{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter No - 3 : Thermodynamic Processes\n", " " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.1 - Page No : 66" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "# Given data\n", "P = 2.15 * 10**5 # in N/m**2\n", "T = 20 # in degree C \n", "T = T + 273 # in K\n", "V = 0.20 # in m**3\n", "R = 0.2927 # in kJ/kg-K\n", "R = R * 10**3 # in J/kg-K\n", "m = (P*V)/(T*R) # in kg\n", "Q = 20*10**3 # in J\n", "C_v = 0.706*10**3 # in J/kg-K\n", "theta = Q/(m*C_v) # in degree C\n", "T = T - 273 # in degree C\n", "T1 = theta + T # new temp. in degree C\n", "print \"New temperature = %0.1f degree C \" %T1\n", "T1 = T1 + 273 # in K\n", "T = T + 273 # in K\n", "P2 = P * (T1/T) # in N/m**2\n", "P2 = P2 * 10**-3# in kN/m**2\n", "print \"New pressure = %0.3f kN/m**2 \" %P2" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "New temperature = 76.5 degree C \n", "New pressure = 256.459 kN/m**2 \n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.2 - Page No : 66" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "P = 350# in kN/m**2\n", "P = P * 10**3# in N/m**2\n", "m = 1# in kg\n", "m = m * 10**3# in gram\n", "V = 0.35# in m**3\n", "C_p = 1.005# in kJ/kg-K\n", "C_v = 0.710# in kJ/kg-K\n", "R = C_p - C_v# in kJ/kg-K\n", "T = (P*V)/(m*R) # in K\n", "T = T - 273# in degree C\n", "print \"The intial temperature = %0.0f K \" %(T+273)\n", "T = T + 273# in K\n", "T1 = 316# in degree C\n", "T1 = T1 + 273# in K\n", "P2 = P * (T1/T) # in N/m**2\n", "P2 = P2 * 10**-3# in kN/m**2\n", "print \"The final pressure of air = %0.1f kN/m**2 \" %P2\n", "T = T - 273# in degree C\n", "T1 = T1 - 273# in degree C\n", "m = m * 10**-3# in kg\n", "Q = m * C_v * (T1-T) # in kJ\n", "print \"Heat added = %0.2f kJ \" %Q\n", "G = m*C_v * (T1-T) # Gain of internal energy # in kJ\n", "print \"Gain of internal energy = %0.2f kJ \" %G\n", "G_enthalpy = m*C_p*(T1-T) # Gain of enthalpy in kJ\n", "print \"Gain of enthalpy = %0.2f kJ \" %G_enthalpy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The intial temperature = 415 K \n", "The final pressure of air = 496.4 kN/m**2 \n", "Heat added = 123.36 kJ \n", "Gain of internal energy = 123.36 kJ \n", "Gain of enthalpy = 174.61 kJ \n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.3 - Page No : 67" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "P = 3.2# in bar\n", "P = P * 10**5# in N/m**2\n", "R = 292.7# in kJ/kg-K\n", "C_p = 1.003# in kJ/kg-K\n", "m = 1#\n", "V1 = 0.3# in m**3\n", "V2 = 2*V1# in m**3\n", "W = P*(V2-V1) # in J\n", "W = W * 10**-3 # in kJ\n", "print \"The work done = %0.0f kJ \" %W\n", "T1 = (P*V1)/(m*R) # in K\n", "print \"The intail Temperature = %0.0f \u00b0C \" %(T1-273)\n", "T2 = T1*(V2/V1) # in K\n", "print \"The final temperature = %0.0f \u00b0C \" %(T2-273)\n", "Q = m*C_p*(T2-T1) # in kJ\n", "print \"The Heat added = %0.0f kJ \" %(Q)\n", "\n", "# Note: To evaluate the value of Heat added, \n", "# wrong value of T1 is putted (i.e 273 k at place of 328 K), so the answer of Heat added is wrong in the book." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The work done = 96 kJ \n", "The intail Temperature = 55 \u00b0C \n", "The final temperature = 383 \u00b0C \n", "The Heat added = 329 kJ \n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.4 - Page No : 67" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "R = 0.29# in kJ/kg-K\n", "R = R * 10**3# in J/kg-K\n", "C_p = 1.005# in kJ/kg-K\n", "T = 185# in degree C\n", "T = T + 273# in K\n", "T2 = 70+273# in K\n", "V1 = 0.23# in m**3\n", "P = 500# in kN/m**2\n", "P = P * 10**3# in N/m**2\n", "m = (P*V1)/(R*T) # in kg\n", "Q = m*C_p*(T2-T) # in kJ\n", "print \"Heat transferred = %0.2f kJ \" %Q\n", "print \"i.e. %0.2f kJ heat has been abstracted from the gas\" %(abs(Q))\n", "V2 = V1*(T2/T) # in m**3\n", "W = P * (V2-V1) # in J\n", "W= W*10**-3#in kJ\n", "print \"The work done = %0.0f kJ \" %W\n", "print \"i.e.