diff options
Diffstat (limited to 'Basic_And_Applied_Thermodynamics_by_P._K._Nag/Chapter10.ipynb')
| -rw-r--r-- | Basic_And_Applied_Thermodynamics_by_P._K._Nag/Chapter10.ipynb | 597 |
1 files changed, 597 insertions, 0 deletions
diff --git a/Basic_And_Applied_Thermodynamics_by_P._K._Nag/Chapter10.ipynb b/Basic_And_Applied_Thermodynamics_by_P._K._Nag/Chapter10.ipynb new file mode 100644 index 00000000..cf4b44fb --- /dev/null +++ b/Basic_And_Applied_Thermodynamics_by_P._K._Nag/Chapter10.ipynb @@ -0,0 +1,597 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 10: Properties of gases and gas mixture" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.1:pg-366" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.1\n", + "\n", + "\n", + " The final equilibrium pressure is 1.16869318853 MPa\n", + "\n", + " The amount of heat transferred to the surrounding is -226.04503125 kJ\n", + " \n", + "\n", + " If the vessel is perfectly insulated\n", + "\n", + " The final temperature is 45.4545454545 degree Celsius\n", + "\n", + " The final pressure is 1.24058552709 MPa\n" + ] + } + ], + "source": [ + "Pa = 1.5 # Pressure in vessel A in MPa\n", + "Ta = 50 # Temperature in vessel A in K\n", + "ca = 0.5 # Content in vessel A in kg mol\n", + "Pb = 0.6 # Pressure in vessel B in MPa\n", + "Tb = 20 # Temperature in vessel B in K\n", + "mb = 2.5 # Content in vessel B in kg mol\n", + "R = 8.3143 # Universal gas constant\n", + "Va = (ca*R*(Ta+273))/(Pa*1e03) # volume of vessel A\n", + "ma = ca*28 # mass of gas in vessel A\n", + "Rn = R/28 # Gas content to of nitrogen\n", + "Vb = (mb*Rn*(Tb+273))/(Pb*1e03) # volume of vessel B\n", + "V = Va + Vb # Total volume\n", + "m = ma + mb # Total mass\n", + "Tf = 27 # Equilibrium temperature in degree Celsius\n", + "P = (m*Rn*(Tf+273))/V # Equilibrium pressure \n", + "g = 1.4 # Heat capacity ratio\n", + "cv = Rn/(g-1) # Heat capacity at constant volume\n", + "U1 = cv*(ma*Ta+mb*Tb) # Initial internal energy \n", + "U2 = m*cv*Tf# Final internal energy \n", + "Q = U2-U1 # heat transferred\n", + "\n", + "print \"\\n Example 10.1\"\n", + "print \"\\n\\n The final equilibrium pressure is \",P/1e3 ,\" MPa\"\n", + "print \"\\n The amount of heat transferred to the surrounding is \",Q ,\" kJ\"\n", + "#The answers vary due to round off error\n", + "\n", + "T_ = (ma*Ta+mb*Tb)/m # final temperature\n", + "P_ = (m*Rn*(T_+273))/V # final pressure\n", + "print \" \\n\\n If the vessel is perfectly insulated\"\n", + "print \"\\n The final temperature is \",T_ ,\" degree Celsius\"\n", + "print \"\\n The final pressure is \",P_/1e3 ,\" MPa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.2:pg-368" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.2\n", + "\n", + "\n", + " Gas constant of the gas is 0.461 kJ/kg K \n", + "\n", + " Molecular weight the gas is 18.0347071584 kg/kg mol\n", + "\n", + " The heat transfer at constant volume is 286.33 kJ\n", + "\n", + " Work done is 0 kJ\n", + "\n", + " The change in internal energy is 286.33 kJ\n", + "\n", + " The change in enthalpy is 373.92 kJ\n", + "\n", + " The change in entropy is 0.0 kJ/k\n" + ] + } + ], + "source": [ + "\n", + "cp = 1.968 # Heat capacity in kJ/kg\n", + "cv = 1.507 # Heat capacity in kJ/kg\n", + "R_ = 8.314 # Gas constant\n", + "V = 0.3 # Volume of chamber in m**3\n", + "m = 2 # mass of gas in kg\n", + "T1 = 5# Initial gas temperature in degree Celsius\n", + "T2 = 100 # Final gas temperature in degree Celsius\n", + "R = cp-cv # Universal gas constant\n", + "mu = R_/R # molecular weight\n", + "Q12 = m*cv*(T2-T1) # The heat transfer at constant volume\n", + "W12 = 0 # work done\n", + "U21 = Q12 # change in internal energy\n", + "H21= m*cp*(T2-T1) # change in enthalpy\n", + "S21 = m*cv*math.log((T2+273)/(T1+273)) #change in entropy \n", + "\n", + "print \"\\n Example 10.2\"\n", + "print \"\\n\\n Gas constant of the gas is \",R ,\" kJ/kg K \"\n", + "print \"\\n Molecular weight the gas is \",mu ,\" kg/kg mol\"\n", + "print \"\\n The heat transfer at constant volume is \",Q12 ,\" kJ\"\n", + "print \"\\n Work done is \",0 ,\" kJ\"\n", + "print \"\\n The change in internal energy is \",U21 ,\" kJ\"\n", + "print \"\\n The change in enthalpy is \",H21 ,\" kJ\"\n", + "print \"\\n The change in entropy is \",S21 ,\" kJ/k\"\n", + "#The answers vary due to round off error\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.3:pg-369" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.3\n", + "\n", + " The work done in the expansion is 300.72200185 kJ\n" + ] + } + ], + "source": [ + "import math\n", + "from scipy import integrate\n", + "m = 1.5 # Mass of gas in kg\n", + "P1 = 5.6 # Initial pressure of gas in MPa\n", + "V1 = 0.06 # Initial volume of gas in m**3\n", + "T2_ = 240 # Final temperature of gas in degree Celsius\n", + "a = 0.946 # Constant\n", + "b = 0.662 # Constant\n", + "k = 1e-4 # Constant\n", + "# Part (b)\n", + "R = a-b # constant\n", + "T2 = T2_+273 # Final temperature of gas in KK\n", + "T1 = (P1*1e03*V1)/(m*R) # Initial temperature\n", + "W12,er =integrate.quad(lambda T:m*(b+k*T),T1,T2) # Work done\n", + "\n", + "print \"\\n Example 10.3\"\n", + "print \"\\n The work done in the expansion is \",-W12 ,\" kJ\"\n", + "#The answers vary due to round off error\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.5:pg-371" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.5\n", + "\n", + " The work transfer for the whole path is 93.4986082985 kJ\n", + "\n", + " The heat transfer for the whole path 571.638005316 kJ\n" + ] + } + ], + "source": [ + "\n", + "m = 0.5 # mass of air in kg\n", + "P1 = 80 # Initial pressure kPa\n", + "T1 = 60 # Initial temperature in degree Celsius\n", + "P2 = 0.4 # Final pressure in MPa\n", + "R = 0.287 # Gas constant\n", + "V1 = (m*R*(T1+273))/(P1) # Volume of air at state 1\n", + "g = 1.4 # Heat capacity ratio\n", + "T2 = (T1+273)*(P2*1e3/P1)**((g-1)/g)# Final temperature\n", + "W12 = (m*R*(T1+273-T2))/(g-1) # Work done in \n", + "V2 = V1*((P1/(P2*1e3))**(1/g)) # Final volume\n", + "W23 = P2*(V1-V2)*1e3 # # Work done\n", + "W = W12+W23 # Net work done\n", + "V3 = V1 # constant volume\n", + "T3 = (T2)*(V3/V2) # Temperature at state 3\n", + "cp = 1.005 # Heat capacity at constant volume in kJ/kgK\n", + "Q = m*cp*(T3-T2)# Heat transfer\n", + "print \"\\n Example 10.5\"\n", + "print \"\\n The work transfer for the whole path is \",W ,\" kJ\"\n", + "#The answers vary due to round off error\n", + "print \"\\n The heat transfer for the whole path \",Q ,\" kJ\"\n", + "#The answer provided in the textbook is wrong\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.6:pg-372" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.6\n", + "\n", + " The heat received in the cycle is 137.268292683 kJ\n", + "\n", + " The heat rejected in the cycle 84.2666952566 kJ\n", + "\n", + " The efficiency of the cycle is 39.0 percent\n" + ] + } + ], + "source": [ + "P1 = 700 # Initial pressure of gas in kPa\n", + "T1 = 260 # Initial temperature of gas in degree Celcius \n", + "T3 = T1 # Temperature at state 3\n", + "V1 = 0.028 # Initial volume of gas in m**3\n", + "V2 = 0.084 # Final volume of gas in m**3\n", + "R = 0.287 # Gas constant\n", + "m = (P1*V1)/(R*(T1+273)) # mass of gas \n", + "P2 = P1 # Pressure at state 2\n", + "T2 = (T1+273)*((P2*V2)/(P1*V1)) # Temperature at state 2\n", + "n = 1.5 # polytropic index \n", + "P3 = P2*(((T3+273)/(T2))**(n/(n-1))) # Pressure at state 3\n", + "cp = 1.005 # COnstant pressure heat capacity in kJ/kgK\n", + "cv = 0.718 # COnstant volume heat capacity in kJ/kgK\n", + "Q12 = m*cp*(T2-T1-273) # HEat transfer\n", + "Q23 = m*cv*(T3+273-T2) + (m*R*(T2-T3-273))/(n-1) # Heat transfer\n", + "Q31 = m*R*(T1+273)*math.log(P3/P2) # Heat transfer\n", + "Q1 = Q12 # Heat equivalance\n", + "Q2 = -(Q23+Q31) # Net heat transfer\n", + "e = 1-(Q2/Q1) # First law efficiency\n", + "\n", + "print \"\\n Example 10.6\"\n", + "print \"\\n The heat received in the cycle is \",Q1 ,\" kJ\"\n", + "print \"\\n The heat rejected in the cycle \",Q2 ,\" kJ\"\n", + "print \"\\n The efficiency of the cycle is \",math. ceil(e*100) ,\" percent\"\n", + "#The answers vary due to round off error" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.7:pg-374" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.7\n", + "\n", + " Cv of the gas is 0.661000944287 kJ/kg K\n", + "\n", + " Cp of the gas is 0.89896128423 kJ/kg K\n", + "\n", + " Increase in the entropy of the gas is 0.080159241414 kJ/kg K\n" + ] + } + ], + "source": [ + "\n", + "P1 = 300 # Initial gas pressure in kPa\n", + "V1 = 0.07 # Initial volume of gas in m**3\n", + "m = 0.25 # Mass of gas in kg\n", + "T1 = 80 # Initial temperature of gas in degree Celsius\n", + "R = (P1*V1)/(m*(T1+273)) # constant\n", + "P2 = P1 # process condition\n", + "V2 = 0.1 # Final volume in m**3\n", + "T2 = (P2*V2)/(m*R) # Final temperature in K\n", + "W = -25 #Work done in kJ\n", + "cv = -W/(m*(T2-T1-273)) # Constant volume heat capacity in kJ/kg\n", + "cp = R+cv #Constant pressure heat capacity in kJ/kg\n", + "S21 = m*cp*math.log(V2/V1) # Entropy change\n", + "print \"\\n Example 10.7\"\n", + "print \"\\n Cv of the gas is \",cv ,\" kJ/kg K\"\n", + "print \"\\n Cp of the gas is \",cp ,\" kJ/kg K\"\n", + "print \"\\n Increase in the entropy of the gas is \",S21 ,\" kJ/kg K\"\n", + "#The answers vary due to round off error\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.8:pg-374" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.8\n", + "\n", + "\n", + " Mole fraction of N2 is 0.485294117647\n", + "\n", + " Mole fraction of CO2 