{ "metadata": { "name": "", "signature": "sha256:af5e98897fdd6a212dc067e1708c75ce618fcbb9ad24c85104d033a4702b884e" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 6 : Thermodynamic Properties of Pure Fluids" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.1 " ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "#Given:\n", "betta = 1.25*10**-3; \t\t\t#coeffecient of math.expansion (K**-1)\n", "V = 0.1; \t\t\t#molar volume of organic liquid (m**3/kmol)\n", "P2 = 20.; \t\t\t#final pressure (bar)\n", "P1 = 1.; \t\t\t#initial pressure (bar)\n", "\n", "# Calculations\n", "#To determine the change in entropy of system\n", "#betta = (1/V)*(del V/del T)p\n", "#Let k = (del V/del T)p\n", "k = betta*V;\n", "\n", "#Considering Maxwell's relation Eq. 6.24 (Page no. 193)\n", "#dS = -k*(dP)\n", "S = -k*(P2-P1)*10**5; \t\t\t#entropy change (J/kmol K)\n", "\n", "# Results\n", "print 'Change in entropy is %f J/kmol K'%S\n", "print ' It is assumed that (del V/del T)p is constant in the pressure range 1 to 20 bar'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Change in entropy is -237.500000 J/kmol K\n", " It is assumed that (del V/del T)p is constant in the pressure range 1 to 20 bar\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.2" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "# Variables\n", "T1 = 363.; \t\t\t#temperature (K)\n", "T2 = 373.; \t\t\t#temperature (K)\n", "P2 = 101.3; \t\t\t#vapour pressure at 373 K (kPa)\n", "H = 2275.*18; \t\t\t#mean heat of vaporisation (kJ/kmol)\n", "R =8.314; \t\t\t#ideal gas constant (kJ/kmol K)\n", "\n", "# Calculations\n", "#To calculate vapour pressure of water at 363 K\n", "#Using eq. 6.28 (Page no. 196)\n", "P1 = P2/(math.e**((H/R)*((1./T1)-(1./T2))))\n", "\n", "# Results\n", "print ' Vapour pressure of water at 363 K is %f kPa'%P1\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Vapour pressure of water at 363 K is 70.408579 kPa\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.3" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "d_l = 13.69*10**3; \t\t\t#density of mercury in liquid state (kg/m**3)\n", "d_s = 14.193*10**3; \t\t\t#density of mercury in solid state (kg/m**3)\n", "T1 = 234.33; \t\t\t#temperature in K\n", "P1 = 1.; \t\t\t#initial pressure in bar\n", "P2 = 10.; \t\t\t#final pressure in bar\n", "Hf = 9.7876; \t\t\t#heat of fusion of mercury (kJ/kg)\n", "\n", "# Calculations\n", "#Assuming del_V/del_H remains constant% math.log(T2/T1) = (del_V/del_H)*(P2-P1)\n", "del_V = (1./d_l)-(1./d_s)\n", "T2 = T1*(math.e**((del_V/Hf)*(P2-P1)))\n", "\n", "# Results\n", "print 'The melting point of mercury at 10 bar is %f K'%T2\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The melting point of mercury at 10 bar is 234.330558 K\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.4, page no:198" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "T1 = 300.; \t\t\t#initial temperature (K)\n", "T2 = 800.; \t\t\t#final temperature (K)\n", "\n", "# Calculations\n", "#Heat capacity (J/mol K)\n", "#Cp = 26.04+(5.586*10**-3*T)+(28.476*10**4*T**-2)\n", "import math\n", "S = 26.04*math.log(T2/T1)+5.586*10**-3*(T2-T1)+28.476*10**4/(-2)*(T2**-2-T1**-2)\n", "\n", "# Results\n", "print 'The increase in entropy of solid magnesium is %f J/mol K'%S\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The increase in entropy of solid magnesium is 29.693325 J/mol K\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.7" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "T = 773.; \t\t\t#temperature (K)\n", "P = 100.; \t\t\t#pressure (bar)\n", "Ho = 0; \t\t\t#enthalpy of nitrogen at 273 K and 1 bar\n", "So = 192.4; \t\t\t#entropy of nitrogen at 298 K and 1 bar\n", "To = 273.; \t\t\t#(K)\n", "Po = 1.; \t\t\t#(bar)\n", "R = 8.314; \t\t\t#ideal gas constant (kJ/kmol K)\n", "\n", "# Calculations\n", "#Cp = 27.3+(4.2*10**-3*T) molal heat capacity at 1 bar\n", "#To calculate internal energy enthalpy entropy and free energyfor one mole of nitrogen\n", "#Step 1:\n", "#Assuming that nitrogen is initially at 273 K and 1 bar\n", "#del_H1 = intg(CpdT)\n", "del_H1 = 27.3*(T-To)+4.2*10**-3*(T**2-To**2)/2;\n", "#Assuming that nitrogen is initially at 298 K and 1 bar\n", "#del_S1 = intg(Cp*(dT/T))\n", "del_S1 = 27.3*math.log(T/To)+4.2*10**-3*(T-To)\n", "H1 = Ho + del_H1;\n", "S1 = So + del_S1;\n", "\n", "#Step 2:\n", "#del_H2 = [V - T*(del_V/del_T)p]dP\n", "#Since nitrogen behaves as ideal gas\n", "#(del_V/del_T)p = R/P% V-(R*T)/P = 0\n", "del_H2 = 0.;\n", "del_S2 = -R*math.log(P/Po)\n", "H = H1 + del_H2;\n", "S = S1 + del_S2;\n", "\n", "#Internal energy: U = H-PV = H-RT (J/mol)\n", "U = H - (R*T)\n", "\n", "#Gibbs free energy (J/mol)\n", "G = H-(T*S)\n", "\n", "# Results\n", "print 'Enthalpy is %5.3e J/mol'%H\n", "print ' Entropy is %f J/mol K'%S\n", "print ' Internal energy is %4.3e J/mol'%U\n", "print ' Gibbs free energy is %4.3e J/mol'%G\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Enthalpy is 1.475e+04 J/mol\n", " Entropy is 184.626653 J/mol K\n", " Internal energy is 8.322e+03 J/mol\n", " Gibbs free energy is -1.280e+05 J/mol\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.8" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "#Equation of state: P(V-B) = RT + (A*P**2)/T\n", "Cp = 33.6; \t\t\t#mean specific heat at atmosheric pressure (J/mol K)\n", "A = 1*10**-3; \t\t\t#m**3 K/(bar)mol\n", "B = 8.0*10**-5; \t\t\t#m**3/mol\n", "R = 8.314*10**-5; \t\t\t#ideal gas constant (m**3 (bar)/mol K)\n", "\n", "import math\n", "#For step 1:\n", "Po = 4.; \t\t\t#pressure at A (bar)\n", "P1 = 1.; \t\t\t#pressure at C (bar)\n", "T = 300.; \t\t\t#temperature (K)\n", "\n", "# Calculations and Results\n", "#del_S1 = intg[(del_V/del_T)pdP]\n", "del_S1 = (R*math.log(Po/P1) - (A/T**2)*(Po**2-P1**2)/2)*10**5; \t\t\t#(J/mol K)\n", "\n", "#For step 2:\n", "T1 = 300.; \t\t\t#temperature at C (K)\n", "T2 = 400.; \t\t\t#temperature at D (K)\n", "del_S2 = Cp*math.log(T2/T1) \t\t\t#(J/mol K)\n", "\n", "#For step 3:\n", "P2 = 1.; \t\t\t#pressure at D (bar)\n", "P3 = 12.; \t\t\t#pressure at B (bar)\n", "T = 400.; \t\t\t#temperature (K)\n", "del_S3 = (R*math.log(P2/P3) - (A/T**2)*(P2**2-P3**2)/2)*10**5; \t\t\t#(J/mol K)\n", "S = del_S1+del_S2+del_S3; \t\t\t#total entropy change\n", "print '(a). Total entropy change is %f J/mol K'%S\n", "\n", "#(b). The mean heat capacity at 12 bar\n", "P1 = 4.; \t\t\t#pressure at A (bar)\n", "P2 = 12.; \t\t\t#pressure at Co (bar)\n", "T = 300.; \t\t\t#temperature (K)\n", "del_S1 = R*math.log(P1/P2) - (A/T**2)*(P1**2-P2**2)/2;\n", "\n", "#For CoB\n", "T2 = 400.; \t\t\t#temperature at B (K)\n", "T1 = 300.; \t\t\t#temperature at Co (K)\n", "del_S2 = S-del_S1;\n", "Cpm = del_S2/(math.log(T2/T1))\n", "print ' (b). The mean heat capacity at 12 bar is %f J/mol K'%Cpm\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a). Total entropy change is 0.568609 J/mol K\n", " (b). The mean heat capacity at 12 bar is 1.976835 J/mol K\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.10" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "betta = 1.8*10**-4; \t\t\t#coeffecient of volume math.expansion (K**-1)\n", "k = 