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+{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9 : Gases and Vapour Mixtures"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.1 Page no : 420"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate :\n",
+ "(i) The partial pressure of each constituent,\n",
+ "(ii) The total pressure in the vessel, and\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "V = 0.35; \t\t\t#m**3\n",
+ "import math \n",
+ "m_CO = 0.4; \t\t\t#kg\n",
+ "m_air = 1; \t\t\t#kg\n",
+ "m_O2 = 0.233; \t\t\t#kg\n",
+ "m_N2 = 0.767; \t\t\t#kg\n",
+ "T = 293.; \t\t\t#K\n",
+ "R0 = 8.314; \t\t\t#kJ/kg K\n",
+ "M_O2 = 32.; \t\t\t#Molecular mass of O2\n",
+ "M_N2 = 28.; \t\t\t#Molecular mass of N2\n",
+ "M_CO = 28.; \t\t\t#Molecular mass of CO\n",
+ "\n",
+ "# Calculations and Results\n",
+ "\n",
+ "p_O2 = m_O2*R0*10**3*T/M_O2/V/10**5; \t\t\t#bar\n",
+ "print (\"partial pressure for p_O2 %.3f\")% (p_O2), (\"bar\")\n",
+ "\n",
+ "p_N2 = m_N2*R0*10**3*T/M_N2/V/10**5; \t\t\t#bar\n",
+ "print (\"partial pressure for p_N2 %.3f\")% (p_N2), (\"bar\")\n",
+ "\n",
+ "p_CO = m_CO*R0*10**3*T/M_CO/V/10**5; \t\t\t#bar\n",
+ "print (\"partial pressure for p_CO %.3f\")%(p_CO), (\"bar\")\n",
+ "\n",
+ "\n",
+ "print (\"(ii) Total pressure in the vessel\")\n",
+ "p = p_O2+p_N2+p_CO;\n",
+ "print (\"p = %.3f\")% (p), (\"bar\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "partial pressure for p_O2 0.507 bar\n",
+ "partial pressure for p_N2 1.907 bar\n",
+ "partial pressure for p_CO 0.994 bar\n",
+ "(ii) Total pressure in the vessel\n",
+ "p = 3.408 bar\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.2 Page no : 421"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate : (i) Gas constant for air ;\n",
+ "(ii) Apparent molecular weight.\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "R0 = 8.314;\n",
+ "M_O2 = 32.;\n",
+ "M_N2 = 28.;\n",
+ "M_Ar = 40.;\n",
+ "M_CO2 = 44.;\n",
+ "\n",
+ "# Calculations\n",
+ "R_O2 = R0/M_O2; \t\t\t#kJ/kg K\n",
+ "R_N2 = R0/M_N2; \t\t\t#kJ/kg K\n",
+ "R_Ar = R0/M_Ar; \t\t\t#kJ/kg K\n",
+ "R_CO2 = R0/M_CO2; \t\t\t#kJ/kg K\n",
+ "\n",
+ "O2 = 0.2314;\n",
+ "N2 = 0.7553;\n",
+ "Ar = 0.0128;\n",
+ "CO2 = 0.0005;\n",
+ "\n",
+ "# Results\n",
+ "print (\"(i) Gas constant for air\")\n",
+ "R = O2*R_O2 + N2*R_N2 + Ar*R_Ar + CO2*R_CO2;\n",
+ "print (\"R = %.3f\")%(R), (\"kJ/kg K\")\n",
+ "\n",
+ "print (\"(ii) Apparent molecular weight.\")\n",
+ "M = R0/R;\n",
+ "print (\"M = %.3f\")%(M)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Gas constant for air\n",
+ "R = 0.287 kJ/kg K\n",
+ "(ii) Apparent molecular weight.\n",
+ "M = 28.954\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.3 Page no : 422"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate the analysis by volume and the partial pressure \n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "p = 1.; \t\t\t#bar\n",
+ "#For oxygen\n",
+ "m_O2 = 0.2314;\n",
+ "M_O2 = 32;\n",
+ "n_O2 = m_O2/M_O2;\n",
+ "#For Nitrogen\n",
+ "m_N2 = 0.7553;\n",
+ "M_N2 = 28.;\n",
+ "n_N2 = m_N2/M_N2;\n",
+ "#For Argon\n",
+ "m_Ar = 0.0128;\n",
+ "M_Ar = 40;\n",
+ "n_Ar = m_Ar/M_Ar;\n",
+ "\n",
+ "#For CO2\n",
+ "m_CO2 = 0.0005;\n",
+ "M_CO2 = 44;\n",
+ "n_CO2 = m_CO2/M_CO2;\n",
+ "\n",
+ "# Calculations and Results\n",
+ "n = n_O2 + n_N2 + n_Ar + n_CO2;\n",
+ "\n",
+ "#Let Vi/V be A\n",
+ "A_O2 = n_O2/n * 100;\n",
+ "print (\"Vi/V of O2 = %.3f\")%(A_O2),(\"%\")\n",
+ "\n",
+ "A_N2 = n_N2/n * 100;\n",
+ "print (\"Vi/V of N2 = %.3f\")%(A_N2), (\"%\")\n",
+ "\n",
+ "A_Ar = n_Ar/n *100;\n",
+ "print (\"Vi/V of Ar %.3f\")% (A_Ar), (\"%\")\n",
+ "\n",
+ "A_CO2 = n_CO2/n * 100;\n",
+ "print (\"Vi/V of CO2 = %.3f\")% (A_CO2), (\"%\")\n",
+ "\n",
+ "\n",
+ "P_O2 = n_O2/n*p;\n",
+ "print (\"Partial pressure of O2 = %.3f\")% (P_O2), (\"bar\")\n",
+ "\n",
+ "P_N2 = n_N2/n*p;\n",
+ "print (\"Partial pressure of N2 = %.3f\")% (P_N2), (\"bar\")\n",
+ "\n",
+ "P_Ar = n_Ar/n*p;\n",
+ "print (\"Partial pressure of Ar = %.3f\")% (P_Ar), (\"bar\")\n",
+ "\n",
+ "P_CO2 = n_CO2/n*p;\n",
+ "print (\"Partial pressure of CO2 = %.4f\")% (P_CO2), (\"bar\")\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Vi/V of O2 = 20.937 %\n",
+ "Vi/V of N2 = 78.103 %\n",
+ "Vi/V of Ar 0.927 %\n",
+ "Vi/V of CO2 = 0.033 %\n",
+ "Partial pressure of O2 = 0.209 bar\n",
+ "Partial pressure of N2 = 0.781 bar\n",
+ "Partial pressure of Ar = 0.009 bar\n",
