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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Chapter 5:Conductivity of Metals and Superconductivity"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.1,Page No:5.5"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "velocity=1.17e-07 m/s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "d = 2*10**-3; #diameter in m \n",
- "I = 5*10**-3; #current in A\n",
- "e = 1.6*10**-19; #charge of electron in coulombs \n",
- "a = 3.61*10**-10; #side of cube in m\n",
- "N = 4; #number of atoms in per unit cell\n",
- " \n",
- " \n",
- "#formula\n",
- "#J=n*v*e\n",
- "\n",
- "#calculation\n",
- "r = d/float(2); #radius in m\n",
- "n = N/float(a**3); #number of atoms per unit volume in atoms/m**3\n",
- "A = math.pi*(r**2); #area in m**2\n",
- "J = I/float(A); #current density in Amp/m**2\n",
- "v = J/float(n*e); #average drift velocity in m/s\n",
- "\n",
- "#result\n",
- "print'velocity=%3.2e'%v,'m/s';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.2,Page No:5.6"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "velocity=1.06e-03 m/s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "I = 6; #current in A\n",
- "d = 1*10**-3; #diameter in m\n",
- "n = 4.5*10**28; #electrons available in electron/m**3\n",
- "e = 1.6*10**-19; #charge of electron in coulombs\n",
- "\n",
- "\n",
- "#calculation\n",
- "r = d/float(2); #radius in m\n",
- "A = math.pi*(r**2); #area in m**2\n",
- "J = I/float(A); #current density in A/m**3\n",
- "vd = J/float(n*e); #density in m/s\n",
- " \n",
- " \n",
- "#result\n",
- "print'velocity=%3.2e'%vd,'m/s';\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.3,Page No:5.6"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "velocity=4.80e-06 m/s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "V = 63.5; #atomic weight in kg\n",
- "d = 8.92*10**3; #density of copper in kg/m**3\n",
- "r = 0.7*10**-3; #radius in m\n",
- "I = 10; #current in A\n",
- "e = 1.6*10**-19; #charge of electronin coulomb\n",
- "h = 6.02*10**28; #planck's constant in (m**2)*kg/s\n",
- "\n",
- "\n",
- "#calculation\n",
- "A = math.pi*(r**2); # area in m**2\n",
- "N = h*d;\n",
- "n = N/float(V);\n",
- "J = I/float(A); #current density in m/s\n",
- "vd = J/float(n*e); #drift velocity in m/s\n",
- "\n",
- "#result\n",
- "print'velocity=%2.2e'%vd,'m/s';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.4,Page No:5.7"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "restivity=1.82e-08 ohm m\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "R = 0.182; #resistance in ohm\n",
- "l = 1; #length in m\n",
- "A = 0.1*10**-6; #area in m**2\n",
- "\n",
- "#formula \n",
- "#R=(p*l)/A\n",
- "\n",
- "#calculation\n",
- "p = (R*A)/float(l); #resistivity in ohm m\n",
- "\n",
- "\n",
- "#result\n",
- "print'restivity=%3.2e'%p,'ohm m';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.5,Page No:5.7"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "velocity=0.7 m/s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "n = 5.8*10**28; #number of silver electrons in electrond/m**3\n",
- "p = 1.45*10**-8; #resistivity in ohm m\n",
- "E = 10**2; #electric field in V/m\n",
- "e = 1.6*10**-19; \n",
- "\n",
- "\n",
- "#formula\n",
- "#sigma = n*e*u \n",
- "#sigma=p\n",
- "#calculation\n",
- "u = 1/float(n*e*p);\n",
- "vd = u*E; #drift velocity in m/s\n",
- "\n",
- "#result\n",
- "print'velocity=%3.1f'%vd,'m/s';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.6,Page No:5.8"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "density=7.25e-03 m**2.V**-1.s**-1\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "W = 107.9; #atomic weight in amu(atomic mass unit)\n",