3.9*10**-6; \t\t\t#coeffecient of compressibility (bar**-1)\n", "T = 273.; \t\t\t#temperature in K\n", "d = 13.596*10**3; \t\t\t#density (kg/m**3)\n", "Cp = 0.14*10**3; \t\t\t#(J/kg K)\n", "\n", "# Calculations\n", "#To calculate Cv for mercury\n", "#Using equation 6.55 (Page no. 208)\n", "Cv = Cp - (betta**2*T*10**5)/(k*d)\n", "\n", "# Results\n", "print 'Cv for mercury is %f J/kg K'%Cv\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Cv for mercury is 123.318623 J/kg K\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.21" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "#Eqution of state: P(V-b) = RT\n", "P = 10.; \t\t\t#pressure (bar)\n", "T = 298.; \t\t\t#temperature (K)\n", "b = 3.707*10**-5; \t\t\t#Vander Waal's constant (m**3/mol)\n", "R = 8.314; \t\t\t#ideal gas constant\n", "\n", "# Calculations\n", "#To estimate the fugacity of ammonia\n", "#Since PV = RT + Pb% Z = 1 + (Pb/RT)\n", "#Using equation 6.127 (Page no. 228)\n", "f = P*(math.e**((b*P*10**5)/(R*T)))\n", "\n", "# Results\n", "print 'Fugacity f = %f bar'%f\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity f = 10.150747 bar\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.22" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "#intg(alphadP) = -556.61 J/mol\n", "P = 50.; \t\t\t#pressure in bar\n", "T = 300.; \t\t\t#temperature in K\n", "R = 8.314; \t\t\t#ideal gas constant\n", "\n", "# Calculations\n", "#To determine the fugacity of gas\n", "#Using equation 6.130 (Page no. 230)\n", "f = P*math.e**(-556.61/(R*T))\n", "\n", "# Results\n", "print 'Fugacity of gas at 50 bar and 300 K is %i bar'%f\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity of gas at 50 bar and 300 K is 39 bar\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.23" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "#Equation of state: PV = RT(1-0.00513P)\n", "P = [1, 5, 10]; \t\t\t#pressures in bar\n", "phi = [0,0,0]\n", "\n", "# Calculations and Results\n", "for i in range(3):\n", " phi[i] = math.e**(-0.00513*P[i])\n", " print ' Fugacity coeffecient at %i bar is %f'%(P[i],phi[i])\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Fugacity coeffecient at 1 bar is 0.994883\n", " Fugacity coeffecient at 5 bar is 0.974676\n", " Fugacity coeffecient at 10 bar is 0.949994\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "P = 100.; \t\t\t#pressure in bar\n", "T = 373.; \t\t\t#temperature in K\n", "a = 0.453; \t\t\t#Vander Waal's constant (J m**3/mol**2)\n", "b = 0.571*10**-4; \t\t\t#Vander Waal's constant (m**3/mol)\n", "V = 2.072*10**-4; \t\t\t#molar volume (m**3/mol)\n", "R = 8.314; \t\t\t#ideal gas constant\n", "\n", "# Calculations\n", "#To determine the fugacity of pure ethylene\n", "#Using eq. 6.139 (Page no. 233)\n", "ln_f = (b/(V-b)) - ((2*a)/(R*T*V)) + math.log((R*T*10**-5)/(V-b) )\n", "f = math.e**ln_f;\n", "\n", "# Results\n", "print 'Fugacity is %f bar'%f\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity is 73.789328 bar\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.26" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "T = 623.; \t\t\t#temperature in K\n", "\n", "#Data from steam tables:\n", "H = 3159.; \t\t\t#enthalpy at 1000 kPa and 623 K (kJ/kg)\n", "S = 7.3; \t\t\t#entropy at 1000 kPa and 623 K (kJ/kg K)\n", "Ho = 3176.; \t\t\t#enthalpy at 101.3 kPa and 623 K (kJ/kg)\n", "So = 8.38; \t\t\t#entropy at 101.3 kPa and 623 K (kJ/kg K)\n", "fo = 101.3; \t\t\t#fugacity at 101.3 kPa (kPa)\n", "R = 8.314/18; \t\t\t#ideal gas consatnt (kJ/kg K)\n", "\n", "# Calculations\n", "#To determine fugacity and fugacity coeffecient of steam\n", "ln_phi = (1/(R*T))*((H-Ho)-T*(S-So))\n", "f = fo*math.e**ln_phi;\n", "phi = f/fo;\n", "\n", "# Results\n", "print 'Fugacity of steam is %f bar'%(f/100)\n", "print ' Fugacity coeffecient is %f'%phi\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity of steam is 9.895333 bar\n", " Fugacity coeffecient is 9.768345\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.27" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "T = 473.; \t\t\t#temperature in K\n", "P = 50.*10**5; \t\t\t#pressure in Pa\n", "d = 24.3; \t\t\t#density of ammonia (kg/m**3)\n", "m = 17.; \t\t\t#molecular wt of ammonia\n", "R = 8.314; \t\t\t#ideal gas constant\n", "\n", "# Calculations\n", "#To estimate the fugacity of ammonia\n", "V = m/(d*1000) \t\t\t#molar volume of ammonia (m**3/kmol)\n", "#Using eq. 6.142 (Page no. 234)\n", "f = (V*(P**2))/(R*T)\n", "\n", "# Results\n", "print 'The fugacity of ammonia is %f bar'%(f/10**5)\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The fugacity of ammonia is 44.474543 bar\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.28" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "T = 303.; \t\t\t#temperature in K\n", "P = 10.; \t\t\t#pressure in bar\n", "Ps = 4.241/100; \t\t\t#saturation pressure (bar)\n", "sp_vol = 1.004 *10**-3; \t\t\t#specific volume at 303 K (m**3/kg)\n", "R = 8.314; \t\t\t#ideal gas constant\n", "\n", "# Calculations\n", "#To calculate the fugacity of liquid water\n", "V = sp_vol*10**-3*18; \t\t\t#molar volume (m**3/mol)\n", "#Assuming vapour behaves as an ideal gas\n", "f_sat = Ps;\n", "#Using Eq. 6.144 (Page no. 235)\n", "ln_phi = (V/(R*T))*(P-Ps)*10**5;\n", "f = f_sat*math.e**ln_phi;\n", "\n", "# Results\n", "print 'Fugacity of liquid water at given conditions is %f bar'%f\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity of liquid water at given conditions is 0.042714 bar\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.29" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "T = 350.; \t\t\t#temperature in K\n", "P = 60.; \t\t\t#pressure in bar\n", "Ps = 9.35; \t\t\t#vapour pressure at 350 K (bar)\n", "V = 0.1072*10**-3; \t\t\t#molar volume (m**3/mol\n", "phi = 0.834; \t\t\t#fugacity coeffecient\n", "R = 8.314; \t\t\t#ideal gas constant\n", "import math\n", "\n", "# Calculations\n", "#To determine fugaity of n butane in liquid state at given conditions\n", "f_sat = phi*Ps;\n", "#Using eq. 6.144 (Page no. 235)\n", "ln_phi = (V/(R*T))*(P-Ps)*10**5;\n", "f = f_sat*math.e**ln_phi;\n", "\n", "# Results\n", "print 'Fugacity of n-butane in liquid state at given conditions is %f bar'%f\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fugacity of n-butane in liquid state at given conditions is 9.397539 bar\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 6.30" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "M = 24.32; \t\t\t#molecular wt of solid magnesium\n", "T = 300.; \t\t\t#temperature in K\n", "P = 10.; \t\t\t#pressure in bar\n", "Po = 1.; \t\t\t#reference state pressure (bar)\n", "R = 8.314\n", "d = 1.745*10**3; \t\t\t#density of Mg at 300 K in kg/m**3\n", "\n", "# Calculations\n", "#To determine the ativity of solid magnesiun\n", "#Using eq. 6.149 (Page no. 237)\n", "ln_a = (M/(d*10**3*R*T))*(P-Po)*10**5;\n", "a = (math.e)**ln_a;\n", "\n", "# Results\n", "print 'Acivity of solid magnesium at 300 K and 10 bar is %f'%a\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Acivity of solid magnesium at 300 K and 10 bar is 1.005042\n" ] } ], "prompt_number": 34 } ], "metadata": {} } ] }