{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 07: Entropy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.1:pg-191"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Example 7.1\n",
"\n",
" Change in entropy of the water is 0.0271 kJ/K\n"
]
}
],
"source": [
"\n",
"import math\n",
"T1 = 37.0 # Final water temperature in degree Celsius \n",
"T2 = 35.0 # Initial water temperature in degree Celsius \n",
"m = 1.0 # Mass of water in kg\n",
"cv = 4.187 # Specific heat capacity of water in kJ/kgK\n",
"print \"\\n Example 7.1\"\n",
"S = m*cv*math.log((T1+273)/(T2+273)) # Change in entropy of the water\n",
"print \"\\n Change in entropy of the water is \",round(S,4) ,\" kJ/K\"\n",
"#The answer provided in the textbook is wrong\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.2:pg-192"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Example 7.2\n",
"\n",
" The entropy change of the universe is -1.12252010724 kJ/K\n"
]
},
{
"ename": "NameError",
"evalue": "name 'log' is not defined",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-13-726fd0a673a1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 16\u001b[0m \u001b[1;31m# Part (b)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 17\u001b[0m \u001b[0mT3\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m323\u001b[0m \u001b[1;31m# Temperature of intermediate reservoir in K\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 18\u001b[1;33m \u001b[0mSw\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mm\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mcv\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlog\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mT3\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mT1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mlog\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mT2\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mT3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# entropy change of water\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 19\u001b[0m \u001b[0mSr1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mcv\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mT3\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mT1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mT3\u001b[0m \u001b[1;31m# Entropy change of universe\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 20\u001b[0m \u001b[0mSr2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mcv\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mT2\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mT3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mT2\u001b[0m \u001b[1;31m# Entropy change of universe\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mNameError\u001b[0m: name 'log' is not defined"
]
}
],
"source": [
"import math\n",
"# Part (a)\n",
"T1 = 273 # Initial temperature of water in Kelvin\n",
"T2 = 373 # Temperature of heat reservoir in Kelvin\n",
"m = 1 # Mass of water in kg\n",
"cv = 4.187 # Specific heat capacity of water\n",
"\n",
"print \"\\n Example 7.2\"\n",
"Ss = m*cv*math.log(T2/T1) # entropy change of water\n",
"Q = m*cv*(T2-T1) # Heat transfer \n",
"Sr = -(Q/T2) # Entropy change of universe\n",
"S = Ss+Sr # Total entropy change\n",
"\n",
"print \"\\n The entropy change of the universe is \",S ,\" kJ/K\"\n",
"\n",
"# Part (b)\n",
"T3 = 323 # Temperature of intermediate reservoir in K\n",
"Sw = m*cv*(log(T3/T1)+log(T2/T3)) # entropy change of water\n",
"Sr1 = -m*cv*(T3-T1)/T3 # Entropy change of universe\n",
"Sr2 = -m*cv*(T2-T3)/T2 # Entropy change of universe\n",
"Su = Sw+Sr1+Sr2 # Total entropy change\n",
"print \"\\n The entropy change of the universe is \",Su ,\" kJ/K\"\n",
"#The answers vary due to round off error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.3:pg-193"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Example 7.3\n",
"\n",
" The entropy change of the universe is -0.238182312568 kJ/K\n",
"\n",
" The minimum work required is -69.7874175824 kJ\n"
]
}
],
"source": [
"import math\n",
"m = 1 # Mass of ice in kg\n",
"\n",
"T1 = -5 # Initial temperature of ice in degree Celsius\n",
"\n",
"T2 = 20# Atmospheric temperature in degree Celsius\n",
"\n",
"T0 = 0# Phase change temperature of ice in degree Celsius\n",
"\n",
"cp = 2.093 # Specific heat capacity of ice in kJ/kgK\n",
"\n",
"cv = 4.187 # Specific heat capacity of water in kJ/kgK\n",
"\n",
"lf = 333.3 # Latent heat of fusion in kJ/kgK\n",
"\n",
"\n",
"\n",
"print \"\\n Example 7.3\"\n",
"\n",
"Q = m*cp*(T0-T1)+1*333.3+m*cv*(T2-T0) # Net heat transfer\n",
"\n",
"Sa = -Q/(T2+273) # Entropy change of surrounding\n",
"\n",
"Ss1 = m*cp*math.log((T0+273)/(T1+273)) # entropy change during \n",
"\n",
"Ss2 = lf/(T0+273) # Entropy change during phase change\n",
"\n",
"Ss3 = m*cv*math.log((T2+273)/(T0+273)) # entropy change of water\n",
"\n",
"St = Ss1+Ss2+Ss3 # total entropy change of ice to convert into water at atmospheric temperature\n",
"\n",
"Su = St+Sa # Net entropy change of universe\n",
"\n",
"print \"\\n The entropy change of the universe is \",Su ,\" kJ/K\"\n",
"\n",
"\n",
"\n",
"#The answer provided in the textbook is wrong\n",
"\n",
"# Part (b)\n",
"\n",
"S = St # Entropy change of system\n",