+ "Partial pressure of CO2 = 0.0003 bar\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.4 Page no : 423"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate for the mixture :\n",
+ "(i) The masses of CO 2 , O 2 and N 2 , and the total mass ;\n",
+ "(ii) The percentage carbon content by mass ;\n",
+ "(iii) The apparent molecular weight and the gas constant for the mixture ;\n",
+ "(iv) The specific volume of the mixture\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "p = 1.*10**5; \t\t\t#Pa\n",
+ "T = 293.; \t\t\t#K\n",
+ "n_CO2 = 1.; \t\t\t#moles of CO2\n",
+ "n = 4.; \t\t\t#moles of air\n",
+ "M_CO2 = 44.;\n",
+ "M_N2 = 28.;\n",
+ "M_O2 = 32.;\n",
+ "\n",
+ "#Let A be the volumeetric analysis\n",
+ "A_O2 = 0.21;\n",
+ "A_N2 = 0.79;\n",
+ "\n",
+ "# Calculations and Results\n",
+ "n_O2 = A_O2*n;\n",
+ "n_N2 = A_N2*n;\n",
+ "\n",
+ "print (\"(i) The masses of CO2, O2 and N2, and the total mass\")\n",
+ "\n",
+ "m_CO2 = n_CO2*M_CO2;\n",
+ "print (\"Mass of CO2 = %.3f\")%(m_CO2),(\"kg\")\n",
+ "\n",
+ "m_O2 = n_O2*M_O2;\n",
+ "print (\"Mass of O2 = %.3f\")%(m_O2),(\"kg\")\n",
+ "\n",
+ "m_N2 = n_N2*M_N2;\n",
+ "print (\"Mass of N2 = %.3f\")%(m_N2),(\"kg\")\n",
+ "\n",
+ "m = m_CO2 + m_O2 + m_N2;\n",
+ "print (\"Total mass = %.3f\")% (m), (\"kg\")\n",
+ "\n",
+ "\n",
+ "print (\"(ii) The percentage carbon content by mass\")\n",
+ "#Since the molecular weight of carbon is 12, therefore, there are 12 kg of carbon present for every mole of CO2\n",
+ "m_C = 12; \t\t\t#kg\n",
+ "\n",
+ "C = m_C/m*100;\n",
+ "print (\"Percentage carbon in mixture %.3f\")%(C),(\"%\")\n",
+ "\n",
+ "\n",
+ "print (\"(iii) The apparent molecular weight and the gas consmath.tant for the mixture\")\n",
+ "n = n_CO2 + n_O2 + n_N2;\n",
+ "M = n_CO2/n*M_CO2 + n_O2/n*M_O2 + n_N2/n*M_N2;\n",
+ "print (\"Apparent Molecular weight %.3f\")%(M)\n",
+ "\n",
+ "R0 = 8.314;\n",
+ "R = R0/M;\n",
+ "print (\"Gas constant for the mixture = %.3f\")%(R),(\"kJ/kg K\")\n",
+ "\n",
+ "\n",
+ "print (\"(iv) The specific volume of the mixture\")\n",
+ "v = R*10**3*T/p;\n",
+ "print (\"specific volume = %.3f\")%(v),(\"m**3/kg\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The masses of CO2, O2 and N2, and the total mass\n",
+ "Mass of CO2 = 44.000 kg\n",
+ "Mass of O2 = 26.880 kg\n",
+ "Mass of N2 = 88.480 kg\n",
+ "Total mass = 159.360 kg\n",
+ "(ii) The percentage carbon content by mass\n",
+ "Percentage carbon in mixture 7.530 %\n",
+ "(iii) The apparent molecular weight and the gas consmath.tant for the mixture\n",
+ "Apparent Molecular weight 31.872\n",
+ "Gas constant for the mixture = 0.261 kJ/kg K\n",
+ "(iv) The specific volume of the mixture\n",
+ "specific volume = 0.764 m**3/kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page no : 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "calculate :\n",
+ "(ii) The volume of the container.\n",
+ "(i) The mass of O 2 required ;\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "p = 1.*10**5; \t\t\t#Pa\n",
+ "T = 298.; \t\t\t#K\n",
+ "M_H2 = 2.;\n",
+ "M_O2 = 32.;\n",
+ "R0 = 8314.;\n",
+ "# ratio = V_H2/V_O2 = 2;\n",
+ "ratio = 2;\n",
+ "\n",
+ "# Calculations and Results\n",
+ "print (\"(i) The mass of O2 required\")\n",
+ "\t\t\t#Let the mass of O2 per kg of H2 = x kg\n",
+ "m_H2 = 1; \t\t\t#kg\n",
+ "n_H2 = m_H2/M_H2;\n",
+ "\n",
+ "# n_O2 = x/M_O2\n",
+ "x = M_O2*n_H2/ratio;\n",
+ "print (\"Mass of O2 per kg of H2 = %.3f\")%(x), (\"kg\")\n",
+ "\n",
+ "print (\"(ii) The volume of the container\")\n",
+ "n_O2 = x/M_O2;\n",
+ "n = n_H2 + n_O2;\n",
+ "V = n*R0*T/p;\n",
+ "print (\"V = %.3f\")%(V), (\"m**3\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The mass of O2 required\n",
+ "Mass of O2 per kg of H2 = 8.000 kg\n",
+ "(ii) The volume of the container\n",
+ "V = 18.582 m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page no : 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate per mole of mixture the mass of mixture to be removed, and mass of CO to be added.\n",
+ "'''\n",
+ "\n",
+ "#Let composition of mixture by volume be denoted by c1\n",
+ "#Let Final composition desired be denoted by c2\n",
+ "\n",
+ "# Variables\n",
+ "c1_H2 = 0.78;\n",
+ "c1_CO = 0.22;\n",
+ "c2_H2 = 0.52;\n",
+ "c2_CO = 0.48;\n",
+ "M_H2 = 2.;\n",
+ "M_CO = 28.;\n",
+ "\n",
+ "# Calculations\n",
+ "M = c1_H2*M_H2 + c1_CO*M_CO;\n",
+ "# Let x kg of mixture be removed and y kg of CO be added.\n",
+ "x = (c1_H2 - c2_H2)/c1_H2*M;\n",
+ "\n",
+ "# Results\n",