- "p = 10.5*10**3; #density in kg/m**3\n",
- "sigma =6.8*10**7; #conductivity in ohm**-1.m**-1\n",
- "e =1.6*10**-19; #charge of electron in coulombs\n",
- "N = 6.02*10**26; #avagadro number in mol**-1\n",
- " \n",
- "\n",
- "#calculation\n",
- "n = (N*p)/float(W); #number of atoms per unit volume \n",
- "u = sigma/float(n*e); #density of electron in m**2.V**-1.s**-1\n",
- "\n",
- "\n",
- "#result\n",
- "print'density=%3.2e'%u,'m**2.V**-1.s**-1';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example 5.7,Page No:5.8"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "time=2.51e-14 s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "#for common metal copper\n",
- "n = 8.5*10**28; #number of atoms in m**-3\n",
- "sigma = 6*10**7; #sigma in ohm**-1 m**-1\n",
- "m = 9.1*10**-31; #mass of electron in kilogram\n",
- "e = 1.6*10**-19; #charge of electron in coulombs\n",
- "\n",
- "#calculation\n",
- "t = (m*sigma)/float(n*(e**2)); #relaxation time in s\n",
- "\n",
- "#result\n",
- "print'time=%3.2e'%t,'s';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.9,Page No:5.14"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "thermal conductivity=1.6731 W/m-K\n",
- " Note: calculation mistake in textbook in calculating K as T value is taken 325 instead of 3.25\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "t = 3.0*10**-14; #time in s\n",
- "n = 2.5*10**22; #in electrons per m**3\n",
- "m = 9.1*10**-31; #mass of electron in kilograms\n",
- "e = 1.6*10**-19; #charge of electron in coulombs\n",
- "T = 3.25; #temperature in K\n",
- "\n",
- "\n",
- "#formula\n",
- "#K/(sigma*T)=2.44*10**-8 from wiedemann Franz law\n",
- "#calculation\n",
- "sigma = (n*(e**2)*t)/float(m*10**-6); #conductivity in m**3\n",
- "K = (2.44*10**-8)*sigma*T; #thermalconductivity in W/m-K\n",
- "\n",
- "\n",
- "#result\n",
- "print'thermal conductivity=%3.4f '%K,'W/m-K';\n",
- "print' Note: calculation mistake in textbook in calculating K as T value is taken 325 instead of 3.25';\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.10,Page No:5.20"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "energy diefference=1.13e+02 eV\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "a = 10**-10; #one dimension in m\n",
- "m = 9.1*10**-31; #mass of kg\n",
- "h = 6.62*10**-34; #planck's constant in joule-s\n",
- "\n",
- "\n",
- "#formula\n",
- "#En = ((n**2)*(h**2))/float(8*m*(a**2))\n",
- "#calculation\n",
- "E1 = (h**2)/float(8*m*(a**2)); #energy in J\n",
- "E2 = (4*(h**2))/float(8*m*(a**2)); #energy in J\n",
- "dE = (3*(h**2))/float(8*m*(a**2)); #energy diefference in J \n",
- "x = dE/float(1.6*10**-19); #energy diefference in eV\n",
- "\n",
- "#result\n",
- "print'energy diefference=%3.2e'%x,'eV';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.11,Page No:5.20"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "fermi energy=3.16 eV\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "N =6.02*10**23; #avagadro number in atoms /mole\n",
- "h = 6.63*10**-34; #planck's constant in joule-s\n",
- "m = 9.11*10**-31; #mass in kg\n",
- "M = 23; #atomic weight in grams /mole\n",
- "p = 0.971; #density in gram/cm**3\n",
- "\n",
- "\n",
- "#formula \n",
- "#x=N/V=(N*p)/M\n",
- "#calculation\n",
- "x = (N*p)/float(M);\n",
- "x1 = x*10**6;\n",
- "eF = (((h**2)/float(2*m)))*(((3*x1)/(8*math.pi))**(2/float(3))); #Fermi energy\n",
- "eF1 = (eF)/float(1.6*10**-19);\n",
- "\n",
- "#result\n",
