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"name": ""
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 5 : The thermodynamic web"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.2 Page No : 278"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Variables\n",
"T_c = 370. ; \t\t\t#[K]\n",
"P_c = 41.58 * 10**5 ;\t\t\t#[N/m**2]\n",
"R = 8.314 ;\n",
"V1 = 0.001 ;\t\t\t#[m**3]\n",
"V2 = 0.04 ; \t\t\t#[m**3]\n",
"q = 10400. ; \t\t\t#[J]\n",
"\n",
"# Calculations\n",
"a = 27./64 * (R **2)*(T_c)**2 / P_c ;\n",
"del_U = -0.96 * (1 / V2 - 1 / V1) ; \n",
"W = round(del_U - q,-1) ;\n",
"\n",
"# Results\n",
"print \" Work done for the expansion = %.f J/mol\"%(W) ;\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Work done for the expansion = -9460 J/mol\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.4 Page No : 282"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from scipy.optimize import fsolve \n",
"from scipy.integrate import quad\n",
"import math \n",
"\n",
"# Variables\n",
"P_1 = 9.43 * 10**5 ; \t\t\t#[N/m**2]\n",
"P_2 = 18.9 * 10**5 ; \t\t\t#[N/m**2]\n",
"T_1 = 80 + 273 ; \t\t\t#[K]\n",
"T_2 = 120 + 273 ; \t\t\t#[K]\n",
"A = 1.935 ;\n",
"B = 36.915 * 10**-3 ;\n",
"C = -11.402 * 10**-6 ;\n",
"T_c = 425.2 ; \t\t\t# [K]\n",
"P_c = 37.9 * 10**5 ;\t\t\t#[N/m**2]\n",
"R = 8.314 ;\n",
"\n",
"\n",
"del_h_1 = 1368 ; \t\t\t#[J/mol]\n",
"del_h_3 = -2542 ; \t\t\t#[J/mol]\n",
"Ws = 2100. ; \t\t\t#[J/mol]\n",
"\n",
"a = 0.42748 * R**2 * T_c**2.5 / P_c ;\n",
"b = 0.08664 * R * T_c / P_c ;\n",
" \n",
"\n",
"def f1(v):\n",
" return R * T_1 / (v - b) - a / (math.sqrt(T_1) * v *(v + b)) - P_1;\n",
"\n",
"za= fsolve( f1,0.001)\n",
"\n",
"def f2(v):\n",
" return R * T_2 / (v - b) - a / (math.sqrt(T_2) * v *(v + b)) - P_2;\n",
"\n",
"zb= fsolve( f2,0.001)\n",
"v1 = zb\n",
"v2 = zb\n",
"def f3(v):\n",
" T = 353.15\n",
" return b*R*T/(v-b) + a/T**0.5 * (3./(2*b) * math.log(v/(v+b)) - 1./(v+b))\n",
" \n",
"delta_h1 = quad(f3,za,zb)\n",
"\n",
" \n",
"def f(T):\n",
" return R * ( A * T + B/2 * T**2 + C/3 * T**3) ;\n",
"\n",
"del_h_2 = f(T_2) - f(T_1) ;\n",
"del_h_total = del_h_1 + del_h_2 + del_h_3 ;\n",
"q = del_h_total - Ws ;\n",
"\n",
"# Results\n",
"print \"v1 = %.2e m**3/mol, v2 = %.2e m**3/mol\"%(za,zb ) ;\n",
"print \"The heat input = %.f J/mol\"%(q);\n",
"\n",
"# Note : answer is slightly different because of rounding error."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"v1 = 2.60e-03 m**3/mol, v2 = 1.27e-03 m**3/mol\n",
"The heat input = 1421 J/mol\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.6 Page No : 289"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sympy import log\n",
"from sympy.solvers import solve\n",
"from sympy import Symbol\n",
"\n",
"#Variables\n",
"A = 2.104 ; \n",