+ "print (\"Mass of mixture removed = %.3f\")%(x), (\"kg\")\n",
+ "\n",
+ "y = M_CO/M*x;\n",
+ "print (\"Mass of CO added = %.3f\")%(y),(\"kg\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mass of mixture removed = 2.573 kg\n",
+ "Mass of CO added = 9.333 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.7 Page no : 425"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate per kg of gas :\n",
+ "(i) The workdone ;\n",
+ "(ii) The heat flow ;\n",
+ "(iii) Change of entropy per kg of mixture.\n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "ratio = 1./8; \t\t\t#volume ratio; v1/v2\n",
+ "T1 = 1223.; \t\t\t#K\n",
+ "cp_CO2 = 1.235; \t\t\t#kJ/kg K\n",
+ "cp_O2 = 1.088; \t\t\t#kJ/kg K\n",
+ "cp_N2 = 1.172; \t\t\t#kJ/kg K\n",
+ "n_CO2 = 0.13;\n",
+ "n_O2 = 0.125;\n",
+ "n_N2 = 0.745;\n",
+ "M_CO2 = 44.;\n",
+ "M_O2 = 32.;\n",
+ "M_N2 = 28.;\n",
+ "\n",
+ "\n",
+ "# Calculations\n",
+ "m_CO2 = M_CO2*n_CO2;\n",
+ "m_O2 = M_O2*n_O2;\n",
+ "m_N2 = M_N2*n_N2;\n",
+ "m = m_CO2 + m_O2 + m_N2;\n",
+ "\n",
+ "# Let Fraction by mass be denoted by F\n",
+ "F_CO2 = m_CO2/m;\n",
+ "F_O2 = m_O2/m;\n",
+ "F_N2 = m_N2/m;\n",
+ "cp = F_CO2*cp_CO2 + F_O2*cp_O2 + F_N2*cp_N2;\n",
+ "R0 = 8.314;\n",
+ "R = F_CO2*R0/M_CO2 + F_O2*R0/M_O2 + F_N2*R0/M_N2;\n",
+ "\n",
+ "cv = cp - R;\n",
+ "n = 1.2;\n",
+ "\n",
+ "print (\"(i) The workdone\")\n",
+ "T2 = T1*(ratio)**(n-1);\n",
+ "W = R*(T1-T2)/(n-1);\n",
+ "print (\"W = %.3f\")%(W), (\"kJ/kg\")\n",
+ "\n",
+ "print (\"(ii) The heat flow\")\n",
+ "du = cv*(T2-T1);\n",
+ "Q = du + W;\n",
+ "print (\"Q = %.3f\")%(Q), (\"kJ/kg\")\n",
+ "\n",
+ "\n",
+ "print (\"(iii) Change of entropy per kg of mixture\")\n",
+ "ds_1A = R*math.log(1/ratio); \t\t\t#isothermal process\n",
+ "ds_2A = cv*math.log(T1/T2);\n",
+ "\n",
+ "ds_12 = ds_1A - ds_2A;\n",
+ "print (\"change of entropy = %.3f\")% (ds_12), (\"kJ/kg K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The workdone\n",
+ "W = 565.669 kJ/kg\n",
+ "(ii) The heat flow\n",
+ "Q = 190.777 kJ/kg\n",
+ "(iii) Change of entropy per kg of mixture\n",
+ "change of entropy = 0.191 kJ/kg K\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.8 Page no : 427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Calculate the values of C p , C v , c p and c v for the mixture.\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "M_CO2 = 44.;\n",
+ "M_H2 = 2.;\n",
+ "M_N2 = 28.;\n",
+ "M_CH4 = 16.;\n",
+ "M_CO = 28.;\n",
+ "\n",
+ "# Let volumetric analysis be denoted by V\n",
+ "V_CO = 0.28;\n",
+ "V_H2 = 0.13;\n",
+ "V_CH4 = 0.04;\n",
+ "V_CO2 = 0.04;\n",
+ "V_N2 = 0.51;\n",
+ "Cp_CO = 29.27; \t\t\t#kJ/mole K\n",
+ "Cp_H2 = 28.89; \t\t\t#kJ/mole K\n",
+ "Cp_CH4 = 35.8; \t\t\t#kJ/mole K\n",
+ "Cp_CO2 = 37.22; \t\t\t#kJ/mole K\n",
+ "Cp_N2 = 29.14; \t\t\t#kJ/mole K\n",
+ "R0 = 8.314; \n",
+ "\n",
+ "# Calculations and Results\n",
+ "Cp = V_CO*Cp_CO + V_H2*Cp_H2 + V_CO2*Cp_CO2 + V_CH4*Cp_CH4 + V_N2*Cp_N2;\n",
+ "print (\"Cp = %.3f\")%(Cp), (\"kJ/mole K\")\n",
+ "\n",
+ "Cv = Cp-R0;\n",
+ "print (\"Cv = %.3f\")% (Cv), (\"kJ/mole K\")\n",
+ "\n",
+ "M = V_CO*M_CO + V_H2*M_H2 + V_CO2*M_CO2 + V_CH4*M_CH4 + V_N2*M_N2;\n",
+ "\n",
+ "cp = Cp/M;\n",
+ "print (\"cp = %.3f\")%(cp), (\"kJ/kg K\")\n",
+ "\n",
+ "cv = Cv/M;\n",
+ "print (\"cv %.3f\")% (cv), (\"kJ/kg K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Cp = 29.733 kJ/mole K\n",
+ "Cv = 21.419 kJ/mole K\n",
+ "cp = 1.200 kJ/kg K\n",
+ "cv 0.864 kJ/kg K\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.9 Page no : 427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determine :\n",
+ "# (i) Partial pressures of the constituents ; (ii) Gas constant of mixture.\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "p = 1.3 \t\t\t#bar\n",
+ "R0 = 8.314;\n",
+ "M_CO2 = 44.;\n",
+ "M_O2 = 32.;\n",
+ "M_N2 = 28.;\n",
+ "M_CO = 28.;\n",
+ "m_O2 = 0.1;\n",
+ "m_N2 = 0.7;\n",
+ "m_CO2 = 0.15;\n",
+ "m_CO = 0.05;\n",
+ "#Considering 1 kg of mixture\n",
+ "m = 1; \t\t\t#kg\n",
+ "\n",
+ "# Calculations\n",
+ "#let moles be denoted by n\n",
+ "n_O2 = m_O2/M_O2;\n",
+ "n_N2 = m_N2/M_N2;\n",
+ "n_CO2 = m_CO2/M_CO2;\n",
+ "n_CO = m_CO/M_CO;\n",
+ "M = 1/(m_O2/M_O2 + m_N2/M_N2 + m_CO2/M_CO2 + m_CO/M_CO);\n",
+ "n = m/M;\n",
+ "x_O2 = n_O2/n;\n",
+ "x_N2 = n_N2/n;\n",
+ "x_CO2 = n_CO2/n;\n",
+ "x_CO = n_CO/n;\n",
+ "\n",
+ "# Results\n",
+ "print (\"(i) Partial pressures of the constituents\")\n",
+ "P_O2 = x_O2*p;\n",
+ "print (\"Partial pressure of O2 = %.3f\")% (P_O2), (\"bar\")\n",