\",round(abs(W),0),\"kJ work has been done on the gas \"\n", "R= R*10**-3# in kJ/kg-K\n", "C_v = C_p - R# in kJ/kg-K\n", "I_E = m*C_v*(T2-T) # Change in internal energy in kJ\n", "print \"Change in internal energy = %0.3f kJ \" %I_E\n", "print \"i.e.\",round(abs(I_E),3),\"kJ energy is decrease in internal energy\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat transferred = -100.07 kJ \n", "i.e. 100.07 kJ heat has been abstracted from the gas\n", "The work done = -29 kJ \n", "i.e. 29.0 kJ work has been done on the gas \n", "Change in internal energy = -71.193 kJ \n", "i.e. 71.193 kJ energy is decrease in internal energy\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.5 - Page No : 71" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "P1 = 1.1# in MN/m**2\n", "P1 = P1 * 10**6# in N/m**2\n", "V1 = 1.5# in m**3\n", "V2 = 7.5# in m**3\n", "P2 = (P1*V1)/V2# in kN/m**2\n", "P2 = P2 * 10**-6# in MN/m**2\n", "P2 = P2 * 10**3# in kN/m**2\n", "print \"The final pressure = %0.0f kN/m**2 \" %P2\n", "W = P1*V1*log(V2/V1) # in J\n", "W = W * 10**-4# in kJ\n", "print \"The work done = %0.0f kJ \" %int(W)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The final pressure = 220 kN/m**2 \n", "The work done = 265 kJ \n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.6 - Page No : 75" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "P1 = 2800000# in N/m**2\n", "P1 = P1 * 10**-6# in MN/m**2\n", "C_p = 1.024# in kJ/kg-K\n", "C_v = 0.7135# in kJ/kg-K\n", "V1 = 1# in m**3. (asuumed )\n", "V2 = 5*V1# in m**3\n", "T1 = 220# in degree C\n", "T1 = T1 + 273# in K\n", "Gamma = C_p/C_v#\n", "P2 = (P1*(V1)**Gamma)/((V2)**Gamma) # in MN/m**2\n", "print \"The final pressure = %0.3f MN/m**2 \" %P2\n", "T2 = (P2/P1)*V2*T1 # in K\n", "print \"The final temperature = %0.1f degree C \" %(T2-273)\n", "R = C_p-C_v# in kJ/kg-K\n", "W = (R*(T1-T2))/(Gamma - 1) # in kJ\n", "print \"Work done = %0.1f kJ \" %W" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The final pressure = 0.278 MN/m**2 \n", "The final temperature = -28.3 degree C \n", "Work done = 177.1 kJ \n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.7 - Page No : 76" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log10\n", "# Given data\n", "W = 89.947# in kJ\n", "T1 = 240# in degree C\n", "T1=T1+273# in K\n", "T2 = 115# in degree C\n", "T2=T2+273# in K\n", "C_v = W/(T1-T2) # in kJ/kg-K\n", "print \"The value of Cv = %0.3f kJ/kg-K \" %C_v\n", "V1 = 1# in m**3 (assumed)\n", "V2 = 2*V1# in m**3\n", "# (T1/T2) = (V2/V1)**(Gamma - 1)\n", "Gamma=log10(T1/T2)/log10(V2/V1)+1#\n", "Gamma = 1.4#\n", "C_p = Gamma * C_v# in kJ/kg-K\n", "print \"The value Cp = %0.3f kJ/kg-K \" %C_p" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of Cv = 0.720 kJ/kg-K \n", "The value Cp = 1.007 kJ/kg-K \n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.8 - Page No : 77" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "P = 7# in bar\n", "P = P *10**5# in N/m**2\n", "R = 0.287# in kJ/kg-K\n", "R=R*10**3# in J/kg-K\n", "Gamma = 1.4#\n", "T = 100# in degree C\n", "T = T + 273# in K\n", "V = (R*T)/P# in m**3\n", "print \"The volume of one kg of air = %0.3f m**3\" %V\n", "C_v = 0.718# in kJ/kg\n", "T=T-273# in degree C\n", "InternalEnergy= C_v*T# in kJ/kg\n", "print \"Internal energy of 1 kg air = %0.1f kJ/kg\" %InternalEnergy\n", "P1= P# in