"B = 2.98 * 10**-3 ;\n",
"R = 8.314 ;\n",
"Beta = 3.5 * 10**-5 ;\n",
"v = 7.1 * 10**-6 # m**3/mol\n",
"P2 = 10000*10**5 ; \t\t#[N/m**2]\n",
"P1 =1 ;\t\t\t #[N/m**2] \n",
"\n",
"#Calculations\n",
"T2 = Symbol('T2')\n",
"q = solve(A*R*log(T2/1000)+B*R*(T2-1000)-(Beta*v*(P2-P1)),T2)\n",
"\n",
"#Result \n",
"print \"Heat input = \",q,\"J/mol\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat input = [1005.88624122037] J/mol\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.7 page no : 296"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.integrate import quad\n",
"\n",
"# Variables ( same as example 5.4)\n",
"R = 8.314\n",
"Tc = 425.2 # K \n",
"Pc = 37.9 # bar \n",
"w = 0.199\n",
"T1 = 353.15 # K\n",
"Tc = 425.2 # K\n",
"P1 = 9.47 # bar\n",
"Pc = 38. # bar\n",
"T2 = 393.15 # K\n",
"P2 = 18.9 # bar\n",
"R = 8.314\n",
"\n",
"# calculations\n",
"T1r = T1/Tc\n",
"P1r = P1/Pc\n",
"T2r = T2/Tc\n",
"P2r = P2/Pc\n",
"\n",
"def f(T):\n",
" return 1.935 + 36.915 * 10**-3 * T - 11.402 * 10**-6 * T**2\n",
"\n",
"cpDt = R * quad(f,353,393)[0]\n",
"h2h1 = .536 * R*Tc +cpDt - .969*R*Tc\n",
"\n",
"# Results\n",
"print \"the heat capacity = %.f J/mol\"%cpDt\n",
"print \"h2 - h1 = %.f J/mol\"%h2h1\n",
"\n",
"# Note : answer is slightly differnt becuase of rounding off error. and this problem is same as 5.4"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the heat capacity = 4695 J/mol\n",
"h2 - h1 = 3164 J/mol\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.10 Page No : 302"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from scipy.integrate import quad\n",
"\n",
"# Variables\n",
"T_c = 126.2; \t \t\t#[K] , From appendix A.1\n",
"P_c = 33.8 * 10**5 ; \t\t\t#[N/m**2] , From appendix A.1\n",
"w = 0.039 ; \t\t \t# From appendix A.1\n",
"enth_dep_1 = -2.81 ; \t\t\t# From table C.1 Appendix C\n",
"A = 3.28 ;\t\t\t # From Appendix A.2\n",
"B = 0.593 * 10**-3 ;\t\t\t# From Appendix A.2\n",
"del_h_dep_l = -5.1 ; \n",
"del_h_dep_v = -0.1 ;\n",
"T1 = 151. \t\t\t#[K]\n",
"P1 = 100. * 10**5 ; \t \t\t#[N/m**2]\n",
"P2 = 1. * 10**5 ; \t\t \t#[N/m**2]\n",
"T2_r = 0.61 ; \t\t\t # From figure 5.4\n",
"\n",
"# Calculations\n",
"T1_r = T1 / T_c ;\n",
"P1_r = round(P1 / P_c) ;\n",
"P2_r = P2 / P_c ;\n",
"T2 = round(T2_r * T_c) ; \t\t\t#[K]\n",
"\n",
"def f(T):\n",
" #return A * T + B/2 * T**2 \n",
" return A + B*T\n",
"\n",
"ans = quad(f,151,T2)[0]\n",
"\n",
"x = 1. / T_c *ans\n",
"y = enth_dep_1 - x ;\n",
"\n",
"# Results\n",
"X = ( y - del_h_dep_l) / (del_h_dep_v - del_h_dep_l);\n",
"print \"Quality = %.2f\"%(X) ;\n",
"\n",
"# Note: answer is different because of quad is giving different value -1.9 instead of -1.28. "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Quality = 0.85\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}