+ "\n",
+ "P_N2 = x_N2*p;\n",
+ "print (\"Partial pressure of N2 = %.3f\")% (P_N2), (\"bar\")\n",
+ "\n",
+ "P_CO2 = x_CO2*p;\n",
+ "print (\"Partial pressure of CO2 = %.3f\")% (P_CO2), (\"bar\")\n",
+ "\n",
+ "P_CO = x_CO*p;\n",
+ "print (\"Partial pressure of CO = %.3f\")% (P_CO), (\"bar\")\n",
+ "\n",
+ "R_mix = R0/M;\n",
+ "print (\"Gas constant of mixture = %.3f\")%(R_mix), (\"kJ/kg K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Partial pressures of the constituents\n",
+ "Partial pressure of O2 = 0.122 bar\n",
+ "Partial pressure of N2 = 0.975 bar\n",
+ "Partial pressure of CO2 = 0.133 bar\n",
+ "Partial pressure of CO = 0.070 bar\n",
+ "Gas constant of mixture = 0.277 kJ/kg K\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.10 Page no : 428"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Find :\n",
+ "(i) The mole fraction of each constituent,\n",
+ "(ii) The equivalent molecular weight of the mixture,\n",
+ "(iii) The equivalent gas constant of the mixture,\n",
+ "(iv) The partial pressures and partial volumes,\n",
+ "(v) The volume and density of the mixture, and\n",
+ "(vi) The c p and c v of the mixture.\n",
+ "\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "p = 4.*10**5; \t\t \t#Pa\n",
+ "import math \n",
+ "T = 293.; \t\t\t #K\n",
+ "R0 = 8.314;\n",
+ "\n",
+ "m_N2 = 4.; \t \t\t #kg\n",
+ "m_CO2 = 6.; \t\t\t #kg\n",
+ "\n",
+ "M_N2 = 28.; \t\t \t #Molecular mass\n",
+ "M_CO2 = 44.; \t\t\t #Molecular mass\n",
+ "\n",
+ "n_N2 = m_N2/M_N2; \t\t\t#moles of N2\n",
+ "n_CO2 = m_CO2/M_CO2; \t\t\t#moles of CO2\n",
+ "\n",
+ "x_N2 = n_N2/(n_N2+n_CO2);\n",
+ "print (\"x_N2 = %.3f\")% (x_N2)\n",
+ "\n",
+ "x_CO2 = n_CO2/(n_CO2+n_N2);\n",
+ "print (\"x_CO2 = %.3f\")% (x_CO2)\n",
+ "\n",
+ "\n",
+ "print (\"(ii) The equivalent molecular weight of the mixture\")\n",
+ "M = x_N2*M_N2 + x_CO2*M_CO2;\n",
+ "print (\"M = %.3f\")%(M), (\"kg/kg-mole\")\n",
+ "\n",
+ "print (\"(iii) The equivalent gas consmath.tant of the mixture\")\n",
+ "m = m_N2+m_CO2;\n",
+ "Rmix = (m_N2*(R0/M_N2) + m_CO2*(R0/M_CO2))/m;\n",
+ "print (\"Rmix = %.3f\")% (Rmix), (\"kJ/kg K\")\n",
+ "\n",
+ "print (\"(iv) The partial pressures and partial volumes\")\n",
+ "P_N2 = x_N2*p/10**5;\n",
+ "print (\"P_N2 = %.3f\")% (P_N2), (\"bar\")\n",
+ "\n",
+ "P_CO2 = x_CO2*p/10**5;\n",
+ "print (\"P_CO2 = %.3f\")% (P_CO2), (\"bar\")\n",
+ "\n",
+ "V_N2 = m_N2*R0/M_N2*T/p*10**3;\n",
+ "print (\"V_N2 %.3f\")% (V_N2), (\"m**3\")\n",
+ "\n",
+ "V_CO2 = m_CO2*R0/M_CO2*T/p*10**3;\n",
+ "print (\"V_CO2 %.3f\")% (V_CO2), (\"m**3\")\n",
+ "\n",
+ "print (\"(v) The volume and density of the mixture\")\n",
+ "\n",
+ "V = m*Rmix*10**3*T/p;\n",
+ "print (\"V = %.3f\")% (V), (\"m**3\")\n",
+ "\n",
+ "rho_mix = m/V;\n",
+ "print (\"Density of mixture = %.3f\")% (rho_mix), (\"kg/m**3\")\n",
+ "\n",
+ "\n",
+ "print (\"(vi) cp and cv of the mixture\")\n",
+ "\n",
+ "y_N2 = 1.4;\n",
+ "cv_N2 = (R0/M_N2)/(y_N2 - 1);\n",
+ "cp_N2 = cv_N2*y_N2;\n",
+ "\n",
+ "y_CO2 = 1.286;\n",
+ "cv_CO2 = (R0/M_CO2)/(y_CO2 - 1);\n",
+ "cp_CO2 = cv_CO2*y_CO2;\n",
+ "\n",
+ "cp = (m_N2*cp_N2 + m_CO2*cp_CO2)/(m_N2+m_CO2);\n",
+ "print (\"cp = %.3f\")%(cp),(\"kJ/kg K\")\n",
+ "\n",
+ "cv = (m_N2*cv_N2 + m_CO2*cv_CO2)/(m_N2+m_CO2);\n",
+ "print (\"cv = %.3f\")%(cv),(\"kJ/kg K\")\n",
+ "\n",
+ "T1 = 293.; \t\t\t#K\n",
+ "T2 = 323.; \t\t\t#K\n",
+ "dU = m*cv*(T2-T1);\n",
+ "print (\"Change in internal energy = %.3f\")% (dU), (\"kJ\")\n",
+ "\n",
+ "dH = m*cp*(T2-T1);\n",
+ "print (\"Change in enthalpy = %.3f\")% (dH), (\"kJ\")\n",
+ "\n",
+ "dS = m*cv*math.log(T2/T1); \t\t\t#Consmath.tant volume process\n",
+ "print (\"Change in entropy = %.3f\")% (dS), (\"kJ/kg K\")\n",
+ "\n",
+ "\n",
+ "print (\"When the mixture is heated at constant pressure\")\n",
+ "\n",
+ "print (\"If the mixture is heated at constant pressure \u0394U and \u0394H will remain the same\")\n",
+ "\n",
+ "dS = m*cp*math.log(T2/T1);\n",
+ "print (\"Change in entropy = %.3f\")% (dS), (\"kJ/kg K\")\n",
+ "\n",
+ "\n",
+ "# Note : Answers are slightly different because of rounding error."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "x_N2 = 0.512\n",
+ "x_CO2 = 0.488\n",
+ "(ii) The equivalent molecular weight of the mixture\n",
+ "M = 35.814 kg/kg-mole\n",
+ "(iii) The equivalent gas consmath.tant of the mixture\n",
+ "Rmix = 0.232 kJ/kg K\n",
+ "(iv) The partial pressures and partial volumes\n",
+ "P_N2 = 2.047 bar\n",
