature in K : %.0f\"%T2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Source temperature in K : 400\n", + "Sink temperature in K : 300\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.6 Page No : 23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 23.+273;\t\t\t#K\n", + "COP_HP = 2.5;\n", + "HeatLost = 60000.;\t\t\t#KJ/hr\n", + "HeatGenerated = 4000.;\t\t\t#KJ/hr\n", + "\n", + "# Calculations\n", + "Q1 = HeatLost-HeatGenerated;\t\t\t#KJ/hr\n", + "W = Q1/COP_HP;\t\t\t#KJ/hr\n", + "W = W/3600;\t\t\t#KJ/s or KW\n", + "\n", + "# Results\n", + "print \"Power input in KW : %.3f\"%W\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power input in KW : 6.222\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.7 Page No : 24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 400.+273;\t\t\t#K\n", + "T2 = 20.+273;\t\t\t#K\n", + "T3 = 100.+273;\t\t\t#K\n", + "T4 = T2;\t\t\t#K\n", + "Q1 = 12000.;\t\t\t#KW\n", + "Q3 = 25000.;\t\t\t#KW\n", + "\n", + "# Calculations and Results\n", + "Eta1 = 1-T2/T1;\t\t\t#Efficiency\n", + "W1 = Eta1*Q1;\t\t\t#KW\n", + "print \"Power of Engine 1, W1 in KW : %.2f\"%W1\n", + "Eta2 = 1-T4/T3;\t\t\t#Efficiency\n", + "W2 = Eta2*Q3;\t\t\t#KW\n", + "print \"Power of Engine 2, W2 in KW : %.2f\"%W2\n", + "print (\"W1>W2, The engine 1 delivers more power.\");\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power of Engine 1, W1 in KW : 6775.63\n", + "Power of Engine 2, W2 in KW : 5361.93\n", + "W1>W2, The engine 1 delivers more power.\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.8 Page No : 25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import *\n", + "\t\t\t\n", + "# Variables :\n", + "Wdot = 200.;\t\t\t#W\n", + "t1 = 40.;\t\t\t#degree centigrade\n", + "\n", + "# Calculations\n", + "#Q2dot = 20*(t1-t2);\t\t\t#W\n", + "#COP = Q2dot/W2dot = T2/(T1-T2)\n", + "#(t1-t2)/(W2dot/20) = (t1+273)/(t1-t2)\n", + "#20*t1**2+20*t2**2-20*2*t1*t2-t1*Wdot-273*Wdot\n", + "#(t2+273)/(t1-t2) = (t1-t2)/(Wdot/20)\n", + "#t2**2-(2*t1+(Wdot/20))*t2-273*(Wdot/20)+t1**2\n", + "P = array([1, -(2*t1+(Wdot/20)), -273*(Wdot/20)+t1**2])\n", + "t2 = roots(P);\n", + "t2 = t2[1];\t\t\t#degree C\n", + "\n", + "# Results\n", + "#Taken only -ve value as t2 cant be greater than t1\n", + "print \"Temperature of cold space(degree C) %.2f\"%t2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature of cold space(degree C) -11.17\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.10 Page No : 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "m = 0.8;\t\t\t#Kg\n", + "hi = 335.;\t\t\t#KJ/Kg-water\n", + "T1 = 24.+273;\t\t\t#K\n", + "T2 = 0.+273;\t\t\t#K\n", + "Wdot = 400.;\t\t\t#W\n", + "Wdot = Wdot/1000.;\t\t\t#KW\n", + "\n", + "# Calculations\n", + "Q2 = m*hi;\t\t\t#KJ\n", + "ActualCOP = T2/(T1-T2)*30/100;\n", + "Q2dot = ActualCOP/Wdot;\t\t\t#KJ/s\n", + "T = Q2/Q2dot;\t\t\t#sec\n", + "\n", + "# Results\n", + "print \"Time required to freeze the water in sec : %.2f\"%T\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time required to freeze the water in sec : 31.41\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.11 Page No : 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 727.