is 0.514705882353\n", + "\n", + " Equivalent molecular weight of mixture is 36.2352941176 kg/kg mol\n", + "\n", + "\n", + " The equivalent gas constant of the mixture is 0.229444805195 kJ/kg K\n", + "\n", + "\n", + " Partial pressures of nitrogen and CO2 are \n", + " 145.588235294 kPa and 154.411764706 kPa respectively\n", + "\n", + " Partial volume of nitrogen and CO2 are \n", + " 0.870000714286 kPa and 0.922728030303 kPa respectively\n", + "\n", + "\n", + " Total volume of mixture is 1.79272874459 m**3\n", + "\n", + " Density of mixture is 4.46247098126 kg/m**3\n", + "\n", + "\n", + " Cp and Cv of mixture are \n", + " 0.920740483948 kJ/kg K and 0.691295678753 kJ/kg K respectively\n", + "\n", + "\n", + " Change in internal energy of the system heated at constant volume is 110.6073086 kJ\n", + "\n", + " Change in enthalpy of the system heated at constant volume is 147.318477432 kJ\n", + "\n", + " Change in entropy of the system heated at constant volume is 0.36517324538 kJ/kg K\n", + "\n", + "\n", + " Change in entropy of the system heated at constant Pressure is 0.486376236695 kJ/kgK\n" + ] + } + ], + "source": [ + "import math\n", + "mn = 3.0 # Mass of nitrogen in kg\n", + "mc = 5.0 # mass of CO2 in kg\n", + "an = 28.0 # Atomic weight of nitrogen\n", + "ac = 44.0 # Atomic weight of CO2\n", + "# Part (a)\n", + "xn = (mn/an)/((mn/an)+(mc/ac)) # mole fraction of nitrogen\n", + "xc = (mc/ac)/((mn/an)+(mc/ac)) # mole fraction of carbon\n", + "\n", + "print \"\\n Example 10.8\"\n", + "print \"\\n\\n Mole fraction of N2 is \",xn \n", + "print \"\\n Mole fraction of CO2 is \",xc\n", + "#The answers vary due to round off error\n", + "\n", + "# Part (b)\n", + "M = xn*an+xc*ac # Equivalent molecular weight\n", + "print \"\\n Equivalent molecular weight of mixture is \",M ,\"kg/kg mol\" \n", + "\n", + "# Part (c)\n", + "R = 8.314 # Gas constant\n", + "Req = ((mn*R/an)+(mc*R/ac))/(mn+mc)\n", + "print \"\\n\\n The equivalent gas constant of the mixture is \",Req ,\" kJ/kg K\" \n", + "\n", + "# Part (d)\n", + "P = 300.0 # Initial pressure in kPa\n", + "T = 20.0 # Initial temperature in degree Celsius\n", + "Pn = xn*P # Partial pressure of Nitrogen\n", + "Pc = xc*P # Partial pressure of CO2 \n", + "Vn = (mn*R*(T+273))/(P*an) # Volume of nitrogen\n", + "Vc = (mc*R*(T+273))/(P*ac) # Volume of CO2\n", + "print \"\\n\\n Partial pressures of nitrogen and CO2 are \\n \",Pn ,\" kPa and \",Pc ,\" kPa respectively\"\n", + "print \"\\n Partial volume of nitrogen and CO2 are \\n \",Vn ,\" kPa and \",Vc ,\" kPa respectively\"\n", + "# Part (e)\n", + "V = (mn+mc)*Req*(T+273)/P # Total volume\n", + "rho = (mn+mc)/V # mass density\n", + "print \"\\n\\n Total volume of mixture is \",V ,\" m**3\" \n", + "print \"\\n Density of mixture is \",rho ,\" kg/m**3\" \n", + "\n", + "# Part (f)\n", + "gn = 1.4 # Heat capacity ratio for nitrogen\n", + "gc = 1.286 # Heat capacity ratio for carbon dioxide \n", + "cvn = R/((gn-1)*an) # cp and cv of N2\n", + "cpn = gn*cvn # Constant pressure heat capacity of nitrogen\n", + "cvc = R/((gc-1)*ac) # cp and cv of CO2\n", + "cpc = gc*cvc# COnstant pressure heat capacity of carbon dioxide \n", + "cp = (mn*cpn+mc*cpc)/(mn+mc) # Constant