+ "P_CO2 = 1.953 bar\n",
+ "V_N2 0.870 m**3\n",
+ "V_CO2 0.830 m**3\n",
+ "(v) The volume and density of the mixture\n",
+ "V = 1.700 m**3\n",
+ "Density of mixture = 5.881 kg/m**3\n",
+ "(vi) cp and cv of the mixture\n",
+ "cp = 0.925 kJ/kg K\n",
+ "cv = 0.693 kJ/kg K\n",
+ "Change in internal energy = 208.001 kJ\n",
+ "Change in enthalpy = 277.644 kJ\n",
+ "Change in entropy = 0.676 kJ/kg K\n",
+ "When the mixture is heated at constant pressure\n",
+ "If the mixture is heated at constant pressure \u0394U and \u0394H will remain the same\n",
+ "Change in entropy = 0.902 kJ/kg K\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.11 Page no : 430"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate :\n",
+ "(i) The final temperature and pressure of the mixture ;\n",
+ "(ii) The change of entropy of the system.\n",
+ "\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "Cv_O2 = 21.07; \t\t\t#kJ/mole K\n",
+ "Cv_CO = 20.86; \t\t\t#kJ/mole K\n",
+ "p_O2 = 8*10**5; \t\t\t#Pa\n",
+ "p_CO = 1*10**5; \t\t\t#Pa\n",
+ "V_O2 = 1.8; \t\t\t#m**3\n",
+ "V_CO = 3.6; \t\t\t#m**3\n",
+ "T_O2 = 323.; \t\t\t#K\n",
+ "T_CO = 293.; \t\t\t#K\n",
+ "R0 = 8314.;\n",
+ "\n",
+ "# Calculations and Results\n",
+ "n_O2 = p_O2*V_O2/R0/T_O2;\n",
+ "n_CO = p_CO*V_CO/R0/T_CO;\n",
+ "n = (n_O2+n_CO);\n",
+ "V = (V_O2+V_CO);\n",
+ "\n",
+ "print (\"(i) Final temperature (T) and pressure (p) of the mixture\")\n",
+ "\n",
+ "#Before mixing\n",
+ "U1 = n_O2*Cv_O2*T_O2 + n_CO*Cv_CO*T_CO;\n",
+ "\n",
+ "T = U1/(n_O2*Cv_O2 + n_CO*Cv_CO);\n",
+ "t = T-273;\n",
+ "\n",
+ "print (\"Final temperature = %.3f\")% (t), (\"\u00b0C\")\n",
+ "\n",
+ "p = n*R0*T/V/10**5;\n",
+ "print (\"Final pressure = %.3f\")% (p), (\"bar\")\n",
+ "\n",
+ "\n",
+ "#For oxygen\n",
+ "dS_O1A = n_O2*R0*math.log(V/V_O2); \t\t\t#isothermal process\n",
+ "dS_O2A = n_O2*Cv_O2*math.log(T_O2/T); \t\t\t#consmath.tant volume process\n",
+ "dS_O12 = dS_O1A - dS_O2A; \t\t\t# Change of entropy of O2\n",
+ "\n",
+ "#For CO\n",
+ "dS_CO12 = n_CO*R0*math.log(V/V_CO) + n_CO*Cv_CO*math.log(T/T_CO); \t\t\t#Change of entropy of CO\n",
+ "dS = (dS_O12 + dS_CO12)/10**3;\n",
+ "print (\"(ii)Change of entropy of system = %.3f\")% (dS), (\"kJ/K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Final temperature (T) and pressure (p) of the mixture\n",
+ "Final temperature = 43.569 \u00b0C\n",
+ "Final pressure = 3.334 bar\n",
+ "(ii)Change of entropy of system = 5.396 kJ/K\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.12 Page no : 432"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "(a) Calculate : (i) The final equilibrium pressure ;\n",
+ "(ii) The amount of heat transferred to the surroundings ;\n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "p_A = 16.*10**5; \t\t\t#Pa\n",
+ "p_B = 6.4*10**5; \t\t\t#Pa\n",
+ "\n",
+ "T_A = 328.; \t\t\t#K\n",
+ "T_B = 298.; \t\t\t#K\n",
+ "\n",
+ "n_A = 0.6 \t\t\t#kg-mole\n",
+ "m_B = 3; \t \t\t#kg\n",
+ "\n",
+ "R0 = 8314.;\n",
+ "M_A = 28.; \n",
+ "y = 1.4;\n",
+ "\n",
+ "V_A = n_A*R0*T_A/p_A;\n",
+ "m_A = n_A*M_A;\n",
+ "R = R0/M_A;\n",
+ "V_B = m_B*R*T_B/p_B;\n",
+ "V = V_A+V_B;\n",
+ "m = m_A+m_B;\n",
+ "T = 303.; \t\t\t#K\n",
+ "\n",
+ "print (\"(a) (i) Final equilibrium pressure, p\")\n",
+ "p = m*R*T/V/10**5;\n",
+ "print (\"p = %.3f\")% (p), (\"bar\")\n",
+ "\n",
+ "cv = R/10**3/(y-1);\n",
+ "\n",
+ "print (\"(ii) Amount of heat transferred, Q :\")\n",
+ "\n",
+ "U1 = cv*(m_A*T_A + m_B*T_B);\n",
+ "U2 = m*cv*T;\n",
+ "Q = U2-U1;\n",
+ "print (\"Q = %.3f\")% (Q),(\"kJ\")\n",
+ "\n",
+ "print (\"(b) If the vessel were insulated :\")\n",
+ "\n",
+ "print (\"(i) Final temperature,\")\n",
+ "\n",
+ "T = cv*(m_A*T_A + m_B*T_B)/(m*cv);\n",
+ "t = T-273;\n",
+ "print (\"T = %.3f\")% (t), (\"\u00b0C\")\n",
+ "\n",
+ "\n",
+ "print (\"(ii) Final pressure\")\n",
+ "\n",
+ "p = m*R*T/V/10**5;\n",
+ "print (\"p = %.3f\")% (p), (\"bar\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a) (i) Final equilibrium pressure, p\n",
+ "p = 12.393 bar\n",
+ "(ii) Amount of heat transferred, Q :\n",
+ "Q = -300.640 kJ\n",
+ "(b) If the vessel were insulated :\n",
+ "(i) Final temperature,\n",
+ "T = 50.455 \u00b0C\n",
+ "(ii) Final pressure\n",
+ "p = 13.230 bar\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.13 Page no : 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate the increase in entropy \n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "m_O2 = 3.; \t\t\t#kg\n",
+ "M_O2 = 32.;\n",