+273;\t\t \t#K\n", + "T2 = 27.+273;\t\t \t#K\n", + "Wdot = 76.;\t\t\t #KW\n", + "FuelBurned = 4.;\t\t \t#Kg/hr\n", + "FuelBurned = 4./3600;\t\t\t#Kg/sec\n", + "FuelHeatingValue = 75000.;\t\t\t#KJ/Kg\n", + "\n", + "# Calculations and Results\n", + "Q1dot = FuelBurned*FuelHeatingValue;\t\t\t#KJ/s or KW\n", + "Eta = Wdot/Q1dot*100;\t\t\t#%\n", + "print \"Actual Efficiency of Engine in % : \",Eta\n", + "\n", + "Eta_c = (1-T2/T1)*100;\t\t\t#%\n", + "print \"Carnot Efficiency of Engine in % : \",Eta_c\n", + "print (\"Claim of inventor is wrong as actual efficiency is greater than carnot efficiency.\");\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Actual Efficiency of Engine in % : 91.2\n", + "Carnot Efficiency of Engine in % : 70.0\n", + "Claim of inventor is wrong as actual efficiency is greater than carnot efficiency.\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.12 Page No : 27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 24.+273;\t\t\t#K\n", + "T2 = 10.+273;\t\t\t#K\n", + "Q1 = 1500.;\t\t\t#kJ/min\n", + "Q1 = Q1/60.;\t\t\t#kW\n", + "\n", + "# Calculations\n", + "COP_ideal = T1/(T1-T2);\n", + "ActualCOP = COP_ideal*30/100;\n", + "W = Q1/ActualCOP;\t\t\t#kW\n", + "\n", + "# Results\n", + "print \"Power required in kW : %.3f\"%W\n", + "\n", + "#Answer is wrong in the book as calculation for Q1 is wrong.\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power required in kW : 3.928\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.13 Page No : 27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables :\n", + "T1 = 450.;\t\t\t#K\n", + "T2 = 280.;\t\t\t#K\n", + "Q1 = 1200.;\t\t\t#KJ\n", + "W = 0.15;\t\t\t#KWh\n", + "W = W*3600.;\t\t\t#KJ\n", + "\n", + "# Calculations and Results\n", + "Eta_a = W/Q1*100;\t\t\t#%\n", + "print \"Actual Efficiency of Engine in % : \",Eta_a\n", + "\n", + "Eta_c = (1-T2/T1)*100;\t\t\t#%\n", + "print \"Carnot Efficiency of Engine in %% : %.1f\"%(Eta_c)\n", + "print (\"We would not issue a patent as actual efficiency is greater than carnot efficiency.\");\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Actual Efficiency of Engine in % : 45.0\n", + "Carnot Efficiency of Engine in % : 37.8\n", + "We would not issue a patent as actual efficiency is greater than carnot efficiency.\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.14 Page No : 28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 1000.;\t\t\t#K\n", + "T3 = 100.;\t\t\t#K\n", + "Q1 = 1680.;\t\t\t#KJ\n", + "\n", + "#Eta_a = Eta_b : 1-T2/T1 = 1-T3/T2\n", + "T2 = math.sqrt(T1*T3);\t\t\t#K\n", + "Eta_a = 1-T2/T1;\n", + "Eta_b = Eta_a;\n", + "W1 = Eta_a*Q1;\t\t\t#KJ\n", + "Q2 = Q1-W1;\t\t\t#KJ\n", + "Q3 = (1-Eta_b)*Q2;\t\t\t#KJ\n", + "print \"Heat rejected by engine B in KJ : \",Q3\n", + "print \"Temperature at which heat is rejected by engine A in K : %.2f\"%T2\n", + "print \"Workdone by engine A in KJ ; %.2f\"%W1\n", + "\n", + "W2 = Eta_b*Q2;\t\t\t#KJ\n", + "print \"Workdone by engine B in KJ ; %.2f\"%W2\n", + "\n", + "#If W1 = W2\n", + "#Q/T = constant\n", + "T2 = (T1+T3)/2;\t\t\t#K\n", + "Eta_a = (1-T2/T1)*100;\t\t\t#%\n", + "Eta_b = (1-T3/T2)*100;\t\t\t#%\n", + "print (\"If Engine A & B deliver equal work.