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-{
- "metadata": {
- "name": "",
- "signature": "sha256:16c7c597c3247782caaceb2ade68420e223aff8e960ccd80320d3e5521140cc3"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "15: Thermal Properties "
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 15.1, Page number 323"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "k = 1.38*10**-23; #Boltzmann constant(J/K)\n",
- "h = 6.626*10**-34; #Planck's constant(Js)\n",
- "f_D = 64*10**11; #Debye frequency for Al(Hz)\n",
- "\n",
- "#Calculation\n",
- "theta_D = h*f_D/k; #Debye temperature(K)\n",
- "theta_D = math.ceil(theta_D*10)/10; #rounding off the value of theta_D to 1 decimal\n",
- "\n",
- "#Result\n",
- "print \"The Debye temperature of aluminium is\",theta_D, \"K\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Debye temperature of aluminium is 307.3 K\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 15.2, Page number 323"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "N = 6.02*10**26; #Avogadro's number(per kmol)\n",
- "k = 1.38*10**-23; #Boltzmann constant(J/K)\n",
- "h = 6.626*10**-34; #Planck's constant(Js)\n",
- "f_D = 40.5*10**12; #Debye frequency for Al(Hz)\n",
- "T = 30; #Temperature of carbon(Ks)\n",
- "\n",
- "#Calculation\n",
- "theta_D = h*f_D/k; #Debye temperature(K)\n",
- "C_l = 12/5*math.pi**4*N*k*(T/theta_D)**3; #Lattice specific heat of carbon(J/k-mol/K)\n",
- "C_l = math.ceil(C_l*10**3)/10**3; #rounding off the value of C_l to 3 decimals\n",
- "\n",
- "#Result\n",
- "print \"The lattice specific heat of carbon is\",C_l, \"J/k-mol/K\"\n",
- "\n",
- "#answer given in the book is wrong in the 2nd decimal"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The lattice specific heat of carbon is 7.132 J/k-mol/K\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 15.3, Page number 323"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "k = 1.38*10**-23; #Boltzmann constant(J/K)\n",
- "h = 6.626*10**-34; #Planck's constant(Js)\n",
- "theta_E = 1990; #Einstein temperature of Cu(K)\n",
- "\n",
- "#Calculation\n",
- "f_E = k*theta_E/h; #Einstein frequency for Cu(K)\n",
- "\n",
- "#Result\n",
- "print \"The Einstein frequency for Cu is\",f_E, \"Hz\"\n",
- "print \"The frequency falls in the near infrared region\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Einstein frequency for Cu is 4.14458194989e+13 Hz\n",
- "The frequency falls in the near infrared region\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 15.4, Page number 323"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n",
- "N = 6.02*10**23; #Avogadro's number(per mol)\n",
- "T = 0.05; #Temperature of Cu(K)\n",
- "E_F = 7; #Fermi energy of Cu(eV)\n",
- "k = 1.38*10**-23; #Boltzmann constant(J/K)\n",
- "h = 6.626*10**-34; #Planck's constant(Js)\n",
- "theta_D = 348; #Debye temperature of Cu(K)\n",
- "\n",
- "#Calculation\n",
- "C_e = math.pi**2*N*k**2*T/(2*E_F*e); #Electronic heat capacity of Cu(J/mol/K)\n",
- "C_V = (12/5)*math.pi**4*(N*k)*(T/theta_D)**3; #Lattice heat capacity of Cu(J/mol/K)\n",
- "\n",
- "#Result\n",
- "print \"The electronic heat capacity of Cu is\",C_e, \"J/mol/K\"\n",
- "print \"The lattice heat capacity of Cu is\",C_V, \"J/mol/K\"\n",
- "\n",
- "#answer for lattice heat capacity given in the book is wrong"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The electronic heat capacity of Cu is 2.52566877726e-05 J/mol/K\n",
- "The lattice heat capacity of Cu is 5.76047891492e-09 J/mol/K\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 15.5, Page number 324"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\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",
- "\n",
- "#Calculation\n",
- "C_V = 3*R*(theta_E/T)**2*math.exp(theta_E/T)/(math.exp(theta_E/T)-1)**2; #Einstein lattice specific heat(J/mol/K)\n",
- "C_V = C_V/3;\n",
- "C_V = math.ceil(C_V*10**3)/10**3; #rounding off the value of C_V to 3 decimals\n",
- "\n",
- "#Result\n",
- "print \"The Einstein lattice specific heat is\",C_V, \"X 3R\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Einstein lattice specific heat is 0.921 X 3R\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 15.6, Page number 324"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n",
- "v = 2; #Valency of Zn atom\n",
- "N = v*6.02*10**23; #Avogadro's number(per mol)\n",
- "T = 300; #Temperature of Zn(K)\n",
- "E_F = 9.38; #Fermi energy of Zn(eV)\n",
- "k = 1.38*10**-23; #Boltzmann constant(J/K)\n",
- "h = 6.626*10**-34; #Planck's constant(Js)\n",
- "\n",
- "#Calculation\n",
- "N = v*6.02*10**23; #Avogadro's number(per mol)\n",
- "C_e = math.pi**2*N*k**2*T/(2*E_F*e); #Electronic heat capacity of Zn(J/mol/K)\n",
- "C_e = math.ceil(C_e*10**4)/10**4; #rounding off the value of C_e to 4 decimals\n",
- "\n",
- "#Result\n",
- "print \"The molar electronic heat capacity of zinc is\",C_e, \"J/mol/K\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The molar electronic heat capacity of zinc is 0.2262 J/mol/K\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-08 19:48:43 +0000