+ "m_N2 = 9.; \t\t\t#kg\n",
+ "M_N2 = 28.;\n",
+ "R0 = 8.314;\n",
+ "\n",
+ "# Calculations\n",
+ "R_O2 = R0/M_O2;\n",
+ "R_N2 = R0/M_N2;\n",
+ "x_O2 = (m_O2/M_O2)/((m_O2/M_O2) + (m_N2/M_N2));\n",
+ "x_N2 = (m_N2/M_N2)/((m_O2/M_O2) + (m_N2/M_N2));\n",
+ "dS = -m_O2*R_O2*math.log(x_O2) -m_N2*R_N2*math.log(x_N2);\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 = 1.844 kJ/kg K\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.14 Page no : 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Calculate the mass of O 2 added.\n",
+ "# Variables\n",
+ "m_N2 = 2.5; \t\t\t#kg \n",
+ "M_N2 = 28.;\n",
+ "p_N2 = 15.; \t\t\t#bar\n",
+ "p_total = 20.; \t\t\t#bar\n",
+ "\n",
+ "# Calculations\n",
+ "n_N2 = m_N2/M_N2;\n",
+ "p_O2 = p_total-p_N2;\n",
+ "n_O2 = p_O2/p_N2*n_N2;\n",
+ "M_O2 = 32;\n",
+ "m_O2 = n_O2*M_O2;\n",
+ "\n",
+ "# Results\n",
+ "print (\"Mass of O2 added = %.3f\")% (m_O2), (\"kg\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mass of O2 added = 0.952 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.15 Page no : 435"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Determine :\n",
+ "(i) The moles of nitrogen per mole of oxygen ;\n",
+ "(ii) The partial pressure of oxygen and nitrogen if the total pressure is atmosphere ;\n",
+ "(iii) The kg of nitrogen per kg of mixture.\n",
+ "\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "n_O2 = 1.;\n",
+ "M_N2 = 28.;\n",
+ "M_O2 = 32.;\n",
+ "\n",
+ "# Calculations and Results\n",
+ "print (\"(i) Moles of N2 per mole of O2 :\")\n",
+ "n_N2 = n_O2*0.79/0.21;\n",
+ "print (\"n_N2 = %.3f\")%(n_N2),(\"moles\")\n",
+ "\n",
+ "n = n_O2+n_N2;\n",
+ "print (\"(ii)\")\n",
+ "p = 1; \t\t\t#atm\n",
+ "\n",
+ "p_O2 = n_O2/n*p;\n",
+ "print (\"p_O2 = %.3f\")% (p_O2), (\"atm\")\n",
+ "\n",
+ "p_N2 = n_N2/n*p;\n",
+ "print (\"p_N2 = %.3f\")% (p_N2), (\"atm\")\n",
+ "\n",
+ "\n",
+ "x = n_N2*M_N2/(n_N2*M_N2+n_O2*M_O2);\n",
+ "print (\"(iii) The kg of nitrogen per kg of mixture = %.3f\")% (x), (\"kg N2/kg mix\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Moles of N2 per mole of O2 :\n",
+ "n_N2 = 3.762 moles\n",
+ "(ii)\n",
+ "p_O2 = 0.210 atm\n",
+ "p_N2 = 0.790 atm\n",
+ "(iii) The kg of nitrogen per kg of mixture = 0.767 kg N2/kg mix\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.16 Page no : 436"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " # Find the masses of O 2 , N 2 and CO 2 in the cylinder.\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "V = 0.6; \t\t\t#m**3\n",
+ "p1 = 12.*10**5; \t\t\t#Pa\n",
+ "p2 = 18.*10**5; \t\t\t#Pa\n",
+ "T = 298.; \t\t\t#K\n",
+ "R0 = 8.314;\n",
+ "x_O2 = 0.23;\n",
+ "x_N2 = 0.77;\n",
+ "\n",
+ "n = p1*V/R0/10**3/T;\n",
+ "#Considering 100 kg of air\n",
+ "m_O2 = 23.; \t\t\t#kg\n",
+ "m_N2 = 77.; \t\t\t#kg\n",
+ "M_O2 = 32.;\n",
+ "M_N2 = 28.;\n",
+ "m = 100.; \t\t\t#kg\n",
+ "\n",
+ "# Calculations and Results\n",
+ "R = (m_O2/M_O2 + m_N2/M_N2)*R0/m; \t\t\t#for air\n",
+ "M = R0/R \t \t\t#for air\n",
+ "\n",
+ "m = p1*V/R/T/10**3;\n",
+ "\n",
+ "m_O2 = x_O2*m;\n",
+ "print (\"Mass of O2 = %.3f\")% (m_O2), (\"kg\")\n",
+ "\n",
+ "m_N2 = x_N2*m;\n",
+ "print (\"Mass of N2 = %.3f\")% (m_N2), (\"kg\")\n",
+ "\n",
+ "#After adding CO2 in the vessel\n",
+ "p2 = 18.*10**5; \t\t\t#Pa;\n",
+ "\n",
+ "p_CO2 = 6.*10**5; \t\t\t#Pa\n",
+ "M_CO2 = 44.;\n",
+ "R_CO2 = R0/M_CO2;\n",
+ "\n",
+ "m_CO2 = p_CO2*V/(R_CO2*10**3*T);\n",
+ "print (\"Mass of CO2 = %.3f\")% (m_CO2), (\"kg\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mass of O2 = 1.927 kg\n",
+ "Mass of N2 = 6.451 kg\n",
+ "Mass of CO2 = 6.393 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.17 Page no : 437"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate-\n",
+ "(i) The partial pressure ;\n",
+ "(ii) The total pressure ;\n",
+ "(iii) The mean value of R for the mixture.\n",
+ "'''\n",
+ "# Variables\n",
+ "V = 6; \t\t \t#m**3\n",
+ "A = 0.45; \n",
+ "B = 0.55;\n",
+ "R_A = 0.288; \t\t\t#kJ/kg K\n",
+ "R_B = 0.295; \t\t\t#kJ/kg K\n",
+ "m = 2. \t\t\t#kg\n",
+ "T = 303. \t\t\t #K\n",
+ "\n",
+ "# Calculations\n",
+ "print (\"(i) The partial pressures\")\n",
+ "m_A = A*m;\n",
+ "m_B = B*m;\n",
+ "\n",
+ "p_A = m_A*R_A*10**3*T/V/10**5; \t\t\t#bar\n",
+ "print (\"p_A = %.3f\")% (p_A), (\"bar\")\n",
+ "\n",
+ "p_B = m_B*R_B*10**3*T/V/10**5; \t\t\t#bar\n",
+ "print (\"p_B = %.3f\")% (p_B), (\"bar\")\n",
+ "\n",
+ "\n",
+ "print (\"(ii) The total pressure\")\n",
+ "p = p_A+p_B;\n",