- "print'fermi energy=%3.2f'%eF1,'eV';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.12,Page No:5.21"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "fermi energy =3.16 eV\n",
- "fermi velocity =1.05e+06 m/s\n",
- "femi temperature =3.66e+04 K\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "x = 2.54*10**28; #number of electrons in per m**2\n",
- "h = 6.63*10**-34; # planck's constant in joule-s\n",
- "m = 9.11*10**-31; # mass in kg\n",
- "p = 0.971; #density in grams/cm**3\n",
- "k = 1.38*10**-23;\n",
- " \n",
- "\n",
- "#calculation\n",
- "#x = (N*p)/float(M);\n",
- "eF = (((h**2)/(2*m)))*(((3*x)/float(8*math.pi))**(2/float(3))); \n",
- "eF1 = (eF)/float(1.6*10**-19); #Fermi energy in eV\n",
- "vF = math.sqrt((2*eF)/float(m)); #fermi velocity in m/s\n",
- "TF = eF/float(k); #fermi temperature in K\n",
- " \n",
- "\n",
- "#result\n",
- "print'fermi energy =%3.2f'%eF1,'eV';\n",
- "print'fermi velocity =%3.2e'%vF,'m/s';\n",
- "print'femi temperature =%3.2e'%TF,'K';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.13,Page No:5.21"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "fermi energy = 11 eV\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "M = 65.4; #atomic weight\n",
- "p = 7.13; #density in g/cm**3\n",
- "h = 6.62*10**-34; # planck's constant in joules-s\n",
- "m = 7.7*10**-31; # mass\n",
- "v = 6.02*10**23; #avagadros number in atoms/gram-atom\n",
- "\n",
- "\n",
- "#calculation\n",
- "#x =N/V\n",
- "V = M/float(p); #volume of one atom in cm**3\n",
- "n = v/float(V); # number of Zn atoms in volume v\n",
- "x = 2*n*(10**6); #number of free electrons in unit volume iper m**2\n",
- "eF = ((h**2)/float(2*m))*(((3*x)/float(8*math.pi))**(2/float(3))); # fermi energy in J\n",
- "eF1 = eF/float(1.6*(10**-19));\n",
- "\n",
- "\n",
- "#result\n",
- "print'fermi energy =%3.2d'%eF1,'eV';\n",
- " "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.14,Page No:5.22"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "number of electrons per unit volume =4e+28 m**-3\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "eF = 4.27; #fermi energy in eV\n",
- "m = 9.11*10**-31; # mass of electron in kg\n",
- "h = 6.63*10**-34; # planck's constant J.s\n",
- "\n",
- "\n",
- "#formula\n",
- "#x= N/V\n",
- "#calculation\n",
- "eF1 = eF*1.6*10**-19; #fermi energy in eV \n",
- "x = (((2*m*eF1)/float(h**2))**(3/float(2)))*((8*math.pi)/float(3)); #number of electrons per unit volume\n",
- "\n",
- "\n",
- "#result\n",
- "print'number of electrons per unit volume =%4.00e'%x,'m**-3';\n",
- " "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "collapsed": true
- },
- "source": [
- "## Example 5.15,Page No:5.23"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "electron density for a metal =1.47e+28 m**-3\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "eF1 = 4.70; # fermi energy in eV\n",
- "eF2 = 2.20; #fermi energy in eV\n",
- "x1 = 4.6*10**28; # electron density of lithium per m**3\n",
- "\n",
- "\n",
- "#formula\n",
- "#N/V = (((2*m*eF1)/(h**2))**(3/2))*((8*math.pi)/3);\n",
- "#N/V = k*(eF**3/2)\n",
- "#N/V = x\n",
- "#calculation\n",
- "x2 = x1*((eF2/float(eF1))**(3/float(2))); #electron density for metal in per m**3\n",
- "\n",
- "\n",
- "#result\n",
- "print'electron density for a metal =%4.2e'%x2,'m**-3';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "collapsed": true
- },
- "source": [
- "## Example 5.16,Page No:5.24"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "average energy =3.24 eV\n",
- "temperature =2.50e+04 K\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "eF = 5.4; #fermi energy in eV\n",