\")\n", + "print \"of Engine A in %% : %.2f\"%Eta_a\n", + "print \"of Engine B in %% : %.2f\"%Eta_b\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat rejected by engine B in KJ : 168.0\n", + "Temperature at which heat is rejected by engine A in K : 316.23\n", + "Workdone by engine A in KJ ; 1148.74\n", + "Workdone by engine B in KJ ; 363.26\n", + "If Engine A & B deliver equal work.\n", + "of Engine A in % : 45.00\n", + "of Engine B in % : 81.82\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.15 Page No : 29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables :\n", + "T1 = 800.+273;\t\t\t#K\n", + "T2 = 30.+273;\t\t\t#K\n", + "T3 = 30.+273;\t\t\t#K\n", + "T4 = -15.+273;\t\t\t#K\n", + "Q1 = 1900.;\t\t\t#KJ\n", + "W2 = 290.;\t\t\t#KJ\n", + "\n", + "# Calculations and Results\n", + "#Eta = 1-T2/T1 = W1/Q1\n", + "W1 = (1-T2/T1)*Q1;\t\t\t#KJ\n", + "Q2 = Q1-W1;\t\t\t#KJ\n", + "W3 = W1-W2;\t\t\t#KJ\n", + "\n", + "#COP = T4/(T3-T4) = Q4/W3\n", + "Q4 = T4/(T3-T4)*W3;\t\t\t#KJ\n", + "print \"Heat absorbed by refrigerant in KJ : %.2f\"%Q4\n", + "\n", + "Q3 = W3+Q4;\t\t\t#KJ\n", + "TotalHeat = Q2+Q3;\t\t\t#KJ\n", + "print \"Total Heat transferred to reservoir at 30 degree centigrade in KJ : %.2f\"%TotalHeat\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat absorbed by refrigerant in KJ : 6154.54\n", + "Total Heat transferred to reservoir at 30 degree centigrade in KJ : 7764.54\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.16 Page No : 30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 840.+273;\t\t\t#K\n", + "T2 = 60.+273;\t\t\t#K\n", + "T3 = 5.+273;\t\t\t#K\n", + "W3 = 30.;\t\t\t#KW\n", + "Q3 = 17.;\t\t\t#KJ/s\n", + "\n", + "# Calculations\n", + "#Q3/T3 = Q4/T4\n", + "T4 = T2;\t\t\t#K\n", + "Q4 = Q3/T3*T4;\t\t\t#KJ/s\n", + "W2 = Q4-Q3;\t\t\t#KJ/s\n", + "W1 = W2+W3;\t\t\t#KJ/s\n", + "Q1subQ2 = W1;\t\t\t#KJ/s\n", + "#Q1/T1 = Q2/T2\n", + "Q1ByQ2 = T1/T2;\n", + "\t\t\t#Q1subQ2 = Q1subQ2*Q2-Q2\n", + "Q2 = Q1subQ2/(Q1ByQ2-1);\t\t\t#KW\n", + "Q1 = Q1ByQ2*Q2;\t\t\t#KW\n", + "\n", + "# Results\n", + "print \"Rate of heat supply from 800 degree C source in KW : %.1f\"%Q1\n", + "print \"Rate of heat rejection to sink in KW : %.3f\"%(Q2+Q4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rate of heat supply from 800 degree C source in KW : 47.6\n", + "Rate of heat rejection to sink in KW : 34.607\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17 Page No : 31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 27.+273;\t\t\t#K\n", + "T2 = -23.+273;\t\t\t#K\n", + "W = 1.;\t\t\t#KW\n", + "Q2 = 20000.;\t\t\t#KJ/hr\n", + "\n", + "# Calculations and Results\n", + "Q2 = Q2/3600;\t\t\t#KJ/s\n", + "ActualCOP = Q2/W;\n", + "print \"COP of machine : %.3f\"%ActualCOP\n", + "\n", + "IdealCOP = T2/(T1-T2);\n", + "print \"Ideal COP of machine : %.0f\"%IdealCOP\n", + "print (\"ActualCOP>IdealCOP, Inventor's claim is wrong.