bar\n", "V1 = 1# in m**3 (assumed)\n", "V2 = 4 * V1# in m**3\n", "T1= T# in degree C\n", "T1=T1+273# in K\n", "P2 = (P * (V1)**Gamma)/((V2)**Gamma) # in N/m**2\n", "print \"The final pressure = %0.3f bar \" %(P2*10**-5)\n", "T2 = (P2*V2)/(P1*V1)*T1# in K\n", "T2 = T2 - 273# in degree \n", "print \"The final temperature = %0.1f degree C \" %T2\n", "I_E = C_v * T2# in kJ/kg\n", "print \"Internal energy = %0.2f kJ/kg \" %I_E" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The volume of one kg of air = 0.153 m**3\n", "Internal energy of 1 kg air = 71.8 kJ/kg\n", "The final pressure = 1.005 bar \n", "The final temperature = -58.8 degree C \n", "Internal energy = -42.20 kJ/kg \n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.9 - Page No : 78" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "Gamma = 1.41#\n", "C_v = 0.703# in kJ/kg-K\n", "P1 = 105# in kN/m**2\n", "P2 = 2835# in kN/m**2\n", "T1 = 15# in degree C\n", "T1 = T1 + 273# in K\n", "m = 0.2# in kg\n", "# Formula T2/T1 = (P2/P1)**((Gamma-1)/Gamma)\n", "T2 = T1*(P2/P1)**((Gamma-1)/Gamma) # in K\n", "T2 = T2 - 273# in degree C\n", "print \"The final temperature = %0.0f degree C \" %T2\n", "T2 = T2+273# in K\n", "I_E = m*C_v*(T2-T1) # in kJ\n", "print \"Change in internal energy = %0.3f kJ \" %I_E\n", "W = I_E# in kJ\n", "print \"Work done = %0.3f kJ \" %W\n", "\n", "# Note: There is an error to calculate the value of T2, and this wrong value is putted to evaluate \n", "# the value of Change in internal energy but the value of Change in internal energy is calculated correct." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The final temperature = 478 degree C \n", "Change in internal energy = 65.089 kJ \n", "Work done = 65.089 kJ \n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.10 - Page No : - Page No : 86" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import pi\n", "# Given data\n", "P1= 100# in N/m**2\n", "T1 = 30# in degree C\n", "T1 = T1 + 273# in K\n", "C_v = 0.718# in kJ/kg-K\n", "#C_v= C_v*10**3# in J/kg-K\n", "R = 287.1# in J/kg-K\n", "d = 15# in cm\n", "l = 20# in cm\n", "V = (pi/4)*(d)**2*l# in cm**3\n", "V = V * 10**-3# in litre\n", "Clear_V = 1.147# clearance volume \n", "Vol = V+Clear_V#volume of air at beginning of compression in litre\n", "ROC = Vol/Clear_V# Ratio of compression\n", "P2 = P1*(Vol/Clear_V)**1.2# in kN/m**2\n", "print \"The pressure at the end of compression = %0.1f kN/m**2 \" %P2\n", "T2 = (P2*Clear_V*T1)/(P1*Vol) # in K\n", "T2 = T2 - 273# in degree C\n", "T1 = T1 - 273# in degree C\n", "T = T2-T1# in degree C\n", "print \"The temperature at the end of compression = %0.1f degree C \" %T\n", "T1 = T1 + 273# in K\n", "m = (P1*Vol)/(R*T1) # in kg\n", "I_E = m*C_v*T# in kJ\n", "print \"The change in internal energy = %0.3f kJ \" %I_E" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The pressure at the end of compression = 540.7 kN/m**2 \n", "The temperature at the end of compression = 98.4 degree C \n", "The change in internal energy = 0.380 kJ \n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.11 - Page No : 87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "V1 = 2.5 # in litre\n", "P1 = 1400 # kN/m**2\n", "P2 = 280 # in kN/m**2\n", "T1 = 1100 # in \u00b0C\n", "T1 = T1 + 273 # in K\n", "n = 1.28\n", "V2 = V1*(P1/P2)**(1/1.28) # in litres\n", "print \"Final volume = %0.1f litres \" %V2\n", "T2 = T1*((P2*V2)/(P1*V1)) # in K\n", "T2 = T2 - 273# in degree C\n", "print \"Final temperature = %0.0f degree C \" %T2\n", "W = (P1* V1 - P2*V2)/(n-1) # in Joules\n", "print \"Work done = %0.2f kJ \" %(W*10**-3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Final volume = 8.8 litres \n", "Final temperature = 693 degree C \n", "Work done = 3.71 kJ \n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.12 - Page No : 87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "Gamma = 1.4#\n", "P1 = 780# in kN/m**2\n", "P2 = 100# in kN/m**2\n", "V1 = 750# in cm**3\n", "V1= V1*10**-6# in m**3\n", "V2 = (1/5)*V1# in m**3\n", "n = (log(P1/P2))/(log(V1/V2))\n", "print \"The value of index = %0.3f\" %n\n", "W = (P1*V2-P2*V1)/(1-n) # in kJ\n", "print \"Work done = %0.3f kJ \" %W\n", "print \"i.e.\",round(abs(W),4),\"kJ work is done on the gas\"\n", "Q = ((Gamma - n)/(Gamma-1)) * (-W) # in kJ\n", "print \"Heat rejected during Compression is :\",round(Q,4),\"kJ or\",round(Q*10**3),\"joules.\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of index = 1.276\n", "Work done = -0.152 kJ \n", "i.e. 0.152 kJ work is done on the gas\n", "Heat rejected during Compression is : 0.047 kJ or 47.0 joules.\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.13 - Page No : 90" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "T1 = 40# in degree C\n", "T1 = T1 +273# in K\n", "P2 = 50# in bar\n", "P1 = 1# in bar\n", "Gamma = 1.4#\n", "C_v = 0.718# in kJ/kg-K\n", "SpeHeat = 1.005# in kJ/kg-K\n", "HeatSupply= 125.6# in kJ/kg\n", "T2 = T1 * (P2/P1)**((Gamma-1)/Gamma) # in K\n", "C_p = C_v * (T2-T1) # in kJ/kg\n", "del_T = HeatSupply/SpeHeat# in degree C\n", "del_U = C_v * del_T# in kJ/kg\n", "print \"Change in internal energy = %0.1f kJ/kg \" %del_U\n", "T3 = T2 + del_T# in K\n", "del_Phi = SpeHeat * log(T3/T2) # in kJ/kg-K\n", "print \"Change in entropy during constant pressure = %0.3f kJ/kg-K \" %del_Phi" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in internal energy = 89.7 kJ/kg \n", "Change in entropy during constant pressure = 0.123 kJ/kg-K \n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.14 - Page No : 91" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "P1 = 30# in bar\n", "P1= P1*10**5# in N/m**2\n", "V1 = 0.85# in m**3\n", "V2 = 4.25# in m**3\n", "W = P1 *V1 * log(V2/V1) # in Joules\n", "W = W * 10**-3# in kJ\n", "T = 400# in K\n", "del_U = W/T# in kJ/K\n", "print \"Change in entropy = %0.3f kJ/K \" %del_U" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in entropy = 10.260 kJ/K \n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.15 - Page No : 91" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "C_P = 1.041# in kJ/kg-K\n", "C_V = 0.743# in kJ/kg-K\n", "R = C_P - C_V# in kJ/kg-K\n", "P1 = 140# in kN/m**2\n", "P2 = 1400# in kN/m**2\n", "V1 = 0.14# in m**3\n", "T1 = 25# in degree C\n", "T1 = T1 + 273# in K\n", "Gamma = 1.4#\n", "n = 1.25#\n", "m = (P1 * 10**3 *V1)/(R * 10**3 * T1) # in kg\n", "V2 = V1 * (P1/P2)**(1/n) # in m**3\n", "del_U = C_P * (log(V2/V1)) + C_V * (log(P2/P1)) # in kJ/kg-K\n", "del_U = m * del_U # in kJ/K\n", "print \"Part (i)\"\n", "print \"Change in entropy = %0.4f kJ/K \" %del_U\n", "T2 = T1 * (V1/V2)**(n-1) # in K\n", "del_U1 = C_P * (log(T2/T1)) - R*(log(P2/P1)) # in kJ/kg-K\n", "print \"Part (ii)\"\n", "print \"Change in entropy = %0.3f kJ/kg-K \" %del_U1\n", "del_U2 = C_V * (log(T2/T1)) + R*(log(V2/V1)) # in kJ/kg-K\n", "print \"Part (iii)\"\n", "print \"Change in entropy = %0.3f kJ/kg-K \" %del_U2\n", "del_U3 = C_V * (Gamma-n) * (log(V2/V1)) # in kJ/kg-K\n", "print \"Part (iv)\"\n", "print \"Change in entropy = %0.3f kJ/kg-K \" %del_U3\n", "del_U4 = C_V * ((Gamma-n)/(n-1)) * (log(T1/T2)) # in kJ/kg-K\n", "print \"Part (v)\"\n", "print \"change in entropy = %0.3f kJ/kg \" %del_U4\n", "del_U5 = C_V * ((Gamma-n)/n) * (log(P1/P2)) # in