{
"metadata": {
"name": "",
"signature": "sha256:f22779b8fff9ea06914fd530daf547f36c0e2d7163616b6b2b466ab75a676e0a"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7 : Entropy"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1 Page No : 185"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"T1 = 37.+273;\n",
"T2 = 35.+273;\n",
"m = 1.;\n",
"cv = 4.187;\n",
"\n",
"# Calculation\n",
"S = m*cv*math.log(T1/T2); \t\t\t# S = S2-S1\n",
"\n",
"# Results\n",
"print \"Change in the entropy of the water is %.4f KJ/K\"%S\n",
"\n",
"# note : answer is accurate. please check."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Change in the entropy of the water is 0.0271 KJ/K\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2 Page No : 186"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Part (a)\n",
"T1 = 273.;\n",
"T2 = 373.;\n",
"m = 1. ;\n",
"cv = 4.187;\n",
"\n",
"# Calculation and Results\n",
"Ss = m*cv*math.log(T2/T1); \t\t\t# S = S2-S1\n",
"Q = m*cv*(T2-T1);\n",
"Sr = -(Q/T2);\n",
"S = Ss+Sr;\n",
"\n",
"print \"The entropy change of the universe is %.3f kJ/K\"%S\n",
"\n",
"# Part (b)\n",
"T3 = 323.;\n",
"Sw = m*cv*(math.log(T3/T1)+math.log(T2/T3));\n",
"Sr1 = -m*cv*(T3-T1)/T3;\n",
"Sr2 = -m*cv*(T2-T3)/T2;\n",
"Su = Sw+Sr1+Sr2;\n",
"print \"The entropy change of the universe is %.3f kJ/K\"%Su\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The entropy change of the universe is 0.184 kJ/K\n",
"The entropy change of the universe is 0.097 kJ/K\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3 Page No : 187"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"# Part (a)\n",
"m = 1.;\n",
"T1 = -5.+273;\n",
"T2 = 20.+273;\n",
"T0 = 0.+273;\n",
"cp = 2.093;\n",
"cv = 4.187;\n",
"lf = 333.3;\n",
"\n",
"# Calculation\n",
"Q = m*cp*(T0-T1)+1*333.3+m*cv*(T2-T0);\n",
"Sa = -Q/T2;\n",
"Ss1 = m*cp*math.log(T0/T1);\n",
"Ss2 = lf/T0;\n",
"Ss3 = m*cv*math.log(T2/T0);\n",
"St = Ss1+Ss2+Ss3;\n",
"Su = St+Sa;\n",
"\n",
"# Results\n",
"print \"The entropy change of the universe is %.4f kJ/K\"%Su\n",
"\n",
"# Part (b)\n",
"S = 1.5549; \t\t\t# S = S4-S1\n",
"Wmin = T2*(S)-Q;\n",
"print \"The minimum risk required is %.1f kJ\"%Wmin\n",
"\n",
"# rounding off error. please check."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The entropy change of the universe is 0.0965 kJ/K\n",
"The minimum risk required is 28.1 kJ\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5 Page No : 190"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"Vo = 8.4;\n",
"Vh = 14.;\n",
"n1 = Vo/22.4; \n",
"n2 = Vh/22.4;\n",
"R = 8.31;\n",
"\n",
"# Calculation\n",
"x1 = n1/(n1+n2);\n",
"x2 = n2/(n1+n2);\n",
"S = -R*(n1*math.log(x1)+n2*math.log(x2));\n",
"\n",
"# Results\n",
"print \"Entropy change for the process is %.2f J/K\"%S\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Entropy change for the process is 5.50 J/K\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.8 Page No : 192"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from hornerc import horner\n",
"import sys\n",
"\n",
"# Variables\n",
"#T = poly(0,'T'); \t\t\t# T = Tf\n",
"Tf_ = [700,-2] #700-2*T; \t\t\t# Tf_ = Tf'\n",
"\n",
"# Calculation\n",
"# Bisection method to solve for the polynomial\n",
"def Temperature(a,b,f):\n",
" N = 100.;\n",
" eps = 1e-5;\n",
" if((f(a)*f(b))>0):\n",
" print ('no root possible f(a)*f(b)>0');\n",
" sys.exit(0);\n",
"\n",
" if(abs(f(a))<eps):\n",
" print ('solution at a');\n",
" sys.exit(0)\n",
"\n",
" if(abs(f(b))<eps):\n",
" print ('solution at b');\n",
" sys.exit(0)\n",
"\n",
" while(N>0):\n",
" c = (a+b)/2\n",
" if(abs(f(c))<eps):\n",
" x = c ;\n",
" return x;\n",
"\n",
" if((f(a)*f(c))<0 ):\n",
" b = c ;\n",
" else:\n",
" a = c ;\n",
" N = N-1;\n",
" print ('no convergence');\n",
" sys.exit(0);\n",
"\n",
"\n",
"def p(T): \n",
"\t return 2*T**3-700*T**2+9000000 \n",
"T = Temperature(100,200,p);\n",
"\n",
"Tf_ = horner(Tf_,T);\n",
"\n",
"print \"The final temperature of the body C is\",Tf_,\"K\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The final temperature of the body C is 400 K\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.9 Page No : 193"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from scipy.integrate import quad \n",
"import sys\n",
"from numpy import poly1d\n",
"from sympy import Symbol\n",
"\n",
"# Variables\n",
"T1 = 200.;\n",
"T2 = 100.;\n",
"A = 0.042;\n",
"\n",
"# Calculation\n",
"def f10(T): \n",
"\t return A*T**2\n",
"\n",
"Q1 = quad(f10,T1,T2)[0]\n",
"\n",
"\n",
"def f11(T): \n",
"\t return A*T**2/T\n",
"\n",
"S = quad(f11,T1,T2)[0]\n",