+ "print (\"p = %.3f\")% (p), (\"bar\")\n",
+ "\n",
+ "\n",
+ "print (\"(iii) The mean value of R for the mixture\")\n",
+ "Rm = (m_A*R_A + m_B*R_B)/(m_A + m_B);\n",
+ "print (\"Rm = %.3f\")% (Rm), (\"kJ/kg K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The partial pressures\n",
+ "p_A = 0.131 bar\n",
+ "p_B = 0.164 bar\n",
+ "(ii) The total pressure\n",
+ "p = 0.295 bar\n",
+ "(iii) The mean value of R for the mixture\n",
+ "Rm = 0.292 kJ/kg K\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.18 Page no : 438"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Determine-\n",
+ "(i) The mole fraction of each component ; (ii) The average molecular weight ;\n",
+ "(iii) The specific gas constant ;\n",
+ "(iv) The volume and density ;\n",
+ "(v) The partial pressures and partial volumes.\n",
+ "'''\n",
+ "\n",
+ "# Variables\n",
+ "m_O2 = 4.; \t\t\t#kg\n",
+ "m_N2 = 6.; \t\t\t#kg\n",
+ "p = 4.*10**5; \t\t\t#Pa\n",
+ "T = 300.; \t\t\t#K\n",
+ "M_O2 = 32.;\n",
+ "M_N2 = 28.;\n",
+ "m = 10.; \t\t\t#kg\n",
+ "\n",
+ "# Calculations and Results\n",
+ "print (\"(i) The mole fraction of each component\")\n",
+ "n_O2 = m_O2/M_O2;\n",
+ "n_N2 = m_N2/M_N2;\n",
+ "\n",
+ "x_O2 = n_O2/(n_O2+n_N2);\n",
+ "print (\"x_O2 = %.3f\")% (x_O2)\n",
+ "\n",
+ "x_N2 = n_N2/(n_N2+n_O2);\n",
+ "print (\"x_N2 = %.3f\")% (x_N2)\n",
+ "\n",
+ "\n",
+ "print (\"(ii) The average molecular weight\")\n",
+ "M = (n_O2*M_O2 + n_N2*M_N2)/(n_O2 + n_N2);\n",
+ "print (\"M = %.3f\")%(M)\n",
+ "\n",
+ "print (\"(iii) The specific gas consmath.tant\")\n",
+ "R0 = 8.314;\n",
+ "R = R0/M;\n",
+ "print (\"R = %.3f\")% (R), (\"kJ/kg K\")\n",
+ "\n",
+ "print (\"(iv) The volume and density\")\n",
+ "V = m*R*T*10**3/p;\n",
+ "print (\"V = %.3f\")%(V), (\"m**3\")\n",
+ "\n",
+ "rho = (m_O2/V) + (m_N2/V);\n",
+ "print (\"density = %.3f\")% (rho), (\"kg/m**3\")\n",
+ "\n",
+ "\n",
+ "print (\"(v) The partial pressures and partial volumes\")\n",
+ "p_O2 = n_O2*R0*10**3*T/V/10**5; \t\t\t#bar\n",
+ "print (\"p_O2 = %.3f\")%(p_O2), (\"bar\")\n",
+ "\n",
+ "p_N2 = n_N2*R0*10**3*T/V/10**5; \t\t\t#bar\n",
+ "print (\"p_N2 = %.3f\")% (p_N2), (\"bar\")\n",
+ "\n",
+ "V_O2 = x_O2*V;\n",
+ "print (\"V_O2 = %.3f\")% (V_O2), (\"m**3\")\n",
+ "\n",
+ "V_N2 = x_N2*V;\n",
+ "print (\"V_N2 = %.3f\")% (V_N2), (\"m**3\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The mole fraction of each component\n",
+ "x_O2 = 0.368\n",
+ "x_N2 = 0.632\n",
+ "(ii) The average molecular weight\n",
+ "M = 29.474\n",
+ "(iii) The specific gas consmath.tant\n",
+ "R = 0.282 kJ/kg K\n",
+ "(iv) The volume and density\n",
+ "V = 2.116 m**3\n",
+ "density = 4.727 kg/m**3\n",
+ "(v) The partial pressures and partial volumes\n",
+ "p_O2 = 1.474 bar\n",
+ "p_N2 = 2.526 bar\n",
+ "V_O2 = 0.779 m**3\n",
+ "V_N2 = 1.336 m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.19 Page no : 439"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Calculate :\n",
+ "(i) The final temperature of the mixture ; \n",
+ "(ii) The change in entropy.\n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "cp_CO2 = 0.85; \t\t\t#kJ/kg K\n",
+ "cp_N2 = 1.04; \t\t\t#kJ/kg K\n",
+ "m_CO2 = 4.; \t\t\t#kg\n",
+ "T1_CO2 = 313.; \t\t\t#K\n",
+ "m_N2 = 8.; \t\t\t#kg\n",
+ "T1_N2 = 433.; \t\t\t#K\n",
+ "p2 = 0.7; \t\t\t#bar\n",
+ "p1_CO2 = 1.4; \t\t\t#bar\n",
+ "p1_N2 = 1.;\n",
+ "R = 8.314;\n",
+ "M_CO2 = 44.;\n",
+ "M_N2 = 28.;\n",
+ "R_CO2 = R/M_CO2;\n",
+ "R_N2 = R/M_N2;\n",
+ "\n",
+ "# Calculations and Results\n",
+ "print (\"(i) Final temperature, T2\")\n",
+ "T2 = (m_CO2*cp_CO2*T1_CO2 + m_N2*cp_N2*T1_N2)/(m_CO2*cp_CO2 + m_N2*cp_N2);\n",
+ "print (\"T2 = %.3f\")%(T2),(\"K\")\n",
+ "\n",
+ "print (\"(ii) Change in entropy\")\n",
+ "n_CO2 = 0.0909;\n",
+ "n_N2 = 0.2857;\n",
+ "n = n_CO2 + n_N2;\n",
+ "x_CO2 = n_CO2/n;\n",
+ "x_N2 = n_N2/n;\n",
+ "p2_CO2 = x_CO2*p2;\n",
+ "p2_N2 = x_N2*p2;\n",
+ "\n",
+ "dS = m_CO2*cp_CO2*math.log(T2/T1_CO2) - m_CO2*R_CO2*math.log(p2_CO2/p1_CO2) + m_N2*cp_N2*math.log(T2/T1_N2) - m_N2*R_N2*math.log(p2_N2/p1_N2);\n",
+ "print (\"dS = %.3f\")%(dS), (\"kJ/K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Final temperature, T2\n",
+ "T2 = 398.188 K\n",
+ "(ii) Change in entropy\n",
+ "dS = 3.223 kJ/K\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.20 Page no : 440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "calculate the entropy change in the mixing process.\n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "cv_O2 = 0.39; \t\t\t#kJ/kg K\n",
