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diff --git a/Engineering_Thermodynamics:_A_Computer_Approach_(SI_Units_Version)/ch5.ipynb b/Engineering_Thermodynamics:_A_Computer_Approach_(SI_Units_Version)/ch5.ipynb new file mode 100755 index 00000000..82caf09b --- /dev/null +++ b/Engineering_Thermodynamics:_A_Computer_Approach_(SI_Units_Version)/ch5.ipynb @@ -0,0 +1,2525 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Chapter 5 : Second Law of Thermodynamics and Entropy" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.1 Page no : 237" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "Q1 = 1500./60; \t\t#kJ/s\n", + "W = 8.2; \t\t\t#kW\n", + "\n", + "# Calculations and Results\n", + "print (\"(i) Thermal efficiency\")\n", + "n = W/Q1;\n", + "print (\"n = \"),(n)\n", + "\n", + "print (\"(ii) Rate of heat rejection\")\n", + "Q2 = Q1-W; \n", + "print (\"Q2 = \"),(Q2), (\"kW\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Thermal efficiency\n", + "n = 0.328\n", + "(ii) Rate of heat rejection\n", + "Q2 = 16.8 kW\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.2 Page no : 238" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "Q_12 = 30.; \t\t#kJ\n", + "W_12 = 60; \t\t\t#kJ\n", + "\n", + "# Calculations\n", + "dU_12 = Q_12-W_12;\n", + "Q_21 = 0;\n", + "W_21 = Q_21+dU_12;\n", + "\n", + "# Results\n", + "print (\"W_21 = \"),(W_21)\n", + "print (\"Thus 30 kJ work has to be done on the system to restore it to original state, by adiabatic process.\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "W_21 = -30.0\n", + "Thus 30 kJ work has to be done on the system to restore it to original state, by adiabatic process.\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.3 Page no : 239" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "Q2 = 12000.; \t\t\t#kJ/h\n", + "W = 0.75*60*60; \t\t#kJ/h\n", + "\n", + "# Calculations and Results\n", + "COP = Q2/W;\n", + "print (\"Coefficient of performance %.3f\")%(COP)\n", + "\n", + "Q1 = Q2+W;\n", + "print (\"heat transfer rate = %.3f\")%(Q1), (\"kJ/h\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coefficient of performance 4.444\n", + "heat transfer rate = 14700.000 kJ/h\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.4 Page no : 239" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T2 = 261.; \t\t\t#K\n", + "T1 = 308.; \t\t\t#K\n", + "Q2 = 2.; \t\t\t#kJ/s\n", + "\n", + "# Calculations\n", + "Q1 = Q2*(T1/T2);\n", + "W = Q1-Q2;\n", + "\n", + "# Results\n", + "print (\"Least power required to pump the heat continuosly %.3f\")%(W),(\"kW\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Least power required to pump the heat continuosly 0.360 kW\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.5 Page no :239" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\n", + "# Variables\n", + "Q1 = 2*10**5; \t\t\t#kJ/h\n", + "W = 3*10**4; \t\t\t#kJ/h\n", + "\n", + "# Calculations and Results\n", + "Q2 = Q1-W;\n", + "print (\"Heat abstracted from outside = \"),(Q2), (\"kJ/h\")\n", + "\n", + "\n", + "COP_hp = Q1/(Q1-Q2);\n", + "print (\"Co-efficient of performance = %.2f\")%(COP_hp)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat abstracted from outside = 170000 kJ/h\n", + "Co-efficient of performance = 6.00\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.6 Page no : 240" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 2373; \t\t\t#K\n", + "T2 = 288.; \t\t\t#K\n", + "\n", + "# Calculations\n", + "n_max = 1-T2/T1;\n", + "\n", + "# Results\n", + "print (\"Highest possible theoritical efficiency = %.3f\")% (n_max*100), (\"%\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Highest possible theoritical efficiency = 87.863 %\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.7 Page no : 240" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 523.; \t\t\t#K\n", + "T2 = 258.; \t\t\t#K\n", + "Q1 = 90.; \t\t\t#kJ\n", + "\n", + "# Calculations and Results\n", + "n = 1-T2/T1;\n", + "print (\"(i) Efficiency of the system %.3f\")%(n*100), (\"%\")\n", + "\n", + "W = n*Q1;\n", + "print (\"(ii) The net work transfer\"),(\"W = %.3f\")%(W),(\"kJ\")\n", + " \n", + "Q2 = Q1-W;\n", + "print (\"(iii) Heat rejected to the math.sink\"),(\"Q2 = %.3f\")%(Q2),(\"kJ\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Efficiency of the system 50.669 %\n", + "(ii) The net work transfer W = 45.602 kJ\n", + "(iii) Heat rejected to the math.sink Q2 = 44.398 kJ\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.8 Page no : 241" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 1023.; \t\t#K\n", + "T2 = 298.; \t\t\t#K\n", + "\n", + "# Calculations\n", + "n_carnot = 1-T2/T1;\n", + "W = 75*1000*60*60;\n", + "Q = 3.9*74500*1000;\n", + "n_thermal = W/Q;\n", + "\n", + "# Results\n", + "print (\"n_carnot = %.3f\")%(n_carnot)\n", + "\n", + "print (\"n_thermal = %.3f\")%(n_thermal)\n", + "\n", + "print (\"Since \u03b7thermal > \u03b7carnot, therefore claim of the inventor is not valid (or possible)\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "n_carnot = 0.709\n", + "n_thermal = 0.929\n", + "Since \u03b7thermal > \u03b7carnot, therefore claim of the inventor is not valid (or possible)\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.9 Page no : 241" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 1273.; \t\t#K\n", + "T2 = 313.; \t\t\t#K\n", + "n_max = 1-T2/T1;\n", + "Wnet = 1.;\n", + "\n", + "# Calculations\n", + "Q1 = Wnet/n_max;\n", + "Q2 = Q1-Wnet;\n", + "\n", + "# Results\n", + "print (\"the least rate of heat rejection = %.3f\")%(Q2), (\"kW\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "the least rate of heat rejection = 0.326 kW\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.10 Page no : 242" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "one_ton_of_refrigeration = 210.; \t\t\t#kJ/min\n", + "Cooling_required = 40*(one_ton_of_refrigeration); \t\t\t#kJ/min\n", + "T1 = 303.; \t\t\t#K\n", + "T2 = 238.; \t\t\t#K\n", + "\n", + "# Calculations\n", + "COP_refrigerator = T2/(T1-T2);\n", + "COP_actual = 0.20*COP_refrigerator;\n", + "W = Cooling_required/COP_actual/60;\n", + "\n", + "# Results\n", + "print (\"power required = %.1f\")% (W), (\"kW\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "power required = 191.2 kW\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.11 Page no : 242" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "E = 12000.; \t\t#kJ/min\n", + "T2 = 308.; \t\t\t#K\n", + "# Source 1\n", + "T1 = 593.; \t\t\t#K\n", + "\n", + "# Calculations\n", + "n1 = 1-T2/T1;\n", + "# Source 2\n", + "T1 = 343.; \t\t\t#K\n", + "n2 = 1-T2/T1;\n", + "W1 = E*n1;\n", + "\n", + "# Results\n", + "print (\"W1 = %.3f\")% (W1),(\"kJ/min\")\n", + "\n", + "W2 = E*n2;\n", + "print (\"W2 = %.3f\")% (W2),(\"kJ/min\")\n", + "\n", + "print (\"Thus, choose source 2.\")\n", + "print (\"The source 2 is selected even though efficiency in this case is lower, because the criterion for selection is the larger output.\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "W1 = 5767.285 kJ/min\n", + "W2 = 1224.490 kJ/min\n", + "Thus, choose source 2.\n", + "The source 2 is selected even though efficiency in this case is lower, because the criterion for selection is the larger output.\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + " Example 5.12 Page no : 243" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 973.; \t\t\t#K\n", + "T2 = 323.; \t\t\t#K\n", + "T3 = 248.; \t\t\t#K\n", + "\n", + "Q1 = 2500.; \t\t\t#kJ\n", + "W = 400.; \t\t\t#kJ\n", + "\n", + "# Calculations and Results\n", + "n_max = 1-T2/T1;\n", + "W1 = n_max*Q1;\n", + "COP_max = T3/(T2-T3);\n", + "W2 = W1-W;\n", + "Q4 = COP_max*W2;\n", + "COP1 = round(Q4/W2,3);\n", + "Q3 = Q4+W2;\n", + "Q2 = Q1-W1;\n", + "print (\"Heat rejection to the 50\u00b0C reservoir = %.3f\")%(Q2+Q3), (\"kJ\")\n", + "\n", + "\n", + "n = 0.45*n_max;\n", + "W1 = n*Q1;\n", + "W2 = W1-W;\n", + "COP2 = 0.45*COP1;\n", + "Q4 = W2*COP2;\n", + "Q3 = Q4+W2;\n", + "Q2 = Q1-W1;\n", + "\n", + "print (\"Heat rejected to 50\u00b0C reservoir = %.3f\")% (Q2+Q3), (\"kJ\")\n", + "\n", + "# Note : Answers are slightly different then book because of Rounding Error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat rejection to the 50\u00b0C reservoir = 6299.773 kJ\n", + "Heat rejected to 50\u00b0C reservoir = 2623.147 kJ\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.13 Page no : 244" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 298.; \t\t\t#K\n", + "T2 = 273.; \t\t\t#K\n", + "Q1 = 24.; \t\t\t#kJ/s\n", + "T3 = 653.; \t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "COP = T1/(T1-T2);\n", + "print (\"(i) determine COP and work input required\")\n", + "\n", + "print (\"Coefficient of performance = \"),(COP)\n", + "\n", + "COP_ref = T2/(T1-T2);\n", + "W = Q1/COP_ref;\n", + "print (\"Work input required = %.3f\")%(W),(\"kW\")\n", + "\n", + " \n", + "Q4 = T1*W/(T3-T1);\n", + "Q3 = Q4+W;\n", + "Q2 = Q1+W;\n", + "COP = Q1/Q3;\n", + "print (\"(ii)Determine overall COP of the system \"),(\"COP = %.3f\")%(COP)\n", + "\n", + "COP_overall = (Q2+Q4)/Q3;\n", + "print (\"Overall COP = %.3f\")%(COP_overall)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) determine COP and work input required\n", + "Coefficient of performance = 11.92\n", + "Work input required = 2.198 kW\n", + "(ii)Determine overall COP of the system COP = 5.937\n", + "Overall COP = 6.937\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.14 Page no : 245" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T_e1 = 493.; \t\t\t#K\n", + "T_e2 = 298.; \t\t\t#K\n", + "T_p1 = 298.; \t\t\t#K\n", + "T_p2 = 273.; \t\t\t#K\n", + "Amt = 15.; \t\t \t#tonnes produced per day\n", + "h = 334.5; \t\t\t #kJ/kg\n", + "Q_abs = 44500.; \t\t#kJ/kg\n", + "\n", + "# Calculations and Results\n", + "Q_p2 = Amt*10**3*h/24/60;\n", + "COP_hp = T_p2/(T_p1-T_p2);\n", + "W = Q_p2/COP_hp/60;\n", + "print (\"(i)Power developed by the engine = %.3f\")%(W),(\"kW\")\n", + "\n", + "print (\"(ii) Fuel consumed per hour\")\n", + "n_carnot = 1-(T_e2/T_e1);\n", + "Q_e1 = W/n_carnot*3600; \t\t\t#kJ/h\n", + "fuel_consumed = Q_e1/Q_abs;\n", + "print (\"Quantity of fuel consumed/hour = %.3f\")%(fuel_consumed),(\"kg/h\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i)Power developed by the engine = 5.318 kW\n", + "(ii) Fuel consumed per hour\n", + "Quantity of fuel consumed/hour = 1.088 kg/h\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.15 Page no : 247" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 550.; \t\t\t#K\n", + "T3 = 350.; \t\t\t#K\n", + "\n", + "# Calculations\n", + "T2 = (T1+T3)/2;\n", + "\n", + "# Results\n", + "print (\"Intermediate temperature = \"), (T2),(\"K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Intermediate temperature = 450.0 K\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.16 Page no : 247" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T1 = 600.; \t\t\t#K\n", + "T2 = 300.; \t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "T3 = 2*T1/(T1/T2+1);\n", + "print (\"(i) When Q1 = Q2\"),(\"T3 = \"),(T3),(\"K\")\n", + "\n", + "\n", + "print (\"(ii) Efficiency of Carnot engine and COP of carnot refrigerator\")\n", + "n = (T1-T3)/T1; \t\t\t#carnot engine\n", + "COP = T2/(T3-T2); \t\t\t#refrigerator\n", + "\n", + "print (\"Efficiency of carnot engine = %.3f\")% (n)\n", + "\n", + "print (\"COP of carnot refrigerator = \"), (COP)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) When Q1 = Q2 T3 = 400.0 K\n", + "(ii) Efficiency of Carnot engine and COP of carnot refrigerator\n", + "Efficiency of carnot engine = 0.333\n", + "COP of carnot refrigerator = 3.0\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.17 Page no : 249" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "T3 = 278.; \t\t\t#K\n", + "T2 = 350.; \t\t\t#K\n", + "T4 = T2;\n", + "T1 = 1350.; \t\t\t#K\n", + "\n", + "# Calculations\n", + "Q1 = 100/(((T4/T1)*(T1-T2)/(T4-T3))+T2/T1) \t#Q4+Q2 = 100; Q4 = Q1*((T4/T1)*(T1-T2)/(T4-T3)); Q2 = T2/T1*Q1;\n", + "\n", + "# Results\n", + "print (\"Q1 = %.3f\")%(Q1),(\"kJ\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Q1 = 25.906 kJ\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.18 Page no : 250" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "Q1 = 300.; \t\t\t#kJ/s\n", + "T1 = 290.; \t\t\t#0C\n", + "T2 = 8.5; \t\t\t#0C\n", + "\n", + "# Calculations and Results\n", + "print (\"let \u03a3dQ/T = A\")\n", + "\n", + "print (\"(i) 215 kJ/s are rejected\")\n", + "Q2 = 215.; \t\t\t#kJ/s\n", + "A = Q1/(T1+273) - Q2/(T2+273)\n", + "print (\"Since, A<0, Cycle is irreversible.\")\n", + "\n", + "\n", + "print (\"(ii) 150 kJ/s are rejected\")\n", + "Q2 = 150; \t\t\t#kJ/s\n", + "A = Q1/(T1+273) - Q2/(T2+273)\n", + "print (\"Since A = 0, cycle is reversible\")\n", + "\n", + "\n", + "print (\"(iii) 75 kJ/s are rejected.\")\n", + "Q2 = 75; \t\t\t#kJ/s\n", + "A = Q1/(T1+273) - Q2/(T2+273)\n", + "print (\"Since A>0, cycle is impossible\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "let \u03a3dQ/T = A\n", + "(i) 215 kJ/s are rejected\n", + "Since, A<0, Cycle is irreversible.\n", + "(ii) 150 kJ/s are rejected\n", + "Since A = 0, cycle is reversible\n", + "(iii) 75 kJ/s are rejected.\n", + "Since A>0, cycle is impossible\n" + ] + } + ], + "prompt_number": 65 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.19 Page no : 251" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "P1 = 0.124*10**5; \t\t\t#N/m**2\n", + "T1 = 433; \t\t\t#K\n", + "T2 = 323; \t\t\t#K\n", + "h_f1 = 687; \t\t\t#kJ/kg\n", + "h2 = 2760; \t\t\t#kJ/kg\n", + "h3 = 2160; \t\t\t#kJ/kg\n", + "h_f4 = 209; \t\t\t#kJ/kg\n", + "\n", + "# Calculations and Results\n", + "Q1 = h2-h_f1;\n", + "Q2 = h_f4-h3;\n", + "print (\"Let A = \u03a3dQ/T\")\n", + "A = Q1/T1+Q2/T2;\n", + "print (A)\n", + "print (\"A<0. Hence classius inequality is verified\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Let A = \u03a3dQ/T\n", + "-3\n", + "A<0. Hence classius inequality is verified\n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.20 Page no :251" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "T1 = 437.; \t\t\t#K\n", + "T2 = 324.; \t \t\t#K\n", + "h2 = 2760.; \t\t\t#kJ/kg\n", + "h1 = 690.; \t\t \t#kJ/kg\n", + "h3 = 2360.; \t\t\t#kJ/kg\n", + "h4 = 450.; \t\t\t #kJkg\n", + "\n", + "# Calculations\n", + "Q1 = h2-h1;\n", + "Q2 = h4-h3;\n", + "\n", + "# Results\n", + "print (\"Let A = \u03a3dQ/T\")\n", + "A = Q1/T1 + Q2/T2;\n", + "print \"%.3f\"%(A)\n", + "print (\"Since A<0, Classius inequality is verified\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Let A = \u03a3dQ/T\n", + "-1.158\n", + "Since A<0, Classius inequality is verified\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.21 Page no : 266" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "T0 = 273.; \t\t\t#K\n", + "T1 = 673.; \t\t\t#K\n", + "T2 = 298.; \t\t\t#K\n", + "m_w = 10.; \t\t\t#kg\n", + "T3 = 323.; \t\t\t#K\n", + "c_pw = 4186.; \t\t#kJ/kg.K\n", + "\n", + "# Calculations and Results\n", + "print (\"Let C = mi*cpi\")\n", + "C = m_w*c_pw*(T3-T2)/(T1-T3);\n", + "S_iT1 = C*math.log(T1/T0); \t\t\t# Entropy of iron at 673 K\n", + "S_wT2 = m_w*c_pw*math.log(T2/T0); \t#Entropy of water at 298 K\n", + "S_iT3 = C*math.log(T3/T0); \t\t\t#Entropy of iron at 323 K\n", + "S_wT3 = m_w*c_pw*math.log(T3/T0); \t#Entropy of water at 323 K\n", + "\n", + "dS_i = S_iT3 - S_iT1;\n", + "dS_w = S_wT3 - S_wT2; \n", + "dS_net = dS_i + dS_w\n", + "\n", + "print (\"Since dS>0, process is irreversible\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Let C = mi*cpi\n", + "Since dS>0, process is irreversible\n" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.23 Page no : 267" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "T1 = 293.; \t\t\t#K\n", + "V1 = 0.025; \t\t\t#m**3\n", + "V3 = V1;\n", + "p1 = 1.05*10**5; \t\t\t#N/m**2\n", + "p2 = 4.5*10**5; \t\t\t#N/m**2\n", + "R = 0.287*10**3; \n", + "cv = 0.718;\n", + "cp = 1.005;\n", + "T3 = 293.; \t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "m = p1*V1/R/T1;\n", + "T2 = p2/p1*T1;\n", + "Q_12 = m*cv*(T2-T1);\n", + "Q_23 = m*cp*(T3-T2)\n", + "\n", + "Q_net = Q_12+Q_23;\n", + "print (\"Net heat flow = \"),(Q_net), (\"kJ\")\n", + "\n", + "\n", + "dS_32 = m*cp*math.log(T2/T1);\n", + "dS_12 = m*cv*math.log(T2/T1);\n", + "dS_31 = dS_32 - dS_12;\n", + "print (\"Decrease in entropy = %.3f\")% (dS_31), (\"kJ/K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Net heat flow = -8.625 kJ\n", + "Decrease in entropy = 0.013 kJ/K\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.24 Page no : 269" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%pylab inline\n", + "\n", + "from matplotlib.pyplot import *\n", + "from numpy import *\n", + "import math \n", + "\n", + "# Variables\n", + "p1 = 1.05*10**5; \t#N/m**2\n", + "V1 = 0.04; \t\t\t#m**3\n", + "T1 = 288.; \t\t\t#K\n", + "p2 = 4.8*10**5;\n", + "T2 = T1;\n", + "R0 = 8314.;\n", + "M = 28.;\n", + "\n", + "# Calculations and Results\n", + "R = R0/M;\n", + "m = p1*V1/R/T1;\n", + "dS = m*R*math.log(p1/p2)\n", + "print (\"Decrease in entropy = %.3f\")% (-dS), (\"J/K\")\n", + "\n", + "\n", + "print \n", + "Q = T1*(-dS);\n", + "print (\"(ii)Heat rejected = \"),(\"Q = %.3f\")%(Q),(\"J\")\n", + "\n", + "\n", + "W = Q;\n", + "print (\"Work done = %.3f\")% (W), (\"J\")\n", + "\n", + "V2 = p1*V1/p2;\n", + "v1 = V1/m; \t\t\t#specific volume\n", + "v2 = V2/m; \t\t\t#specific volume\n", + "\n", + "v = linspace(v2,0.8081571,64);\n", + "\n", + "\n", + "def f(v):\n", + " return p1*v1/v\n", + "plot(v,f(v))\n", + "\n", + "p = []\n", + "for i in range(len(v)):\n", + " p.append(p1)\n", + "plot(v,p,'--')\n", + "\n", + "p = [0 ,p2]\n", + "v = [v2 ,v2]\n", + "plot(v,p,'--')\n", + "\n", + "p = [0 ,p1]\n", + "v = [v1 ,v1]\n", + "plot(v,p,'--')\n", + "\n", + "T = [288, 288]\n", + "s = [10 ,(10-dS)]\n", + "plot(s,T)\n", + "\n", + "s = [10 ,10]\n", + "T = [0 ,288]\n", + "plot(s,T,'--')\n", + "\n", + "s = [(10-dS), (10-dS)]\n", + "T = [0 ,288]\n", + "plot(s,T,'--')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "Decrease in entropy = 22.164 J/K\n", + "\n", + "(ii)Heat rejected = Q = 6383.268 J\n", + "Work done = 6383.268 J\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 13, + "text": [ + "[<matplotlib.lines.Line2D at 0x2c3da90>]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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UKQuA5yyIiIyiVFnwMBQRkTGUKgsehiIiMgbLgoiIYlKmLM7/nyoehiIiMogyZdH9cy9H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\nZgAAAABJRU5ErkJggg==\n", + "text": [ + "<matplotlib.figure.Figure at 0x2124290>" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.25 Page no : 270" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "R = 287.; \t\t\t#kJ/kg.K\n", + "dU = 0;\n", + "W = 0;\n", + "Q = dU+W;\n", + "\n", + "# Calculations\n", + "dS = R*math.log(2); \t\t\t#v2/v1 = 2\n", + "\n", + "# Results\n", + "print (\"Change in entropy = %.3f\")%(dS),(\"kJ/kg.K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Change in entropy = 198.933 kJ/kg.K\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.26 Page no : 271" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "m = 0.04; \t\t\t#kg\n", + "p1 = 1*10.**5; \t\t\t#N/m**2\n", + "T1 = 293.; \t\t\t#K\n", + "p2 = 9*10.**5; \t\t\t#N/m**2\n", + "V2 = 0.003; \t\t\t#m**3\n", + "cp = 0.88; \t\t\t#kJ/kg.K\n", + "R0 = 8314.;\n", + "M = 44.;\n", + "\n", + "# Calculations\n", + "R = R0/M;\n", + "T2 = p2*V2/m/R;\n", + "ds_2A = R/10**3*math.log(p2/p1);\n", + "ds_1A = cp*math.log(T2/T1);\n", + "ds_21 = ds_2A - ds_1A;\n", + "dS_21 = m*ds_21;\n", + "\n", + "# Results\n", + "print (\"Decrease in entropy = %.3f\")% (dS_21),(\"kJ/K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Decrease in entropy = 0.010 kJ/K\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.27 Page no : 272" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "p1 = 7.*10**5; \t\t\t#N/m**2\n", + "T1 = 873.; \t\t\t#K\n", + "p2 = 1.05*10**5; \t\t\t#N/M62\n", + "n = 1.25;\n", + "m = 1.; \t\t\t#kg\n", + "R = 0.287;\n", + "cp = 1.005;\n", + "\n", + "# Calculations\n", + "T2 = T1*(p2/p1)**((n-1)/n);\n", + "\n", + "# At constant temperature from 1 to A\n", + "ds_1A = R*math.log(p1/p2);\n", + "# At constant pressure from A to 2\n", + "ds_2A = cp*math.log(T1/T2);\n", + "ds_12 = ds_1A - ds_2A;\n", + "\n", + "# Results\n", + "print (\"Increase in entropy = %.3f\")% (ds_12), (\"kJ/kg.K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Increase in entropy = 0.163 kJ/kg.K\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.28 Page no : 274" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "p1 = 7*10**5; \t\t#Pa\n", + "T1 = 733.; \t\t\t#K\n", + "p2 = 1.012*10**5; \t#Pa\n", + "T2a = 433.; \t\t#K\n", + "y = 1.4;\n", + "cp = 1.005;\n", + "\n", + "# Calculations and Results\n", + "print (\"(i) To prove that the process is irreversible\")\n", + "T2 = T1*(p2/p1)**((y-1)/y);\n", + "print (\"T2 = %.3f\")% (T2)\n", + "print (\"But the actual temperature is 433K at th epressure of 1.012 bar, Hence the process is irreversible. Proved.\")\n", + "\n", + "\n", + "print (\"(ii) Change of entropy per kg of air\")\n", + "ds = cp*math.log(T2a/T2);\n", + "print (\"Increase of entropy = %.3f\")% (ds), (\"kJ/kg.K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) To prove that the process is irreversible\n", + "T2 = 421.820\n", + "But the actual temperature is 433K at th epressure of 1.012 bar, Hence the process is irreversible. Proved.\n", + "(ii) Change of entropy per kg of air\n", + "Increase of entropy = 0.026 kJ/kg.K\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.29 Page no : 275" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V1 = 0.3; \t\t\t#m**3\n", + "p1 = 4*10**5; \t\t#N/m**2\n", + "V2 = 0.08; \t\t\t#m**3\n", + "n = 1.25; \n", + "\n", + "# Calculations and Results\n", + "p2 = p1*(V1/V2)**n;\n", + "\n", + "dH = n*(p2*V2-p1*V1)/(n-1)/10**3;\n", + "print (\"(i) Change in enthalpy\"), (\"dH = %.3f\")% (dH), (\"kJ\")\n", + "\n", + "dU = dH-(p2*V2 - p1*V1)/10**3;\n", + "print (\"(ii) Change in internal energy\"),(\"dU = %.3f\")% (dU), (\"kJ\")\n", + "\n", + "dS = 0;\n", + "print (\"(iii) Change in entropy\"),(\"dS\"), (dS)\n", + "\n", + "Q = 0;\n", + "print (\"(iv)Heat transfer\"),(\"Q = \"), (Q)\n", + "\n", + "W = Q-dU;\n", + "print (\"(v) Work transfer\"),(\"W = %.3f\")%(W),(\"kJ\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Change in enthalpy dH = 234.947 kJ\n", + "(ii) Change in internal energy dU = 187.958 kJ\n", + "(iii) Change in entropy dS 0\n", + "(iv)Heat transfer Q = 0\n", + "(v) Work transfer W = -187.958 kJ\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.30 Page no : 277" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "m = 20.; \t\t\t#kg\n", + "p1 = 4.*10**5; \t\t\t#Pa\n", + "p2 = 8.