"\n",
"W = Symbol('W');\n",
"Z = (-Q1-W)/T2 + S; \t\t\t# Polynomial to be solved for W\n",
"\n",
"# Bisection method to solve for the Work\n",
"def Work(a,b,f):\n",
" N = 100.;\n",
" eps = 1e-5;\n",
" if((f(a)*f(b))>0):\n",
" print ('no root possible f(a)*f(b)>0');\n",
" sys.exit(0);\n",
"\n",
" if(abs(f(a))<eps):\n",
" print ('solution at a');\n",
" sys.exit(0)\n",
"\n",
" if(abs(f(b))<eps):\n",
" print ('solution at b');\n",
" sys.exit(0)\n",
"\n",
" while(N>0):\n",
" c = (a+b)/2\n",
" if(abs(f(c))<eps):\n",
" x = c ;\n",
" return x;\n",
" if((f(a)*f(c))<0 ):\n",
" b = c ;\n",
" else:\n",
" a = c ;\n",
" N = N-1;\n",
" print ('no convergence');\n",
" sys.exit(0)\n",
"\n",
"def p(W): \n",
"\t return 350-0.01*W \n",
"\n",
"W = Work(34000,36000,p);\n",
"\n",
"print \"The maximum work that can be recovered is\",W/1000,\"kJ\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum work that can be recovered is 35 kJ\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.10 Page No : 194"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from scipy.integrate import quad \n",
"\n",
"# Variables\n",
"P1 = 0.5e06;\n",
"V1 = 0.2\n",
"V2 = 0.05;\n",
"n = 1.3\n",
"\n",
"# Calculation\n",
"P2 = P1*(V1/V2)**n;\n",
"def H(p):\n",
" return ((P1*V1**n)/p)**(1./n);\n",
"\n",
"def f0(p): \n",
"\t return H\n",
"\n",
"H = quad(H,P1,P2)[0]\n",
"\n",
"U = H-(P2*V2-P1*V1);\n",
"W12 = -U;\n",
"\n",
"# Results\n",
"print \"Change in enthalpy is %.1f kJ\"%(H/1000)\n",
"print \"Change in internal energy is %.2f kJ\"%(U/1000)\n",
"print \"The change in entropy and heat transfer are\",0,\"and\",0,\"kJ\"\n",
"print \"The work transfer during the process is %.2f kJ\"%(W12/1000)\n",
"\n",
"# rounding off error."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Change in enthalpy is 223.5 kJ\n",
"Change in internal energy is 171.91 kJ\n",
"The change in entropy and heat transfer are 0 and 0 kJ\n",
"The work transfer during the process is -171.91 kJ\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.11 Page No : 195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from scipy.integrate import quad \n",
"\n",
"# Variables\n",
"Pa = 130e03; \n",
"Pb = 100e03;\n",
"Ta = 50+273; \n",
"Tb = 13+273;\n",
"cp = 1.005;\n",
"\n",
"# Calculation\n",
"def f1(T): \n",
"\t return cp/T\n",
"\n",
"def f2(p):\n",
" return .287/p\n",
"Ss = quad(f1,Ta,Tb)[0] - quad(f2,Pa,Pb)[0]\n",
"Ssy = 0;\n",
"Su = Ss+Ssy;\n",
"\n",
"# Results\n",
"print \"Change in the entropy of the universe is %.3f kJ/Kg k\"%Su\n",
"print \"As the change in entropy of the universe in the process A-B is negative so the flow must be from B-A\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Change in the entropy of the universe is -0.047 kJ/Kg k\n",
"As the change in entropy of the universe in the process A-B is negative so the flow must be from B-A\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.12 Page No : 196"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"T1 = 300.\n",
"T2 = 330.\n",
"T3 = 270.\n",
"P1 = 4.\n",
"P2 =1.\n",
"P3 =1.\n",
"cp = 1.0005\n",
"R = 0.287;\n",
"\n",
"# Calculation\n",
"S21 = cp*math.log(T2/T1)-R*math.log(P2/P1); \t\t\t# S21 = S2-S1\n",
"S31 = cp*math.log(T3/T1)-R*math.log(P3/P1); \t\t\t# S31 = S3-S1\n",
"Sgen = 1*S21 + 1*S31;\n",
"\n",
"# Results\n",
"print \"The entropy generated during the process is %.3f kW/K\"%Sgen\n",
"print \"As the entropy generated is positive so such device is possible\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The entropy generated during the process is 0.786 kW/K\n",
"As the entropy generated is positive so such device is possible\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.13 Page No : 197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"A = 5.*7;\n",
"k = 0.71;\n",
"L = 0.32;\n",
"Ti = 21.+273;\n",
"To = 6.+273;\n",
"\n",
"# Calculation and Results\n",
"Q = k*A*(Ti-To)/L ;\n",
"print \"The rate of heat transfer through the wall is %.2f W\"%Q\n",
"\n",
"Sgen_wall = Q/To - Q/Ti;\n",
"print \"The rate of entropy through the wall is %.3f W/K\"%Sgen_wall\n",
"\n",
"Tr = 27+273.;\n",
"Ts = 2+273.;\n",
"Sgen_total = Q/Ts-Q/Tr;\n",
"print \"The rate of total entropy generation with this heat transfer process is %.3f W/K\"%Sgen_total\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The rate of heat transfer through the wall is 1164.84 W\n",
"The rate of entropy through the wall is 0.213 W/K\n",
"The rate of total entropy generation with this heat transfer process is 0.353 W/K\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}