+ "cv_N2 = 0.446; \t\t\t#kJ/kg K\n",
+ "n_O2 = 1.;\n",
+ "n_N2 = 2.;\n",
+ "M_O2 = 32.;\n",
+ "M_N2 = 28.;\n",
+ "m_O2 = 32.; \t\t\t#kg\n",
+ "m_N2 = 2*28.; \t\t\t#kg\n",
+ "T_O2 = 293.; \t\t\t#K\n",
+ "T_N2 = 301.; \t\t\t#K\n",
+ "R0 = 8.314;\n",
+ "\n",
+ "# Calculations\n",
+ "p_O2 = 2.5*10**5; \t\t\t#Pa\n",
+ "p_N2 = 1.5*10**5; \t\t\t#Pa\n",
+ "T2 = (m_O2*cv_O2*T_O2 + m_N2*cv_N2*T_N2)/(m_O2*cv_O2 + m_N2*cv_N2);\n",
+ "V_O2 = n_O2*R0*10**5*T_O2/p_O2;\n",
+ "V_N2 = n_N2*R0*10**5*T_N2/p_N2;\n",
+ "V = V_O2+V_N2;\n",
+ "dS = m_O2*(cv_O2*math.log(T2/T_O2) + R0/M_O2*math.log(V/V_O2)) + m_N2*(cv_N2*math.log(T2/T_N2) + R0/M_N2*math.log(V/V_N2));\n",
+ "\n",
+ "# Results\n",
+ "print (\"Entropy change in the mixing process = %.3f\")%(dS),(\"kJ\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Entropy change in the mixing process = 16.627 kJ\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.21 Page no : 421"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Determine :\n",
+ "(i) The temperature of the equilibrium mixture ;\n",
+ "(ii) The pressure of the mixture ;\n",
+ "(iii) The change in entropy for each component and total value.\n",
+ "'''\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "cv_N2 = 0.744; \t\t\t#kJ/kg K\n",
+ "cv_H2 = 10.352; \t\t\t#kJ/kg K\n",
+ "cp_N2 = 1.041; \t\t\t#kJ/kg K\n",
+ "cp_H2 = 14.476; \t\t\t#kJ/kg K\n",
+ "V = 0.45; \t\t\t#m**3\n",
+ "V_H2 = 0.3; \t\t\t#m**3\n",
+ "V_N2 = 0.15; \t\t\t#m**3\n",
+ "p_H2 = 3.*10**5; \t\t\t#Pa\n",
+ "p_N2 = 6.*10**5; \t\t\t#Pa\n",
+ "T_H2 = 403.; \t\t\t#K\n",
+ "T_N2 = 303.; \t\t\t#K\n",
+ "\n",
+ "# Calculations and Results\n",
+ "R_H2 = 8.314/2;\n",
+ "R_N2 = 8.314/28;\n",
+ "\n",
+ "print (\"(i) Temperature of equilibrium mixture\")\n",
+ "\n",
+ "m_H2 = p_H2*V_H2/(R_H2*10**3)/T_H2;\n",
+ "m_N2 = p_N2*V_N2/(R_N2*10**3)/T_N2;\n",
+ "T2 = (m_H2*cv_H2*T_H2 + m_N2*cv_N2*T_N2)/(m_H2*cv_H2 + m_N2*cv_N2);\n",
+ "print (\"T2 = %.3f\")%(T2),(\"K\")\n",
+ "\n",
+ "print (\"(ii) Pressure of the mixture\")\n",
+ "p2_H2 = m_H2*R_H2*10**3*T2/V;\n",
+ "p2_N2 = m_N2*R_N2*10**3*T2/V;\n",
+ "\n",
+ "p2 = p2_H2+p2_N2;\n",
+ "print (\"p2 = %.3f\")%(p2/10**5),(\"bar\")\n",
+ "\n",
+ "print (\"(iii) Change in entropy :\")\n",
+ "\n",
+ "dS_H2 = m_H2*(cp_H2*math.log(T2/T_H2) - R_H2*math.log(p2_H2/p_H2));\n",
+ "print (\"Change in entropy of H2 = %.3f\")%(dS_H2),(\"kJ/K\")\n",
+ "\n",
+ "dS_N2 = m_N2*(cp_N2*math.log(T2/T_N2) - R_N2*math.log(p2_N2/p_N2));\n",
+ "print (\"Change in entropy of N2 = %.3f\")%(dS_N2),(\"kJ/K\")\n",
+ "\n",
+ "dS = dS_H2+dS_N2;\n",
+ "\n",
+ "print (\"Total change in entropy = %.3f\")%(dS),(\"kJ/K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Temperature of equilibrium mixture\n",
+ "T2 = 345.767 K\n",
+ "(ii) Pressure of the mixture\n",
+ "p2 = 3.998 bar\n",
+ "(iii) Change in entropy :\n",
+ "Change in entropy of H2 = 0.006 kJ/K\n",
+ "Change in entropy of N2 = 0.425 kJ/K\n",
+ "Total change in entropy = 0.430 kJ/K\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.22 Page no : 443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Calculate c v and c p of the mixture.\n",
+ "\n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "cv_N2 = 0.745; \t\t\t#kJ/kg K\n",
+ "cv_CO2 = 0.653; \t\t#kJ/kg K\n",
+ "cp_N2 = 1.041; \t\t\t#kJ/kg K\n",
+ "cp_CO2 = 0.842; \t\t#kJ/kg K\n",
+ "m_N2 = 4.; \t\t\t#kg\n",
+ "m_CO2 = 6.; \t\t#kg\n",
+ "pmix = 4.; \t\t \t#bar\n",
+ "m = m_N2+m_CO2;\n",
+ "\n",
+ "T1 = 298.; \t\t\t #K\n",
+ "T2 = 323.; \t\t\t #K\n",
+ "\n",
+ "# Calculations and Results\n",
+ "cv_mix = (m_N2*cv_N2 + m_CO2*cv_CO2)/(m_N2+m_CO2);\n",
+ "print (\"cv_mix = %.3f\")% (cv_mix), (\"kJ/kg K\")\n",
+ "\n",
+ "cp_mix = (m_N2*cp_N2 + m_CO2*cp_CO2)/(m_N2+m_CO2);\n",
+ "print (\"cp_mix = %.3f\")% (cp_mix), (\"kJ/kg K\")\n",
+ "\n",
+ "dU = m*cv_mix*(T2-T1);\n",
+ "print (\"Change in internal energy = %.3f\")% (dU), (\"kJ\")\n",
+ "\n",
+ "dH = m*cp_mix*(T2-T1);\n",
+ "print (\"Change in enthalpy = %.3f\")% (dH), (\"kJ\")\n",
+ "\n",
+ "dS = m_N2*cv_N2*math.log(T2/T1) + m_CO2*cv_CO2*math.log(T2/T1);\n",
+ "print (\"Change in entropy = %.3f\")% (dS), (\"kJ/K\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "cv_mix = 0.690 kJ/kg K\n",
+ "cp_mix = 0.922 kJ/kg K\n",
+ "Change in internal energy = 172.450 kJ\n",
+ "Change in enthalpy = 230.400 kJ\n",
+ "Change in entropy = 0.556 kJ/K\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 16:38:55 +0000