kJ/kg-K\n", "print \"Part (vi)\"\n", "print \"Change in entropy = %0.3f kJ/kg-k \" %del_U5" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part (i)\n", "Change in entropy = -0.0456 kJ/K \n", "Part (ii)\n", "Change in entropy = -0.207 kJ/kg-K \n", "Part (iii)\n", "Change in entropy = -0.207 kJ/kg-K \n", "Part (iv)\n", "Change in entropy = -0.205 kJ/kg-K \n", "Part (v)\n", "change in entropy = -0.205 kJ/kg \n", "Part (vi)\n", "Change in entropy = -0.205 kJ/kg-k \n" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.16 - Page No : 93 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "P1 = 1# in bar\n", "P2 = 15# in bar\n", "T1 = 0# in degree C\n", "T1 = T1 + 273# in K\n", "T2 = 200# in degree C\n", "T2 = T2 + 273# in K\n", "C_P = 1.005# in kJ/kg-K\n", "C_V = 0.718# in kJ/kg-K\n", "R = C_P-C_V# in kJ/kg-K\n", "del_U = C_P * (log(T2/T1)) - R*(log(P2/P1)) # in kJ/kg-K\n", "print \"Change in entropy = %0.3f kJ/kg-K \" %del_U" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in entropy = -0.225 kJ/kg-K \n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.17 - Page No : 94" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "C_V = 2.174# in kJ/kg-K\n", "R = 0.5196# in kJ/kg-K\n", "C_P = C_V+R# in kJ/kg-K\n", "V2 = 1# in m**3\n", "V1 = 8# in m**3\n", "P1 = 0.7# in bar\n", "P2 = 7# in bar\n", "del_U = C_P * (log(V2/V1)) + C_V * (log(P2/P1)) # in kJ/kg-K\n", "m = 0.9# in kg\n", "del_U = m * del_U# in kJ/K\n", "print \"Change in entropy = %0.3f kJ/K \" %del_U\n", "print \"It is a loss of entropy\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in entropy = -0.536 kJ/K \n", "It is a loss of entropy\n" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.18 - Page No : 95 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "C_P = 1.005# in kJ/kg-K\n", "C_V = 0.718# in kJ/kg-K\n", "R = C_P - C_V# in kJ/kg-K\n", "R= R*10**3#in J/kg-K\n", "P1 = 3*10**5#in N/m**2\n", "V1 = 1.5# m**3\n", "T1 = 15# in degree C\n", "T1 = T1 +273# in K\n", "m1 = (P1*V1)/(R* T1) # in kg\n", "m2 = m1+2#final mass of air in kg\n", "P2 = P1 * (m2/m1) # in kN/m**2\n", "T1 = T1 - 273# in degree C\n", "T2 = 0# in degree C\n", "m = 1# in kg\n", "del_U = m * C_P * (T1-T2) # in kJ\n", "print \"Total enthapy of air = %0.3f kJ \" %del_U" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Total enthapy of air = 15.075 kJ \n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.19 - Page No : 96" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "R = 0.287# in kJ/kg-K\n", "P1 = 30# in bar\n", "V1 = 0.12# in m**3\n", "m = 1.8# in kg\n", "U= 8.3143# in kJ/kg-mol-K\n", "T1 = (P1 * 10**5 * V1)/(m*R*10**3) # in K\n", "T1 = T1 - 273# in degree C\n", "print \"The temperature = %0.0f degree C \" %int(T1)\n", "m_m = U/R# in kg\n", "print \"The molecular mass = %0.2f kg \" %m_m\n", "V_s = V1/m# in m**3\n", "print \"The Specific volume = %0.4f m**3 \" %V_s\n", "V_m = V_s * m_m# in m**3\n", "print \"Molecular volume = %0.2f m**3 \" %V_m" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The temperature = 423 degree C \n", "The molecular mass = 28.97 kg \n", "The Specific volume = 0.0667 m**3 \n", "Molecular volume = 1.93 m**3 \n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.20 - Page No : 96" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "T=15+273#in K\n", "U= 8.3143# in kJ/kg-mol-K\n", "GasConstant = 0.618# in kJ/kg-K\n", "GasVolume= 1# in m**3 (assume)\n", "AirVolume= 1.5*GasVolume# in m**3\n", "P=760# in mm\n", "P= P/750# in bar\n", "P= P*10**5#in N/m**2\n", "MixtureVolume= GasVolume+AirVolume#in m**3\n", "PGM= GasVolume/MixtureVolume*100# in %\n", "print \"Percentage of gas by volume in the