\");\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "COP of machine : 5.556\n", + "Ideal COP of machine : 5\n", + "ActualCOP>IdealCOP, Inventor's claim is wrong.\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.18 Page No : 32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import *\n", + "\t\t\t\n", + "# Variables :\n", + "#Heat Pump in winter\n", + "Q1 = 2400.;\t\t\t#KJ/hr/degree temperature difference\n", + "t1 = 20.;\t\t\t#degreeC\n", + "t2 = 0.;\t\t\t#degreeC\n", + "\n", + "# Calculations and Results\n", + "Q1 = Q1*(t1-t2)/3600;\t\t\t#KJ/s\n", + "T1 = t1+273;\t\t\t#K\n", + "T2 = t2+273;\t\t\t#K\n", + "COP = T1/(T1-T2);\n", + "W = Q1/COP;\t\t\t#KW\n", + "print \"Power required to drive heat pump in KW : %.2f\"%W\n", + "\n", + "#Refrigerating unit in summer\n", + "T4 = 20+273;\t\t\t#K\n", + "#Q4 = 2400*(T3-T4)/3600;\t\t\t#KJ/s\n", + "Q3subQ4 = W;\t\t\t#KJ\n", + "#COP = Q4/(Q3subQ4) = T4/(T3-T4);\n", + "#T3**2-2*T3*T4+T4**2-T4*3600/2400*(Q3subQ4) = 0\n", + "P = array([1, -2*T4, T4**2-T4*3600./2400*(Q3subQ4)])\n", + "T3 = roots(P);\n", + "T3 = T3[0];\t\t\t#K(Maximum outside temperature)\n", + "print \"Maximum outside temperature in K : %.0f\"%T3\n", + "print \"in degree C : %.0f\"%(T3-273)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power required to drive heat pump in KW : 0.91\n", + "Maximum outside temperature in K : 313\n", + "in degree C : 40\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.20 Page No : 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "VcByVa = 14.;\t\t\t#Overall expansion ratio\n", + "T1 = 257+273.;\t\t\t#K\n", + "T2 = 27+273.;\t\t\t#K\n", + "Gamma = 1.4;\n", + "Ta = T1;\t\t\t#K\n", + "Tb = T1;\t\t\t#K\n", + "Tc = T2;\t\t\t#K\n", + "Td = T2;\t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "VcByVb = (Tb/Tc)**(1/(Gamma-1));\t\t\t#Expansion ratio for Adiabatic Process : \n", + "print \"ratio for adiabatic process : %.2f\"%VcByVb\n", + "\n", + "VbByVa = VcByVa/VcByVb;\t\t\t#Expansion ratio for Isothermal Process : \n", + "print \"Expansion ratio for Isothermal process : %.3f\"%VbByVa\n", + "Eta = (1-T2/T1)*100;\t\t\t#%\n", + "print \"Thermal Efficiency of carnot cycle in %% : %.1f\"%Eta\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio for adiabatic process : 4.15\n", + "Expansion ratio for Isothermal process : 3.375\n", + "Thermal Efficiency of carnot cycle in % : 43.4\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.21 Page No : 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "W = 10.;\t\t\t#KW\n", + "\t\t\t#For flat plate collector\n", + "T1 = 90.+273;\t\t\t#K\n", + "T2 = 27.+273;\t\t\t#K\n", + "Tmax = T1;\t\t\t#K\n", + "IE = 1.;\t\t\t#KW/m**2 incident energy\n", + "EtaCollection = 60./100;\n", + "\n", + "# Calculations and Results\n", + "#Eta = 1-T2/T1 = W/Q1\n", + "Q1 = W/(1-T2/T1);\t\t\t#KJ/s\n", + "A1 = Q1/IE/EtaCollection;\t\t\t#m**2\n", + "print \"Solar Collector Area required in m**2 : %.3f\"%A1\n", + "\n", + "#For parabolic collector\n", + "T3 = 250.+273;\t\t\t#K\n", + "T4 = 27.