1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
|
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 15: THERMAL PROPERTIES"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15.1: Debye_temperature_of_aluminium.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex15.1: Page-323 (2010)\n",
"k = 1.38e-023; // Boltzmann constant, J/K\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"f_D = 64e+011; // Debye frequency for Al, Hz\n",
"theta_D = h*f_D/k; // Debye temperature, K\n",
"printf('\nThe Debye temperature of aluminium = %5.1f K', theta_D);\n",
"\n",
"// Result\n",
"// The Debye temperature of aluminium = 307.3 K "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15.2: Lattice_specific_heat_of_carbo.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex15.2: Page-323 (2010)\n",
"N = 6.02e+026; // Avogadro's number, per kmol\n",
"k = 1.38e-023; // Boltzmann constant, J/K\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"f_D = 40.5e+012; // Debye frequency for Al, Hz\n",
"T = 30; // Temperature of carbon, Ks\n",
"theta_D = h*f_D/k; // Debye temperature, K\n",
"C_l = 12/5*%pi^4*N*k*(T/theta_D)^3; // Lattice specific heat of carbon, J/k-mol/K\n",
"printf('\nThe lattice specific heat of carbon = %4.2f J/k-mol/K', C_l);\n",
"\n",
"// Result\n",
"// The lattice specific heat of carbon = 7.13 J/k-mol/K "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15.3: Einstein_frequency_for_Cu.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex15.3: Page-323 (2010)\n",
"k = 1.38e-023; // Boltzmann constant, J/K\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"theta_E = 1990; // Einstein temperature of Cu, K\n",
"f_E = k*theta_E/h; // Einstein frequency for Cu, K\n",
"printf('\nThe Einstein frequency for Cu = %4.2e Hz', f_E);\n",
"printf('\nThe frequency falls in the near infrared region');\n",
"\n",
"// Result\n",
"// The Einstein frequency for Cu = 4.14e+013 Hz\n",
"// The frequency falls in the near infrared region "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15.4: Electronic_and_lattice_heat_capacities_for_Cu.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex15.4: Page-323 (2010)\n",
"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n",
"N = 6.02e+023; // Avogadro's number, per mol\n",
"T = 0.05; // Temperature of Cu, K\n",
"E_F = 7; // Fermi energy of Cu, eV\n",
"k = 1.38e-023; // Boltzmann constant, J/K\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"theta_D = 348; // Debye temperature of Cu, K\n",
"C_e = %pi^2*N*k^2*T/(2*E_F*e); // Electronic heat capacity of Cu, J/mol/K\n",
"C_V = 12/5*%pi^4*N*k*(T/theta_D)^3; // Lattice heat capacity of Cu, J/mol/K\n",
"printf('\nThe electronic heat capacity of Cu = %4.2e J/mol/K', C_e);\n",
"printf('\nThe lattice heat capacity of Cu = %4.2e J/mol/K', C_V);\n",
"\n",
"// Result\n",
"// The electronic heat capacity of Cu = 2.53e-005 J/mol/K\n",
"// The lattice heat capacity of Cu = 5.76e-009 J/mol/K "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15.5: Einstein_lattice_specific_heat.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex15.5: Page-324 (2010)\n",
"T = 1; // For simplicity assume temperature to be unity, K\n",
"R = 1; // For simplicity assume molar gas constant to be unity, J/mol/K\n",
"theta_E = T; // Einstein temperature, K\n",
"C_V = 3*R*(theta_E/T)^2*exp(theta_E/T)/(exp(theta_E/T)-1)^2; // Einstein lattice specific heat, J/mol/K\n",
"printf('\nThe Einstein lattice specific heat, C_v = %4.2f X 3R', C_V/3);\n",
"\n",
"// Result\n",
"// The Einstein lattice specific heat, C_v = 0.92 X 3R"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15.6: Molar_electronic_heat_capacity_of_zinc.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex15.6: Page-324 (2010)\n",
"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n",
"v = 2; // Valency of Zn atom\n",
"N = v*6.02e+023; // Avogadro's number, per mol\n",
"T = 300; // Temperature of Zn, K\n",
"E_F = 9.38; // Fermi energy of Zn, eV\n",
"k = 1.38e-023; // Boltzmann constant, J/K\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"C_e = %pi^2*N*k^2*T/(2*E_F*e); // Electronic heat capacity of Zn, J/mol/K\n",
"printf('\nThe molar electronic heat capacity of zinc = %5.3f J/mol/K', C_e);\n",
"\n",
"// Result\n",
"// The molar electronic heat capacity of zinc = 0.226 J/mol/K "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Scilab",
"language": "scilab",
"name": "scilab"
},
"language_info": {
"file_extension": ".sce",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
],
"mimetype": "text/x-octave",
"name": "scilab",
"version": "0.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