*10**5; \t\t\t#Pa\n", + "V1 = 4.; \t\t\t#m**3\n", + "V2 = V1;\n", + "cp = 1.04; \t\t\t#kJ/kg.K\n", + "cv = 0.7432; \t\t\t#kJ/kg.K\n", + "R = cp-cv;\n", + "T1 = p1*V1/R/1000.; \t\t\t#kg.K; T = mass*temperature\n", + "T2 = p2*V2/R/1000.; \t\t\t#kg.K\n", + "\n", + "# Calculations and Results\n", + "dU = cv*(T2-T1);\n", + "print (\"(i) Change in internal energy\"),(\"dU = %.3f\")% (dU), (\"kJ\")\n", + "\n", + "Q = 0;\n", + "W = Q-dU;\n", + "print (\"(ii) Work done\"),(\"W %.3f\")% (W), (\"kJ\")\n", + "\n", + "print (\"(iii) Heat transferred = \"), (Q)\n", + "\n", + "dS = m*cv*math.log(T2/T1);\n", + "print (\"(iv) Change in entropy = %.3f\")%(dS), (\"kJ/K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Change in internal energy dU = 4006.469 kJ\n", + "(ii) Work done W -4006.469 kJ\n", + "(iii) Heat transferred = 0\n", + "(iv) Change in entropy = 10.303 kJ/K\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.31 Page no : 278" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from matplotlib.pyplot import *\n", + "%pylab inline\n", + "\n", + "# Variables\n", + "V1 = 5.; \t\t\t#m**3\n", + "p1 = 2.*10**5; \t\t\t#Pa\n", + "T1 = 300.; \t\t\t#K\n", + "p2 = 6.*10**5; \t\t\t#Pa\n", + "p3 = 2.*10**5; \t\t\t#Pa\n", + "R = 287.;\n", + "n = 1.3;\n", + "y = 1.4;\n", + "\n", + "# Calculations and Results\n", + "m = p1*V1/R/T1;\n", + "T2 = T1*(p2/p1)**((n-1)/n);\n", + "T3 = T2*(p3/p2)**((y-1)/y);\n", + "W_12 = m*R*(T1-T2)/(n-1)/1000; \t\t\t#polytropic compression\n", + "W_23 = m*R*(T2-T3)/(y-1)/1000; \t\t\t#Adiabatic expansion\n", + "\n", + "\n", + "W_net = W_12+W_23;\n", + "print (\"Net work done on the air = %.3f\")%(-W_net), (\"kJ\")\n", + "\n", + "T = [T1, 310, 320, 330, 340, 350, 360, 370, 380, T2];\n", + "def f(T):\n", + " return (y-n)/(y-1)/(1-n)*R/10**3*math.log(T);\n", + "\n", + "s = [f(T1), f(310), f(320), f(330), f(340), f(350), f(360), f(370), f(380), f(T2)]\n", + "\n", + "plot(s,T)\n", + "\n", + "T = [T2, T3];\n", + "s = [f(T2), f(T2)];\n", + "plot(s,T,'r')\n", + "\n", + "# Answers are slightly diffferent because of rounding error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "Net work done on the air = 94.023 kJ\n" + ] + }, + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "WARNING: pylab import has clobbered these variables: ['f', 'draw_if_interactive']\n", + "`%pylab --no-import-all` prevents importing * from pylab and numpy\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 9, + "text": [ + "[<matplotlib.lines.Line2D at 0x2aa0d90>]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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TExPD+vXrAXC73WRmZuJ2uwkNDSU/P7/FpiIREXFWq0NE/XJRDREVEWk3R4aI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\nkSCmIiAiEsT+P3S/G55r8UZJAAAAAElFTkSuQmCC\n", + "text": [ + "<matplotlib.figure.Figure at 0x2aa0bd0>" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.32 Page no : 279" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Variables\n", + "V1 = 0.004; \t\t\t#m**3\n", + "p1 = 1.*10**5; \t\t\t#Pa\n", + "T1 = 300.; \t\t\t#K\n", + "T2 = 400.; \t\t\t#K\n", + "y = 1.4;\n", + "M = 28.;\n", + "R0 = 8.314;\n", + "R = R0/M;\n", + "\n", + "# Calculations and Results\n", + "print (\"(i) The heat supplied\")\n", + "m = p1*V1/R/1000/T1; \t\t\t#kg\n", + "cv = R/(y-1);\n", + "Q = m*cv*(T2-T1);\n", + "print (\"Q %.3f\")%(Q), (\"kJ\")\n", + "\n", + "print (\"(ii) The entropy change\")\n", + "dS = m*cv*math.log(T2/T1);\n", + "print (\"dS = %.8f\")%(dS), (\"kJ/kg.K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) The heat supplied\n", + "Q 0.333 kJ\n", + "(ii) The entropy change\n", + "dS = 0.00095894 kJ/kg.K\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.33 Page no : 279" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V1 = 0.05; \t\t\t#m**3\n", + "p1 = 1.*10**5; \t\t\t#Pa\n", + "T1 = 280.; \t\t\t#K\n", + "p2 = 5.*10**5; \t\t\t#Pa\n", + "\n", + "# Calculations\n", + "print (\"(i) Change in entropy\")\n", + "R0 = 8.314;\n", + "M = 28.;\n", + "R = R0/M;\n", + "m = p1*V1/R/T1/1000;\n", + "dS = m*R*math.log(p1/p2);\n", + "\n", + "# Results\n", + "print (\"dS = %.3f\")%(dS), (\"kJ/K\")\n", + "\n", + "print (\"(ii)Work done\")\n", + "Q = T1*dS;\n", + "print (\"Q = %.3f\")%(Q),(\"kJ\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Change in entropy\n", + "dS = -0.029 kJ/K\n", + "(ii)Work done\n", + "Q = -8.047 kJ\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.34 Page no : 280" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "R = 0.287; \t\t\t#kJ/kg.K\n", + "m = 1.; \t\t\t#kg\n", + "p1 = 8.*10**5; \t\t\t#Pa\n", + "p2 = 1.6*10**5; \t\t\t#Pa\n", + "T1 = 380.; \t\t\t#K\n", + "n = 1.2;\n", + "y = 1.4;\n", + "\n", + "\n", + "# Calculations and Results\n", + "print (\"(i) Final specific volume and temperature\")\n", + "v1 = R*T1/p1*10**3; \t\t\t#m**3/kg\n", + "v2 = v1*(p1/p2)**(1/n);\n", + "T2 = T1*(p2/p1)**((n-1)/n);\n", + "\n", + "print (\"v2 = %.3f\")%(v2), (\"m**3/kg\")\n", + "print (\"T2 = %.3f\")% (T2),(\"K\")\n", + "\n", + "print (\"(ii) Change of internal energy, work done and heat interaction\")\n", + "dU = R/(y-1)*(T2-T1);\n", + "print (\"dU = %.3f\")%(dU), (\"kJ/kg\")\n", + "\n", + "W = R*(T1-T2)/(n-1);\n", + "print (\"W = %.3f\")%(W), (\"kJ/kg\")\n", + "\n", + "Q = dU + W;\n", + "print (\"Q = %.3f\")%(Q),(\"kJ/kg\")\n", + "\n", + "print (\"(iii) Change in entropy\")\n", + "dS = R/(y-1)*math.log(T2/T1) + R*math.log(v2/v1)\n", + "print (\"dS = %.3f\")%(dS),(\"kJ/kg.K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Final specific volume and temperature\n", + "v2 = 0.521 m**3/kg\n", + "T2 = 290.595 K\n", + "(ii) Change of internal energy, work done and heat interaction\n", + "dU = -64.148 kJ/kg\n", + "W = 128.296 kJ/kg\n", + "Q = 64.148 kJ/kg\n", + "(iii) Change in entropy\n", + "dS = 0.192 kJ/kg.K\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.35 Page no : 281" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%pylab inline\n", + "import math\n", + "from matplotlib.pyplot import *\n", + "\n", + "# Variables\n", + "y = 1.4;\n", + "cv = 0.718; \t\t#kJ/kg.K\n", + "m = 1.; \t\t\t #kg\n", + "T1 = 290.; \t\t\t#K\n", + "n = 1.3;\n", + "r = 16.;\n", + "y = 1.4;\n", + "\n", + "# Calculations and Results\n", + "T2 = T1*(r)**(n-1);\n", + "\n", + "print (\"(a)\")\n", + "\n", + "T = [T1, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 550, 560, 570, 580, 590, 600, 610, 620, 630, 640, 650, 660, T2];\n", + "def f(T):\n", + " return (y-n)*cv/(1-n)/10**3*math.log(T);\n", + "\n", + "s = [f(T1),f(300),f(310),f(320),f(330),f(340),f(350),f(360),f(370),f(380),f(390),f(400),f(410),f(420),f(430),f(440),f(450),f(460),f(470),f(480),f(490),f(500),f(510),f(520),f(530),f(540),f(550),f(560),f(570),f(580),f(590),f(600),f(610),f(620),f(630),f(640),f(650),f(660), f(T2)];\n", + "plot(s,T)\n", + "\n", + "T = [0, T2];\n", + "s = [f(T2), f(T2)];\n", + "plot(s,T,'r--')\n", + "\n", + "T = [0 ,T1];\n", + "s = [f(T1),f(T1)];\n", + "plot(s,T,'r--')\n", + "\n", + "T = [T1 ,T2];\n", + "s = [f(T1), f(T2)];\n", + "plot(s,T,'r--' )\n", + "suptitle(\"T-S diagram\")\n", + "xlabel(\"S\")\n", + "ylabel(\"T\")\n", + "text(-0.00150,400,\"pV**n = C\")\n", + "\n", + "print (\"(b)Entropy change\")\n", + "dS = cv*((n-y)/(n-1))*math.log(T2/T1);\n", + "print (\"dS = %.3f\")%(dS), (\"kJ/kg.K\")\n", + "print (\"There is decrease in entropy\")\n", + "\n", + "Q = cv*((y-n)/(n-1))*(T1-T2);\n", + "Tmean = (T1+T2)/2;\n", + "dS_app = Q/Tmean;\n", + "\n", + "error = ((-dS) - (-dS_app))/(-dS) * 100;\n", + "print (\"age error = %.3f\")%(error), (\"%\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "(a)\n", + "(b)Entropy change" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "dS = -0.199 kJ/kg.K\n", + "There is decrease in entropy\n", + "age error = 5.393 %\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "<matplotlib.figure.Figure at 0x3b860d0>" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.36 Page no : 282" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from matplotlib.pyplot import *\n", + "from numpy import *\n", + "# Variables\n", + "cp = 1.005; \t\t\t#kJ/kg.K\n", + "R = 0.287; \t\t\t#kJ/kg.K\n", + "V1 = 1.2; \t\t\t#m**3\n", + "p1 = 1.*10**5; \t\t\t#Pa\n", + "p2 = p1;\n", + "T1 = 300.; \t\t\t#K\n", + "T2 = 600.; \t\t\t#K\n", + "T3 = T1;\n", + "p1 = 1.*10**5; \t\t\t#Pa\n", + "cv = cp-R;\n", + "\n", + "# Calculations and Results\n", + "print (\"(i) The net heat flow\")\n", + "m = p1*V1/R/1000/T1; \t\t\t#kg\n", + "Q = m*R*(T2-T1);\n", + "print (\"Q = \"), (Q), (\"kJ\")\n", + "\n", + "print (\"(ii) The overall change in entropy\")\n", + "dS_12 = m*cp*math.log(T2/T1);\n", + "dS_23 = m*(cp-R)*math.log(T3/T2); \t\t\t#cv = cp-R\n", + "dS_overall = dS_12+dS_23;\n", + "print (\"Overall change in entropy = %.3f\")%(dS_overall),(\"kJ/K\")\n", + "\n", + "s = linspace(math.sqrt(300),math.sqrt(600),100);\n", + "T = s**2;\n", + "plot(s,T)\n", + "\n", + "s = linspace(22.18,math.sqrt(600),100)\n", + "T = 10*(s-16.725)**2;\n", + "plot(s,T,'r')\n", + "\n", + "s = [17, 25];\n", + "T = [600, 600];\n", + "plot(s,T,'--')\n", + "\n", + "s = [17 ,25];\n", + "T = [300 ,300];\n", + "plot(s,T,'--')\n", + "\n", + "suptitle(\"T-s diagram \")\n", + "xlabel(\"S\")\n", + "ylabel(\"T\")\n", + "text(24,400,\"v = C\")\n", + "text(20,450,\"p = C\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) The net heat flow\n", + "Q = 120.0 kJ\n", + "(ii) The overall change in entropy\n", + "Overall change in entropy = 0.277 kJ/K\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 2, + "text": [ + "<matplotlib.text.Text at 0x4787450>" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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SQog/UlSk90FaulS/To8adZX7IV2NQ4ege3e9n7cLbcvtUiuki4qKKCoqAuD06dOsW7eO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\n1vLUqXDXXdX9kwpRx+zfr7c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+ "text": [ + "<matplotlib.figure.Figure at 0x46d17d0>" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.37 Page no : 283" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from matplotlib.pyplot import *\n", + "\n", + "# Variables\n", + "cv = 0.718; \t\t\t#kJ/kg.K\n", + "R = 0.287 \t\t\t#kJ/kg.K\n", + "p1 = 1.*10**5; \t\t\t#Pa\n", + "T1 = 300. \t\t\t#K\n", + "V1 = 0.018; \t\t\t#m**3\n", + "p2 = 5.*10**5 \t\t\t#Pa\n", + "T3 = T1;\n", + "cp = cv+R;\n", + "p3 = p2;\n", + "\n", + "# Calculations and Results\n", + "m = p1*V1/R/T1/1000; \t\t\t#kg\n", + "T2 = T1*p2/p1;\n", + "\n", + "print (\"(i) constant volume process\")\n", + "dS_12 = m*cv*math.log(T2/T1);\n", + "print (\"dS = %.3f\")%(dS_12), (\"kJ/K\")\n", + "\n", + "print (\"(ii) Constant prssure process \")\n", + "dS_23 = m*cp*math.log(T3/T2);\n", + "print (\"dS = %.3f\")%(dS_23), (\"kJ/K\")\n", + "\n", + "print (\"(iii) Isothermal process\")\n", + "dS_31 = m*R*math.log(p3/p1);\n", + "print (\"dS = %.5f\")%(dS_31),(\"kJ/K\")\n", + "\n", + "print (\"T-s diagram\")\n", + "s = linspace(math.sqrt(300),math.sqrt(600),72);\n", + "T = s**2;\n", + "#plot(s,T)\n", + "\n", + "s = linspace(22.18,math.sqrt(600),24)\n", + "T = 10*(s-16.725)**2;\n", + "#plot(s,T,'r')\n", + "\n", + "s = [math.sqrt(300), 22.18];\n", + "T = [300 ,300];\n", + "#plot(s,T,'g')\n", + "\n", + "print (\"p-V diagram\")\n", + "\n", + "V = [0.018, 0.018];\n", + "p = [1 ,5];\n", + "#plot(V,p)\n", + "\n", + "p = [5 ,5];\n", + "V = [0.0036, 0.018];\n", + "#plot(V,p,'r')\n", + "\n", + "V = linspace(0.0036,0.018,145)\n", + "\n", + "def f():\n", + " return 1*0.018/V;\n", + "f1 = f()\n", + "\n", + "plot(V,f1,'g')\n", + "suptitle(\"p-V diagram\")\n", + "xlabel(\"V\")\n", + "ylabel(\"p\")\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) constant volume process\n", + "dS = 0.024 kJ/K\n", + "(ii) Constant prssure process \n", + "dS = -0.034 kJ/K\n", + "(iii) Isothermal process\n", + "dS = 0.00966 kJ/K\n", + "T-s diagram\n", + "p-V diagram\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 3, + "text": [ + "<matplotlib.text.Text at 