mixture = %0.0f %%\" %PGM\n", "PAM= AirVolume/MixtureVolume*100# in %\n", "print \"Percentage of air by volume in the mixture = %0.0f %%\" %PAM\n", "M1= U/0.287# in mol\n", "M2= U/0.618# in mol\n", "M= PAM/100*M1+PGM/100*M2# mass of mixture in mol\n", "R= U/M# gas constant in kJ/kg-K\n", "R= R*10**3#in J/kg-K\n", "print \"The gas constant = %0.3f kJ/kg-K\" %(R*10**-3)\n", "PAM1= PAM*M1/M# in %\n", "print \"Percentage of air by mass in the mixture = %0.2f %%\" %PAM1\n", "PGM1= PGM*M2/M# in %\n", "print \"Percentage of gas by mass in the mixture = %0.2f %%\" %PGM1\n", "Rho= P/(R*T) # kg/m**3\n", "print \"The density of the gas = %0.3f kg/m**3\" %Rho" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Percentage of gas by volume in the mixture = 40 %\n", "Percentage of air by volume in the mixture = 60 %\n", "The gas constant = 0.365 kJ/kg-K\n", "Percentage of air by mass in the mixture = 76.36 %\n", "Percentage of gas by mass in the mixture = 23.64 %\n", "The density of the gas = 0.963 kg/m**3\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.21 - Page No : 97" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from math import log\n", "# Given data\n", "Gamma = 1.4#\n", "P1 = 7# in bar\n", "P1= P1*10**5# in N/m**2\n", "V1 = 1.6# in m**3\n", "V2 = 8# in m**3\n", "P2 = (P1 * (V1)**(Gamma))/((V2)**(Gamma)) # in bar\n", "W1 = (P1*V1-P2*V2)/(Gamma-1) # work done by the gas during isentropic expansion in J\n", "Rho = V2/V1#\n", "W2 = P1*V1*(log(Rho)) # work done by the gas during isothermal expansion in J\n", "del_W = W2-W1# in J\n", "del_W = del_W*10**-3 # in kJ\n", "print \"Difference between the work done during isentropic and isothemal expansion = %0.0f kJ \" %del_W" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Difference between the work done during isentropic and isothemal expansion = 473 kJ \n" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.22 - Page No : 98" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "P1 = 1# in bar\n", "V1 = 400# in cm**3\n", "V2 = 80# in Cm**3\n", "T1 = 110# in degree C\n", "T1 = T1 + 273# in K\n", "Gamma = 1.3#\n", "P2 = P1*((V1/V2)**(Gamma)) # in bar\n", "print \"The pressure = %0.1f bar \" %P2\n", "T2 = T1 * ((P2*V2)/(P1*V1)) # in K\n", "T2 = int(T2-273)#in degree C\n", "print \"The temperature = %0.0f degree C \" %T2\n", "T2 = T2 + 273# in K\n", "m = 1#\n", "C_V = 0.75#\n", "del_U = m*C_V*(T2-T1) # in kJ\n", "print \"Change in internal energy = %0.2f kJ \" %del_U\n", "P1= P1*10**5# in N/m**2\n", "P2= P2*10**5# in N/m**2\n", "V1= V1*10**-3# in litre\n", "V2= V2*10**-3# in litre\n", "W = (P1*V1-P2*V2)/(Gamma-1) # in J\n", "W = abs(W * 10**-3) # in kJ\n", "print \"Work done = %0.2f kJ \" %W\n", "P3 = 40*10**5# in N/m**2\n", "T3 = (P3/P2) * T2# in K\n", "T3 = T3 - 273# in degree C\n", "print \"Temperature of gas = %0.0f degree C \" %T3" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The pressure = 8.1 bar \n", "The temperature = 347 degree C \n", "Change in internal energy = 177.75 kJ \n", "Work done = 82.75 kJ \n", "Temperature of gas = 2787 degree C \n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.23 - Page No : 99" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "C_P = 1.068# in kJ/kg-K\n", "C_V = 0.775#in kJ/kg-K\n", "R = C_P-C_V# in kJ/kg-K\n", "R= R*10**3# in J/kg-K\n", "P1 = 12# in bar\n", "P1= P1*10**5# in N/m**2\n", "V1 = 0.15#in m**3\n", "V2= 0.28# in m**3\n", "m = 1# in kg\n", "T1 = (P1*V1)/(R* m) # in K\n", "T2 = (T1 * (V2/V1)) # in K\n", "print \"Temperature at the end of Constant pressure = %0.3f \u00b0C \" %(T2-273)\n", "W = P1* (V2-V1) # in J\n", "W = W * 10**-3# in kJ\n", "Gamma = 1.38\n", "V3 = 1.5# in m**3\n", "T3 = T2/((V3/V2)**(Gamma-1)) # in K\n", "T3 = (T3 - 273)# in degree C\n", "print \"Temperature at the end of Isentropic = %0.0f \u00b0C \" %T3\n", "T3 = T3 + 273# in K\n", "W1 = m *C_V*(T2-T3) # work done during isentropic expansion in kJ\n", "W2 = W+W1# in kJ\n", "print \"Total Work done = %0.2f kJ \" %W2" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature at the end of Constant pressure = 873.758 \u00b0C \n", "Temperature at the end of Isentropic = 333 \u00b0C \n", "Total Work done = 575.08 kJ \n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.24 - Page No : 100" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.integrate import quad\n", "# Given data\n", "C_P = 1.005# in kJ/kg-K\n", "C_V = 0.718# in kJ/kg-K\n", "R = C_P-C_V# in kJ/kg-K\n", "P1 = 20#in bar\n", "P2 = 12# in bar\n", "T1 = 200#in degree C\n", "T1 = T1 + 273# in K\n", "T2 = 125#in degree c\n", "T2 = T2 + 273# in K\n", "V1 = (R*10**3*T1)/(P1*10**5) # in m**3\n", "V2 = (R*10**3*T2)/(P2*10**5) # in m**3\n", "def integrand(V):\n", " return -293*V+40\n", "ans, err = quad(integrand, 0.0679,0.0952)\n", "W = 10**5 * ans# in Joules\n", "W = round(W * 10**-3) # in kJ\n", "print \"Work done = %0.0f kJ \" %W\n", "m = 1# in kg\n", "del_U = m*C_V*(T2-T1) # change in internal energy in kJ\n", "print \"Change in internal energy = %0.2f kJ \" %del_U\n", "print \"Negative sign indicates that there is decrease in internal energy of the gas. \"\n", "C_Enthalpy = m*C_P*(T2-T1) # change in enthalpy in kJ\n", "print \"The change in enthalpy = %0.1f kJ\" %C_Enthalpy\n", "print \"Negative sign indicates that there is decrease in enthalpy of the gas\"\n", "Q = W+ del_U# in kJ\n", "print \"Heat transfer = %0.2f kJ \" %Q\n", "print \"Negative sign indicates that the heat is rejected by the air\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Work done = 44 kJ \n", "Change in internal energy = -53.85 kJ \n", "Negative sign indicates that there is decrease in internal energy of the gas. \n", "The change in enthalpy = -75.4 kJ\n", "Negative sign indicates that there is decrease in enthalpy of the gas\n", "Heat transfer = -9.85 kJ \n", "Negative sign indicates that the heat is rejected by the air\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.25 - Page No : 101" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "import math\n", "# Given data\n", "P1 = 14# in bar\n", "P3 = 2.222# in bar\n", "V3byV1 = P1/P3#\n", "P2 = 1.05# in bar\n", "Gamma = log(P1/P2)/log(V3byV1)\n", "C_P = 1.005# in kJ/kg-K\n", "C_V = C_P/Gamma# in kJ/kg-K\n", "T3 = 343# in degree C\n", "T3 = T3 + 273# in K\n", "T2 = math.ceil(T3*P2)/P3# in K\n", "m = 0.5# in kg \n", "del_U = m*C_V*(T2-T3) # in kJ\n", "print \"Change in internal energy = %0.3f kJ \" %del_U\n", "print \"i.e. there is a loss of\",round(abs(del_U),3),\"kJ of internal energy\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in internal energy = -115.986 kJ \n", "i.e. there is a loss of 115.986 kJ of internal energy\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.26 - Page No : 102" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "R = 0.26# in kJ/kg-K\n", "R = R * 10**3# in J/kg-K\n", "Gamma = 1.4#\n", "P1 = 3.1# MN/m**2\n", "P1 = P1 * 10**6# N/m**2\n", "P2 = 1.7# in MN/m**2\n", "P2 = P2 * 10**6# in N/m**2\n", "V1 = 500# in cm**3\n", "T = 18# in degree C\n", "T = T + 273# in K\n", "T2 = 15# in degree C\n", "T2 = T2 + 273# in K\n", "m = (P1*V1)/(R*T)*10**-3# in kg\n", "m_desh = (P2*V1)/(R*T2)*10**-3#in kg\n", "M = m-m_desh# in kg\n", "print \"The mass of oxygen = %0.2f kg \" %M\n", "R = R * 10**-3# in kJ/kg-K\n", "C_v = R/(Gamma-1) # in kJ/kg-K\n", "Q = m_desh*C_v * (T-T2) # in kJ\n", "print \"Heat transfered = %0.3f kJ \" %Q" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The mass of oxygen = 9.13 kg \n", "Heat transfered = 22.135 kJ \n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.27 - Page No : 103" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "P1 = 1 * 10**5# in N/m**2\n", "V1 = 0.1# in m**3\n", "V2 = 0.01# in m**3\n", "T1 = 90# in degree C\n", "T1 = T1 +273# in K\n", "R = 0.287# in kJ/kg-K\n", "R = R *10**3#\n", "C_v = 0.717# in kJ/kg-K\n", "C_P = 1.005# in kJ/kg-K\n", "m = (P1 * V1)/(R*T1) # in kg\n", "Gamma = 1.4#\n", "T2 = T1 * ((V1/V2)**(Gamma - 1)) # in K\n", "del_U = m*C_v*(T1-T2) # in kJ\n", "print \"The change in internal energy = %0.2f kJ\" %del_U\n", "del_E = m * C_P*(T2-T1) # in kJ\n", "print \"The change in enthalpy = %0.2f kJ\" %del_E\n", "U2 = m*C_v*T2#Internal energy at 2 in kJ\n", "T= 473# temp. of entering air\n", "E = V1*C_P*T#Enthalpy of entering air in kJ\n", "# U3= (m+V1)*C_v*T3 # (internal energy at 3)\n", "# U3= U2+E\n", "T3 = (E+U2)/( (m+V1)*C_v ) # in K\n", "print \"Temperature = %0.0f K\" %T3\n", "m=m+.1#\n", "P3 =m* R*T3/V2# in N/m**2\n", "print \"The pressure = %0.3f MN/m**2 \" %(P3*10**-6)\n", "\n", "# Note: There is a calculation error to evaluating the value of P3. So the answer in the book of P3 is wrong." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The change in internal energy = -37.77 kJ\n", "The change in enthalpy = 52.94 kJ\n", "Temperature = 785 K\n", "The pressure = 4.415 MN/m**2 \n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.28 - Page No : 104" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "T= 60+273# in K\n", "T2= 25+273# in K\n", "P1=3.5*10**6# in Pa\n", "P2=1.7*10**6# in Pa\n", "Gamma=0.4# value of Cp-Cv\n", "m1=1# (assumed value)\n", "# R= P1*V/(m*T) (i)\n", "# R= P2*V/((m-m1)*T2) (ii)\n", "# From eq(i) and (ii)\n", "m= m1*P1*T2/(P1*T2-P2*T)\n", "# U= m*Cv*T and U1= (m-m1)*Cv*T2+m1*Cv*T1\n", "# U-U1= P1*V1= m1*R*T1 or\n", "# m1*R*T1= m*Cv*T-[(m-m1)*Cv*T2+m1*Cv*T1]\n", "T1= (m*T-(m-m1)*T2)/(m1*Gamma+m1) # in K\n", "print \"The temperature of gas in the cylinder = %0.2f \u00b0C\" %(T1-273)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The temperature of gas in the cylinder = -5.47 \u00b0C\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.29 - Page No : 105" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given data\n", "U=180# energy received by system in kJ\n", "RH= 200# rejected heat by system in kJ\n", "RcHeat= 50# received heat by system in kJ\n", "W= U-RH+RcHeat# in kJ\n", "U1 = 0# in kJ\n", "U2= U+U1# in kJ\n", "U3 = RcHeat-RH+U2# in kJ\n", "print \"Internal energy = %0.0f kJ \" %U3" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Internal energy = 30 kJ \n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.30 - Page No : 105" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import log\n", "# Given data\n", "C_P = 1.045# in kJ/kg-K\n", "Q = 100# in kJ\n", "del_T = Q/C_P# in degree C\n", "T1 = 25# in degree C\n", "T1 = T1 + 273# in K\n", "T = 0# in degree C\n", "T = T + 273# in K\n", "T2 = T1 + del_T# in K\n", "del_Phi = C_P * (log(T2/T1)) # in kJ/kg-K\n", "print \"The change in entropy in the process = %0.3f kJ/kg-K \" %del_Phi\n", "ini_entropy = C_P * (log(T1/T)) # initial entropy in kJ/kg-K\n", "print \"The initial entropy = %0.3f kJ/kg-K \" %ini_entropy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The change in entropy in the process = 0.291 kJ/kg-K \n", "The initial entropy = 0.092 kJ/kg-K \n" ] } ], "prompt_number": 41 } ], "metadata": {} } ] }