"\n",
"Wmin = (T2+273)*(S)-Q # minimum work required\n",
"\n",
"print \"\\n The minimum work required is \",Wmin ,\" kJ\"\n",
"\n",
"#The answers vary due to round off error\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.7:pg-200"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Example 7.7\n",
"\n",
" Change in enthalpy is 223.48 kJ\n",
"\n",
" Change in internal energy is 171.91 kJ\n",
"\n",
" The change in entropy and heat transfer are is 0 kJ\n",
"\n",
" The work transfer during the process is -171.91 kJ\n"
]
}
],
"source": [
"import math\n",
"P1 = 0.5 # Initial pressure in MPa\n",
"\n",
"V1 = 0.2 # Initial volume in m**3\n",
"\n",
"V2 = 0.05 # Final volume in m**3\n",
"\n",
"n = 1.3 # Polytropic index\n",
"\n",
"\n",
"\n",
"from scipy import integrate \n",
"\n",
"print \"\\n Example 7.7\"\n",
"\n",
"P2 = P1*(V1/V2)**n \n",
"\n",
"def f(p):\n",
" y = ((P1*V1**n)/p)**(1/n) \n",
" return y\n",
" \n",
"\n",
" \n",
"H, err = integrate.quad(f,P1,P2) # H = H2-H1\n",
"\n",
"U = H-(P2*V2-P1*V1) \n",
" \n",
"W12 = -U \n",
" \n",
"print \"\\n Change in enthalpy is \",round(H*1e3,2),\" kJ\"\n",
" \n",
"print \"\\n Change in internal energy is \",round(U*1000,2),\" kJ\"\n",
" \n",
"print \"\\n The change in entropy and heat transfer are is \",0 ,\" kJ\"\n",
" \n",
"print \"\\n The work transfer during the process is \",round(W12*1000,2) ,\" kJ\"\n",
" \n",
" #The answers vary due to round off error\n",
" \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.8:pg-201"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Example 7.8\n",
"\n",
" Change in the entropy of the universe is -1.2785104723 kJ/Kg K\n",
"\n",
" As the change in entropy of the universe in the process A-B is negative \n",
" so the flow must be from B-A\n"
]
}
],
"source": [
"\n",
"import math\n",
"from scipy import integrate \n",
"\n",
"\n",
"Pa = 130.0 # Pressure at station A in kPa\n",
"\n",
"Pb = 100.0# Pressure at station B in kPa\n",
"\n",
"Ta = 50.0 # Temperature at station A in degree Celsius\n",
"\n",
"Tb = 13.0# Temperature at station B in degree Celsius\n",
"\n",
"cp = 1.005 # Specific heat capacity of air in kJ/kgK\n",
"\n",
"x= lambda t:cp/t\n",
"y= lambda p:0.287/p\n",
"\n",
"print \"\\n Example 7.8\"\n",
"\n",
"Sb,error = integrate.quad(x,Ta,Tb)#-\n",
"Sa,eror=integrate.quad(y,Pa,Pb) \n",
"\n",
"Ss=Sb-Sa\n",
"Ssur=0 \n",
"Su = Ss+Ssur\n",
"\n",
"print \"\\n Change in the entropy of the universe is \",Su ,\" kJ/Kg K\"\n",
"\n",
"#The answers given in the book is wrong\n",
"\n",
"print \"\\n As the change in entropy of the universe in the process A-B is negative \\n so the flow must be from B-A\"\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.9:pg-202"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Example 7.9\n",
"\n",
" The entropy generated during the process is 0.785677602261 kW/K\n",
"\n",
" As the entropy generated is positive so such device is possible\n"
]
}
],
"source": [
"import math\n",
"T1 = 300.0 # Inlet temperature of air in K\n",
"\n",
"T2 = 330.0 # Exit temperature of first air stream in K\n",
"\n",
"T3 = 270.0 # Exit temperature of second air stream in K\n",
"\n",
"P1 = 4.0 # Pressure of inlet air stream in bar\n",
"\n",
"P2 =1.0 # Pressure of first exit air stream in bar\n",
"\n",
"P3 =1.0 # Pressure of second exit air stream in bar\n",
"\n",
"cp = 1.0005 # Specific heat capacity of air in kJ/kgK\n",
"\n",
"R = 0.287 # Gas constant\n",
"\n",
"\n",
"\n",
"print \"\\n Example 7.9\"\n",
"\n",
"S21 = cp*math.log(T2/T1)-R*math.log(P2/P1) # Entropy generation\n",
"\n",
"S31 = cp*math.log(T3/T1)-R*math.log(P3/P1) # Entropy generation\n",
"\n",
"Sgen = (1.0*S21) + (1.0*S31) # Total entropy generation\n",
"\n",
"print \"\\n The entropy generated during the process is \",Sgen ,\" kW/K\"\n",
"\n",
"#The answers vary due to round off error\n",
"\n",
"\n",
"\n",
"print \"\\n As the entropy generated is positive so such device is possible\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.10:pg-203"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Example 7.10\n",
"\n",
" The rate of heat transfer through the wall is 1164.84375 W\n",
"\n",
" The rate of entropy through the wall is 0.213013632873 W/K\n",
"\n",
" The rate of total entropy generation with this heat transfer process is 0.352982954545 W/K\n"
]
}
],
"source": [
"import math\n",
"A = 5*7 # Area of wall in m**2\n",
"k = 0.71# Thermal conductivity in W/mK \n",
"L = 0.32 # Thickness of wall in m\n",
"Ti = 21 # Room temperature in degree Celsius \n",
"To = 6 # Surrounding temperature in degree Celsius\n",
"print \"\\n Example 7.10\"\n",
"Q = k*A*(Ti-To)/L # Heat transfer\n",
"Sgen_wall = Q/(To+273) - Q/(Ti+273) # Entropy generation in wall\n",
"print \"\\n The rate of heat transfer through the wall is \",Q ,\" W\"\n",
"print \"\\n The rate of entropy through the wall is \",Sgen_wall ,\" W/K\"\n",
"Tr = 27 # Inner surface temperature of wall in degree Celsius \n",
"Ts = 2 # Outer surface temperature of wall in degree Celsius \n",
"Sgen_total = Q/(Ts+273)-Q/(Tr+273) # Total entropy generation in process \n",
"print \"\\n The rate of total entropy generation with this heat transfer process is \",Sgen_total ,\" W/K\"\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
}