pressure heat capacity ratio of mixture\n", + "cv = (mn*cvn+mc*cvc)/(mn+mc) # Constant volume Heat capacity ratio of mixture\n", + "print \"\\n\\n Cp and Cv of mixture are \\n \",cp ,\"kJ/kg K and \",cv ,\"kJ/kg K respectively\" \n", + "T1 = T \n", + "T2 = 40 \n", + "U21 = (mn+mc)*cv*(T2-T1)\n", + "H21 = (mn+mc)*cp*(T2-T1)\n", + "S21v = (mn+mc)*cv*math.log((T2+273)/(T1+273)) # If heated at constant volume\n", + "S21p = (mn+mc)*cp*math.log((T2+273)/(T1+273)) # If heated at constant Pressure\n", + "\n", + "print \"\\n\\n Change in internal energy of the system heated at constant volume is \",U21 ,\"kJ\" \n", + "print \"\\n Change in enthalpy of the system heated at constant volume is \",H21 ,\"kJ\" \n", + "print \"\\n Change in entropy of the system heated at constant volume is \",S21v ,\" kJ/kg K\"\n", + "print \"\\n\\n Change in entropy of the system heated at constant Pressure is \",S21p ,\"kJ/kgK\" \n", + "\n", + "#The answers vary due to round off error\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.9:pg-375" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.9\n", + "\n", + " Increase in entropy is 1.22920562691 kJ/kg K\n" + ] + } + ], + "source": [ + "import math\n", + "mo = 2.0 # mass of oxygen in kg\n", + "mn = 6.0 # mass of nitrogen in kg\n", + "muo = 32.0 # molecular mass of oxygen\n", + "mun = 28.0 # molecular mass of nitrogen\n", + "o = mo/muo # mass fraction of oxygen\n", + "n = mn/mun # mass fraction of nitrogen\n", + "xo = o/(n+o) # mole fraction of oxygen\n", + "xn = n/(n+o) # mole fraction of nitrogen\n", + "R = 8.314 # Universal gas constant\n", + "Ro = R/muo # Gas constant for oxygen\n", + "Rn = R/mun # Gas constant for nitrogen\n", + "dS = -mo*Ro*math.log(xo)-mn*Rn*math.log(xn) # Increase in entropy \n", + "\n", + "print \"\\n Example 10.9\"\n", + "print \"\\n Increase in entropy is \",dS ,\" kJ/kg K\"\n", + "#The answers vary due to round off error\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex10.10:pg-376" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Example 10.10\n", + "\n", + " Specific volume is 3.05515367719 *10**-3 m3/kg\n", + "\n", + " Specific temperature is 57.85 K\n", + "\n", + " Specific pressure is 5.46 MPa\n", + "\n", + " Reduced volume is 1.48226362179 m3/kg\n" + ] + } + ], + "source": [ + "\n", + "an = 20.183 # molecular weight of neon\n", + "Pc = 2.73 # Critical pressure\n", + "Tc = 44.5 # Critical tmperature in Kelvin\n", + "Vc = 0.0416 # volume of gas in m**3\n", + "Pr = 2 # Reduced Pressure\n", + "Tr = 1.3 # Reduced temperature\n", + "Z = 0.7 # Compressibility factor\n", + "P = Pr*Pc # Corresponding Pressure \n", + "T = Tr*Tc # Corresponding temperature\n", + "R = 8.314 # Gas constant\n", + "v = (Z*R*T)/(P*an) # Corresponding volume\n", + "vr = (v*an)/(Vc*1e3) # reduced volume\n", + "\n", + "print \"\\n Example 10.10\"\n", + "print \"\\n Specific volume is \",v ,\" *10**-3 m3/kg\"\n", + "print \"\\n Specific temperature is \",T ,\" K\"\n", + "print \"\\n Specific pressure is \",P ,\" MPa\"\n", + "print \"\\n Reduced volume is \",vr ,\" m3/kg\"\n", + "#The answers vary due to round off error\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |