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{
"metadata": {
"name": "",
"signature": "sha256:99c63cd5d461a992de3be34298ef557332677985056a4e6a31ae5dace5faabc1"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9: Statistical Physics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4, Page 303"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"k = 1.38e-023; # Boltzmann constant, J/K\n",
"N_A = 6.023e+023; # Avogadro's number\n",
"T = 293; # Room temperature, K\n",
"e = 1.6e-019; # Energy equivalent of 1 eV, J\n",
"\n",
"#Calculations\n",
"# For a single molecule\n",
"K_bar_single = 3./2*k*T/e; # Mean translational kinetic energy of a single gas molecule, J\n",
"# For a 1 mole of molecules\n",
"K_bar_mole = K_bar_single*N_A*e; # Mean translational kinetic energy of 1 mole of gas molecules, J\n",
"\n",
"#Results\n",
"print \"The mean translational kinetic energy of the single idela gas molecule = %5.3f eV\"%K_bar_single\n",
"print \"The mean translational kinetic energy of the one mole of ideal gas molecules = %4d J\"%(math.ceil(K_bar_mole))\n",
"\n",
"#Answer differs due to rounding error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mean translational kinetic energy of the single idela gas molecule = 0.038 eV\n",
"The mean translational kinetic energy of the one mole of ideal gas molecules = 3654 J\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.3, Page 310"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"k = 1.38e-023; # Boltzmann constant, J/K\n",
"u = 1.67e-027; # Mass equivalent of one atomic mass unit, kg\n",
"T = 293; # Room temperature, K\n",
"m_H = 1.008*u; # Gram atomic mass of hydrogen, kg\n",
"\n",
"#Calculations&Results\n",
"m = 2*m_H; # Gram molecular mass of hydrogen molecule, kg\n",
"v_bar = 4/math.sqrt(2*math.pi)*math.sqrt(k*T/m); # Mean molecular speed in the light gas hydrogen, m/s\n",
"print \"The mean molecular speed in the light gas hydrogen = %4d m/s\"%(math.ceil(v_bar))\n",
"m = 222*u; # Gram atomic mass of Radon, kg\n",
"v_bar = 4/math.sqrt(2*math.pi)*math.sqrt(k*T/m); # Mean molecular speed in the heavy radon gas, m/s\n",
"print \"The mean molecular speed in the heavy radon gas = %3d m/s\"%(math.ceil(v_bar))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mean molecular speed in the light gas hydrogen = 1749 m/s\n",
"The mean molecular speed in the heavy radon gas = 167 m/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4, Page 310"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import scipy\n",
"from scipy.integrate import quad\n",
"\n",
"#Variable declaration\n",
"m = 1; # For simplicity assume mass of gas molecule to be unity, kg\n",
"k = 1.38e-023; # Boltzmann constant, J/K\n",
"T = 293; # Room temperature, K\n",
"\n",
"#Calculations\n",
"bita = k*T; # Energy associated with three degrees of freedom, J\n",
"v_mps = math.sqrt(2/(bita*m)); # For simplcity assume most probable speed to be unity, m/s\n",
"C = (bita*m/(2*math.pi))**(3./2); # Constant in the distribution function\n",
"p = lambda v: 4*math.pi*C*math.exp(-1./2*bita*m*v**2)*v**2\n",
"P,err = scipy.integrate.quad(p,0.99*v_mps, 1.01*v_mps)\n",
"\n",
"#Result\n",
"print \"The fraction of molecules in an ideal gas in equilibrium which have speeds within 1 percent above and below the most probable speed = %5.3f\"%P"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The fraction of molecules in an ideal gas in equilibrium which have speeds within 1 percent above and below the most probable speed = 0.017\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.6, Page 315"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy\n",
"import math\n",
"\n",
"#Variable declaration\n",
"k = 1.38e-023; # Boltzmann constant, J/K\n",
"T = [293, 5000, 1e+006]; # Room temperature, temperature at the surface of the star and temperature at the star interior respectively, K\n",
"e = 1.6e-019; # Energy equivalent of 1 eV, J\n",
"g_E1 = 2; # Possible configuration of the electrons in ground state of H-atom\n",
"g_E2 = 8; # Possible configuration of the electrons in the first excited state of H-atom\n",
"E1 = -13.6; # Energy of the ground state, eV\n",
"E2 = -3.4; # Energy of the first excited state state, eV\n",
"\n",
"#Calculations&Results\n",
"n_ratio = numpy.zeros(3);\n",
"for i in range(0,3):\n",
" n_ratio[i] = g_E2/g_E1*math.exp(1./(k*T[i])*(E1 - E2)*e);\n",
" print \"For T = %4.2e K, n_E2/n_E1 = %4.2e\"%(T[i], n_ratio[i])\n",
"\n",
"#Incorrect answer given in textbook for the first part"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"For T = 2.93e+02 K, n_E2/n_E1 = 2.05e-175\n",
"For T = 5.00e+03 K, n_E2/n_E1 = 2.14e-10\n",
"For T = 1.00e+06 K, n_E2/n_E1 = 3.55e+00\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.7, Page 320"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"e = 1.6e-019; # Energy equivalent of 1 eV, J\n",
"n = 8.47e+028; # Number density of conduction electrons in copper, per metre cube\n",
"k = 1.38e-023; # Boltzmann constant, J/K\n",
"h = 6.626e-034; # Planck's constant, Js\n",
"m = 9.11e-031; # Mass of an electron, kg\n",
"\n",
"#Calculations\n",
"E_F = h**2/(8*m*e)*(3*n/math.pi)**(2./3); # Fermi energy for copper, eV\n",
"T_F = E_F*e/k; # Fermi temperature for copper, K\n",
"\n",
"#Results\n",
"print \"The Fermi energy for copper = %4.2f eV\"%E_F\n",
"print \"The Fermi temperature for copper = %4.2e K\"%T_F"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Fermi energy for copper = 7.04 eV\n",
"The Fermi temperature for copper = 8.16e+04 K\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.8, Page 323"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"R = 1; # For simplicity assume the molar gas constant to be unity, J/mol/K\n",
"T = 293; # Room temperature, K\n",
"T_F = 8.16e+004; # The Fermi temperature for copper\n",
"\n",
"#Calculations&Results\n",
"C_V = math.pi**2*T/(2*T_F)*R; # Electronic contribution to the molar heat capacity for copper, J/mol/K\n",
"print \"The electronic contribution to the molar heat capacity for copper = %6.4fR\"%C_V\n",
"T_F = 6.38e+004; # The Fermi temperature for silver\n",
"C_V = math.pi**2*T/(2*T_F)*R; # Electronic contribution to the molar heat capacity for silver, J/mol/K\n",
"print \"The electronic contribution to the molar heat capacity for silver = %6.4fR\"%C_V"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The electronic contribution to the molar heat capacity for copper = 0.0177R\n",
"The electronic contribution to the molar heat capacity for silver = 0.0227R\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