+273;\t\t\t#K\n", + "Tmax = T3;\t\t\t#K\n", + "IE = 1.;\t\t\t#KW/m**2 incident energy\n", + "EtaCollection = 50./100;\n", + "\n", + "#Eta = 1-T2/T1 = W/Q1\n", + "Q3 = W/(1-T4/T3);\t\t\t#KJ/s\n", + "A2 = Q3/IE/EtaCollection;\t\t\t#m**2\n", + "print \"Parabolic Solar Collector Area required in m**2 : %.3f\"%A2\n", + "\t\t\t#Answer of 2nd part is wrong in the book.\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Solar Collector Area required in m**2 : 96.032\n", + "Parabolic Solar Collector Area required in m**2 : 46.906\n" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.24 Page No : 37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 40.+273;\t\t\t#K\n", + "T2 = 5.+273;\t\t\t#K\n", + "T3 = 400.+273;\t\t\t#K\n", + "T4 = T1;\t\t\t#K\n", + "Q2 = 1500.;\t\t\t#KJ/min\n", + "\n", + "# Calculations and Results\n", + "COP_R = T2/(T1-T2);\n", + "print \"COP of refrigerator is : %.3f\"%COP_R\n", + "\n", + "Q2dot = Q2/60;\t\t\t#KJ/s\n", + "Wdot = Q2dot/COP_R;\t\t\t#KW\n", + "print \"Work Input to refrigerator in KW : %.4f\"%Wdot\n", + "\n", + "Eta = (1-T4/T3);\t\t\t#%\n", + "Q3dot = Wdot/Eta;\t\t\t#KW\n", + "OverallCOP = Q2dot/Q3dot;\t\t\t#\n", + "print \"Overall COP of refrigerator : %.4f\"%OverallCOP\n", + "\t\t\t\n", + "#Ans of overall COP is wrong in the book.\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "COP of refrigerator is : 7.943\n", + "Work Input to refrigerator in KW : 3.1475\n", + "Overall COP of refrigerator : 4.2488\n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.25 Page No : 38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 1500.;\t\t\t#K\n", + "T2 = 450.;\t\t\t#K\n", + "T3 = 150.;\t\t\t#K\n", + "Q3 = 250.;\t\t\t#KJ\n", + "\n", + "# Calculations and Results\n", + "COP_CR = T3/(T2-T3);\n", + "print \"COP of cold refrigerator is : %.1f\"%COP_CR\n", + "\n", + "COP_HR = T2/(T1-T2);\n", + "print \"COP of hotter refrigerator is : %.4f\"%COP_HR\n", + "COP = T3/(T1-T3);\n", + "print \"COP of composite system is : %.3f\"%COP\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "COP of cold refrigerator is : 0.5\n", + "COP of hotter refrigerator is : 0.4286\n", + "COP of composite system is : 0.111\n" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.26 Page No : 38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables :\n", + "T1 = 870.;\t\t\t#K\n", + "T2 = 580.;\t\t\t#K\n", + "T3 = 290.;\t\t\t#K\n", + "Wdot = 85.;\t\t\t#KW\n", + "Q3 = 3000.;\t\t\t#KJmin\n", + "Q3 = Q3/60.;\t\t\t#KJ/s\n", + "Q1plusQ2 = Wdot+Q3;\t\t\t#KJ\n", + "\n", + "#sigma(Q/T) = 0\n", + "#Q1/T1+Q2/T2 = Q3/T3\n", + "#Q1/T1+(Q1plusQ2-Q1)/T2-Q3/T3 = 0\n", + "Q1 = (-Q3*T1*T2/T3+Q1plusQ2*T1)/(T1-T2);\t\t\t#KW\n", + "print \"Heat Supplied by source1 in KW : %.0f\"%Q1\n", + "\n", + "Q2 = Q1plusQ2-Q1;\t\t\t#KW\n", + "print \"Heat Supplied by source2 in KW : %.0f\"%Q2\n", + "\n", + "Eta = Wdot/(Q1+Q2)*100;\t\t\t#%\n", + "print \"Efficiency of engine in %% : %.2f\"%Eta\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat Supplied by source1 in KW : 105\n", + "Heat Supplied by source2 in KW : 30\n", + "Efficiency of engine in % : 62.96\n" + ] + } + ], + "prompt_number": 45 + } + ], + "metadata": {} + } + ] +}
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