0x4047ad0>" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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p06eYNGkSZs6cWa0kAMDKygo5OTmqx7m5ubCyshIrDjVxTu2dcHjWYbyveB/z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\n6sSiICKiOrEoiIioTiwKIiKq0/8HJIEAIIPDm7IAAAAASUVORK5CYII=\n", + "text": [ + "<matplotlib.figure.Figure at 0x4232ad0>" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.39 Page no : 285" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "m = 4; \t\t\t #kg\n", + "T1 = 400; \t\t\t#K\n", + "T2 = 500; \t\t\t#K\n", + "\n", + "# Calculations\n", + "def f12( T): \n", + "\t return m*(0.48+0.0096*T)/T\n", + "\n", + "dS = quad(f12, T1,T2)[0]\n", + "\n", + "# Results\n", + "print (\"dS = %.3f\")%(dS), (\"kJ\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "dS = 4.268 kJ\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.40 Page no : 286" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "p1 = 1*10**5; \t\t\t#Pa\n", + "T1 = 273; \t\t\t#K\n", + "p2 = 25*10**5; \t\t\t#Pa\n", + "T2 = 750; \t\t\t#K\n", + "R = 0.29; \t\t\t#kJ/kg.K ; cp = 0.85+0.00025*T; cv = 0.56+0.00025*T; R = cp-cv;\n", + "\n", + "# Calculations\n", + "v2 = R*T2/p2;\n", + "v1 = R*T1/p1;\n", + "\n", + "def f8( T): \n", + "\t return (0.56+0.00025*T)/T\n", + "\n", + "def f9(v):\n", + " return R/v\n", + "ds = quad(f8, T1, T2)[0] + quad(f9,v1,v2)[0]\n", + "\n", + "# Results\n", + "print (\"ds = %.3f\")%(ds),(\"kJ/kg K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ds = 0.045 kJ/kg K\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.41 Page no : 287" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "cv = 0.715; \t\t\t#kJ/kg K\n", + "R = 0.287; \t\t\t#kJ/kg K\n", + "V_A = 0.25; \t\t\t#m**3\n", + "p_Ai = 1.4; \t\t\t#bar\n", + "T_Ai = 290; \t\t\t#K\n", + "V_B = 0.25; \t\t\t#m**3\n", + "p_Bi = 4.2; \t\t\t#bar\n", + "T_Bi = 440; \t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "print (\"(i) Final equilibrium temperature\")\n", + "m_A = p_Ai * 10**5 * V_A / R / 1000/ T_Ai; \t\t\t#kg\n", + "m_B = p_Bi * 10**5 * V_B / R / 1000/ T_Bi; \t\t\t#kg\n", + "\n", + "T_f = (m_B * T_Bi + m_A * T_Ai)/(m_A + m_B);\n", + "print (\"T_f = %.3f\")% (T_f), (\"K\")\n", + "\n", + "\n", + "print (\"(ii) Final pressure on each side of the diaphragm\")\n", + "p_Af = p_Ai*T_f/T_Ai;\n", + "print (\"p_Af = %.3f\")%(p_Af),(\"bar\")\n", + "\n", + "p_Bf = p_Bi*T_f/T_Bi;\n", + "print (\"p_Bf = %.3f\")%(p_Bf),(\"bar\")\n", + "\n", + "\n", + "print (\"(iii) Entropy change of the system\")\n", + "dS_A = m_A*cv*math.log(T_f/T_Ai);\n", + "dS_B = m_B*cv*math.log(T_f/T_Bi);\n", + "dS_net = dS_A+dS_B;\n", + "print (\"Net change of entropy = %.3f\")%(dS_net), (\"kJ/K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Final equilibrium temperature\n", + "T_f = 389.618 K\n", + "(ii) Final pressure on each side of the diaphragm\n", + "p_Af = 1.881 bar\n", + "p_Bf = 3.719 bar\n", + "(iii) Entropy change of the system\n", + "Net change of entropy = 0.016 kJ/K\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.42 Page no : 287" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "cv = 1.25; \t\t\t#kJ/kg.K\n", + "T1 = 530.; \t\t\t#K\n", + "v1 = 0.0624; \t\t\t#m**3/kg\n", + "v2 = 0.186; \t\t\t#m**3/kg\n", + "dT_31 = 25.; \t\t\t#K\n", + "T3 = T1-dT_31; \t\t\t#K\n", + "dT_21 = 165.; \t\t\t#K\n", + "\n", + "# Calculations\n", + "T2 = T1-dT_21; \t\t\t#K\n", + "# Path 1-2 : Reversible adiabatic process\n", + "ds_12 = 0;\n", + "v3 = 0.186; \t\t\t#m**3/kg\n", + "v3 = v2;\n", + "ds_13 = cv*math.log(T3/T2);\n", + "\n", + "# Results\n", + "print (\"Chang in entropy = %.4f\")%(ds_13), (\"kJ/kgK\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Chang in entropy = 0.4058 kJ/kgK\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.44 Page no : 289" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import *\n", + "\n", + "# Variables\n", + "T1 = 500.; \t\t\t#K\n", + "T2 = 400.; \t\t\t#K\n", + "T3 = 300.; \t\t\t#K\n", + "Q1 = 1500.; \t\t\t#kJ/min\n", + "W = 200.; \t\t\t#kJ/min\n", + "\n", + "# Calculations and Results\n", + "A = [[1,-1],[(1./400),(-1./300)]];\n", + "B = [(-1300),(-3)];\n", + "X = linalg.solve(A,B)\n", + "\n", + "Q2 = X[0];\n", + "print (\"Q2 = \"), (Q2), (\"kJ/min\")\n", + "\n", + "Q3 = X[1];\n", + "print (\"Q3 = \"), (Q3), (\"kJ/min\")\n", + "\n", + "print (\"(ii) Entropy change \")\n", + "dS1 = (-Q1)/T1;\n", + "print (\"Entropy change of source 1 = \"), (dS1), (\"kJ/K\")\n", + "\n", + "dS2 = (-Q2)/T2;\n", + "print (\"Entropy change of math.sink 2 = \"), (dS2), (\"kJ/K\")\n", + "\n", + "dS3 = Q3/T3;\n", + "print (\"Entropy change of source 3 = \"),(dS3), (\"kJ/K\")\n", + "\n", + "\n", + "print (\"(iii) Net change of the entropy\")\n", + "dSnet = dS1 + dS2 + dS3;\n", + "print (\"dSnet = %d\")% (dSnet)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Q2 = -1600.0 kJ/min\n", + "Q3 = -300.0 kJ/min\n", + "(ii) Entropy change \n", + "Entropy change of source 1 = -3.0 kJ/K\n", + "Entropy change of math.sink 2 = 4.0 kJ/K\n", + "Entropy change of source 3 = -1.0 kJ/K\n", + "(iii) Net change of the entropy\n", + "dSnet = 0\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.45 Page no : 291" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "T1 = 250; \t\t\t#K\n", + "T2 = 125; \t\t\t#K\n", + "\n", + "# Calculations\n", + "#cv = 0.0045*T**2\n", + "def f10( T): \n", + "\t return 0.045*T**2\n", + "\n", + "Q1 = quad(f10, T1, T2)[0]\n", + "\n", + "def f11( T): \n", + "\t return 0.045*T\n", + "\n", + "dS_system = quad(f11, T1, T2)[0]\n", + "\n", + "dS_universe = 0;\n", + "\n", + "W_max = ((-Q1) -T2*(dS_universe-dS_system))/1000;\n", + "\n", + "# Results\n", + "print (\"W_max = %.3f\")%(W_max), (\"kJ\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "W_max = 73.242 kJ\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.46 Page no : 292" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "cp = 1.005; \t\t\t#kJ/kg K\n", + "T_A = 333.; \t\t\t#K\n", + "T_B = 288.; \t\t\t#K\n", + "p_A = 140.; \t\t\t#kPa\n", + "p_B = 110.; \t\t\t#kPa\n", + "#h = cp*T\n", + "#v/T = 0.287/p\n", + "\n", + "# Calculations\n", + "def f9( T): \n", + "\t return cp/T\n", + "\n", + "def f10(p):\n", + " return 0.287/p\n", + " \n", + "ds_system = quad(f9, T_B, T_A)[0] + quad(f10,p_A,p_B)[0]\n", + "ds_surr = 0;\n", + "ds_universe = ds_system+ds_surr;\n", + "\n", + "# Results\n", + "print (\"change in entropy of universe = -%.4f\")% (ds_universe), (\"kJ/kgK\")\n", + "print (\"Since change in entropy of universe from A to B is -ve\")\n", + "print (\"The flow is from B to A\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "change in entropy of universe = -0.0767 kJ/kgK\n", + "Since change in entropy of universe from A to B is -ve\n", + "The flow is from B to A\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.47 Page no : 292" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "m1 = 3.; \t\t\t#kg\n", + "m2 = 4.; \t\t\t#kg\n", + "T0 = 273.; \t\t\t#K\n", + "T1 = 80.+273; \t\t\t#K\n", + "T2 = 15.+273; \t\t\t#K\n", + "c_pw = 4.187; \t\t\t#kJ/kgK\n", + "\n", + "# Calculations\n", + "tm = (m1*T1 + m2*T2)/(m1+m2);\n", + "Si = m1*c_pw*math.log(T1/T0) + m2*c_pw*math.log(T2/T0);\n", + "Sf = (m1+m2)*c_pw*math.log(tm/T0);\n", + "dS = Sf-Si;\n", + "\n", + "# Results\n", + "print (\"Net change in entropy = %.3f\")%(dS),(\"kJ/K\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Net change in entropy = 0.150 kJ/K\n" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.49 Page no : 294" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "# Variables\n", + "m = 1.; \t\t\t#kg\n", + "T1 = 273.; \t\t\t#K\n", + "T2 = 363.; \t\t\t#K\n", + "c = 4.187;\n", + "\n", + "# Calculations and Results\n", + "print (\"(a)\")\n", + "ds_water = m*c*math.log(T2/T1);\n", + "print (\"(i) Entropy of water = %.3f\")%(ds_water), (\"kJ/kgK\")\n", + "\n", + "print (\"(ii) Entropy change of the reservoir \")\n", + "Q = m*c*(T2-T1);\n", + "ds_reservoir = -Q/T2;\n", + "print (\"ds_reservoir = %.3f\")% (ds_reservoir), (\"kJ/K\")\n", + "\n", + "ds_universe = ds_water+ds_reservoir;\n", + "print (\"(iii) Entropy change of universe = %.3f\")% (ds_universe), (\"kJ/K\")\n", + "\n", + "print (\"(b)\")\n", + "T3 = 313; \t\t\t#K\n", + "ds_water = m*c*(math.log(T3/T1) + math.log(T2/T3));\n", + "ds_res1 = -m*c*(T3-T1)/T3;\n", + "ds_res2 = -m*c*(T2-T3)/T2;\n", + "\n", + "ds_universe = ds_water+ds_res1+ds_res2;\n", + "print (\"(iii) Entropy change of universe = %.3f\")%(ds_universe), (\"kJ/K\")\n", + "\n", + "print (\"(c) The entropy change of universe would be less and less, if the water is heated in more and more stages, by bringing\")\n", + "print (\"the water in contact successively with more and more heat reservoirs, each succeeding reservoir being at a higher temperature\") \n", + "print (\"than the preceding one.\")\n", + "\n", + "print (\"When water is heated in infinite steps, by bringing in contact with an infinite number of reservoirs in succession, so that\") \n", + "print (\"at any insmath.tant the temperature difference between the water and the reservoir in contact is infinitesimally small, then\") \n", + "print (\"the entropy change of the universe would be zero and the water would be reversibly heated.\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)\n", + "(i) Entropy of water = 1.193 kJ/kgK\n", + "(ii) Entropy change of the reservoir \n", + "ds_reservoir = -1.038 kJ/K\n", + "(iii) Entropy change of universe = 0.155 kJ/K\n", + "(b)\n", + "(iii) Entropy change of universe = 0.081 kJ/K\n", + "(c) The entropy change of universe would be less and less, if the water is heated in more and more stages, by bringing\n", + "the water in contact successively with more and more heat reservoirs, each succeeding reservoir being at a higher temperature\n", + "than the preceding one.\n", + "When water is heated in infinite steps, by bringing in contact with an infinite number of reservoirs in succession, so that\n", + "at any insmath.tant the temperature difference between the water and the reservoir in contact is infinitesimally small, then\n", + "the entropy change of the universe would be zero and the water would be reversibly heated.\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.50 Page no : 295" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "# Variables\n", + "cp = 2.093; \t\t\t#kJ/kg0C\n", + "c = 4.187;\n", + "Lf = 333.33; \t\t\t#kJ/kg\n", + "m = 1.; \t\t\t#kg\n", + "T0 = 273.; \t\t\t#K\n", + "T1 = 268.; \t\t\t#K\n", + "T2 = 298.; \t\t\t#K\n", + "\n", + "# Calculations and Results\n", + "Q_s = m*cp*(T0-T1);\n", + "Q_f = m*Lf;\n", + "Q_l = m*c*(T2-T0);\n", + "Q = Q_s+Q_f+Q_l;\n", + "\n", + "print (\"(i) Entropy increase of the universe\")\n", + "ds_atm = -Q/T2;\n", + "ds_sys1 = m*cp*math.log(T0/T1);\n", + "ds_sys2 = Lf/T0;\n", + "ds_sys3 = m*c*math.log(T2/T0);\n", + "ds_total = ds_sys1+ds_sys2+ds_sys3;\n", + "ds_universe = ds_total+ds_atm;\n", + "\n", + "print (\"Entropy increase of universe = %.3f\")%(ds_universe), (\"kJ/K\")\n", + "\n", + "\n", + "print (\"(ii) Minimum amount of work necessary to convert the water back into ice at \u2013 5\u00b0C, Wmin.\")\n", + "dS_refrigerator = 0;\n", + "\n", + "dS_system = -1.6263; \t\t\t#kJ/kg K\n", + "T = 298; \t\t\t#K\n", + "#For minimum work \n", + "W_min = T*(-dS_system)-Q;\n", + "\n", + "print (\"Minimum work done = %.3f\")% (W_min), (\"kJ\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) Entropy increase of the universe\n", + "Entropy increase of universe = 0.122 kJ/K\n", + "(ii) Minimum amount of work necessary to convert the water back into ice at \u2013 5\u00b0C, Wmin.\n", + "Minimum work done = 36.167 kJ\n" + ] + } + ], + "prompt_number": 43 + } + ], + "metadata": {} + } + ] +}
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