- "k = 1.38*10**-23; # k in joule/K\n",
- "\n",
- "\n",
- "#calculation\n",
- "e0 = (3*eF)/float(5); #average energy in eV\n",
- "T = (e0*(1.6*10**-19)*2)/float(3*k); #temperature in K\n",
- " \n",
- "\n",
- "#result\n",
- "print'average energy =%3.2f'%e0,'eV';\n",
- "print'temperature =%3.2e'%T,'K';\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.17,Page No:5.25"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "average energy =9.0 eV\n",
- "speed =1.78e+06 m/s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "EF = 15; #fermi energy in eV\n",
- "m = 9.1*10**-31; #mass of electron in kilogarams\n",
- "\n",
- "\n",
- "#calculation\n",
- "E0 = (3*EF)/float(5); #average energy en eV\n",
- "v = math.sqrt((2*E0*1.6*10**-19)/float(m)); #speed of electron in m/s\n",
- "\n",
- "\n",
- "#result\n",
- "print'average energy =%3.1f'%E0,'eV';\n",
- "print'speed =%3.2e'%v,'m/s';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.18,Page No:5.25"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "average energy =4.50 eV\n",
- " speed =1.26e+06 m/s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "EF = 7.5; #fermi energy in eV\n",
- "m = 9.1*10**-31; #mass of electron in kilograms\n",
- "\n",
- "#calculation\n",
- "E0 = (3*EF)/float(5); #average energy en eV\n",
- "v = math.sqrt((2*E0*1.6*10**-19)/float(m)); #speed in m\n",
- "\n",
- "#result\n",
- "print'average energy =%3.2f'%E0,'eV';\n",
- "print' speed =%3.2e'%v,'m/s';\n",
- " "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.19,Page No:5.25"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "energy=3.12 eV\n",
- " speed= =1.05e+06 m/s\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "m = 9.1*10**-31; #mass of electron in kg\n",
- "h = 6.62*10**-34; #planck's constant in (m**2)*kg/s\n",
- "#formula\n",
- "#x=N/V\n",
- "x = 2.5*10**28;\n",
- "\n",
- "#calculation\n",
- "EF = ((h**2)/float(8*(math.pi**2)*m))*((3*(math.pi**2)*x)**(2/float(3))); #fermi energy in J\n",
- "EF1 = EF/float(1.6*10**-19); #fermi energy in eV\n",
- "vF = (h/float(2*m*math.pi))*((3*(math.pi**2)*x)**(1/float(3))); #fermi velocity in m/s\n",
- "\n",
- "\n",
- "#result\n",
- "print'energy=%3.2f'%EF1,'eV';\n",
- "print' speed= =%3.2e'%vF,'m/s';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.20,Page No:5.29"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "efficiency =99.998163 %\n",
- "voltage drop =1.8 %\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Ps = 10**7; #power in W\n",
- "V = 33*10**3; #power transmitted in W\n",
- "R = 2; #resistance in ohm\n",
- " \n",
- "#calculation\n",
- "I = Ps/float(V); #current in A\n",
- "Pd = (I**2*R)/float(1000); #power lost in feeder in kW \n",
- "n = ((Ps-Pd)/float(Ps))*100; #efficiency in %\n",
- "v = I*R; #voltage drop in V\n",
- "Vd = (v/float(V))*100; #percentage voltage drop\n",
- " \n",
- "#result\n",
- "print'efficiency =%0f '%n,'%';\n",
- "print'voltage drop =%3.1f'%Vd,'%';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.21,Page No:5.36"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "aCu,Fe = -13.8 uV/°C\n",
- " bCu,Fe = 0.042 uV/(°C)**2\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "a1 = 2.76; #a1 in uv/°C\n",
- "a2 = 16.6; #a2 in uv/°C\n",
- "b1 = 0.012; #b1 in uv/°C\n",
- "b2 = -0.03; #b2 in uv/°C\n",
- "\n",
- "#calculation\n",
- "#aFe,Pb =a1 \n",
- "#aCu,Pb = a2\n",
- "#bCu,Fe = b1\n",
- "#bFe,Pb = b2\n",
- "\n",
- "#calculation\n",
- "a3 = a1-a2; #a3 in uv/°C\n",
- "b3 = b1-b2; #b3 in uv/(°C)**2\n",
- "\n",
- "#result\n",
- "print'aCu,Fe = %3.1f'%a3,'uV/°C';\n",
- "print' bCu,Fe = %3.3f'%b3,'uV/(°C)**2';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.23,Page No:5.37"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "neutral temperature =225 °C\n",
- "temperature of inversin = 450 °C\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "a = 15; #a in uv/°C\n",
- "b = -1/float(30); #b in uv/°C\n",
- "\n",
- "#E = at+bt^2\n",
- "#dE/dT =a+2*b*t\n",
- "#t=tn\n",
- "#dE/dT =0\n",
- "#calculation\n",
- "tn = -(a/float(2*(b))) #neutral temperature in °C\n",
- "#t1+t2 = 2*t2;\n",
- "t2 = 2*tn #inversion temperature in °C\n",
- " \n",
- "#result\n",
- "print'neutral temperature =%3.2d '%tn,'°C';\n",
- "print'temperature of inversin = %3.2d '%t2,'°C';\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.24,Page No:5.37"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "resistivity of alloy =4.4533 uΩ-cm\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "p2 = 2.75; #resistivity of alloy 1 percent of Ni in uΩ-cm\n",
- "p1 = 1.42; #resistivity of pure copper in uΩ-cm\n",
- "p3 = 1.98; #resistivity of alloy 3 percent of silver in uΩ-cm\n",
- " \n",
- "#p(Ni+Cu) =p1\n",
- "#pCu =p2\n",
- "#p(Cu+silver)=p3\n",
- "#calculation\n",
- "pNi = p2-p1;\n",
- "p4 = (p3-p1)/float(3);\n",
- "palloy = p1+(2*pNi)+(2*p4); #resistivity of alloy 2 percent of silver and 2 percent of nickel in uΩ-cm\n",
- " \n",
- "#result\n",
- "print'resistivity of alloy =%3.4f'%palloy,'uΩ-cm';\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.25,Page No:5.41"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "transition temperature =4.174 K\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "M1 = 202; #mass number\n",
- "M2 = 200; # mass number\n",
- "Tc1 = 4.153; # temperature in K\n",
- "alpha = 0.5;\n",
- " \n",
- "\n",
- "#formula\n",
- "#m**alpha*(Tc)= conatant\n",
- "#calculation\n",
- "Tc2 = ((M1**alpha)*Tc1)/float(M2**alpha); #transition temperature in K\n",
- " \n",
- "\n",
- "#result\n",
- "print'transition temperature =%3.3f'%Tc2,'K';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.26,Page No:5.41"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "critical temperature =1.92 K\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaraion\n",
- "Tc1 = 2.1; #temperature in K\n",
- "M1 = 26.91; #mass number \n",
- "M2 = 32.13; #mass number \n",
- "\n",
- "\n",
- "#formula\n",
- "#Tc*(M1**2) = constant\n",
- "#calculation\n",
- "Tc2 = (Tc1*(M1**(1/float(2))))/float(M2**(1/float(2))); #critical temperature in K\n",
- "\n",
- "\n",
- "#result\n",
- "print'critical temperature =%3.2f'%Tc2,'K';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.27,Page No:5.42"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "transition temperature =14.67 K\n",
- "critical field =1.70e+06 A/m\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Hc1 = 1.41*10**5; #critical fields in amp/m\n",
- "Hc2 = 4.205*10**5; # critical fields in amp/m\n",
- "T1 = 14.1; #temperature in K\n",
- "T2 = 12.9; # temperature in K\n",
- "T3 = 4.2; #temperature in K\n",
- " \n",
- "\n",
- "#formula\n",
- "#Hcn =Hc*((1-((T/Tc)**4)))\n",
- "#calculation\n",
- "Tc =(((((Hc2*(T1**2))-(Hc1*(T2**2)))/float(Hc2-Hc1)))**(1/float(2))); #temperature in K\n",
- "Hc0 = Hc1/float(1-((T1/float(Tc))**2)); #critical field in A/m\n",
- "Hc2 = Hc0*(1-(T3/float(Tc))**2); #critical field in A/m\n",
- "\n",
- "\n",
- "#result\n",
- "print'transition temperature =%3.2f'%Tc,'K';\n",
- "print'critical field =%3.2e'%Hc2,'A/m';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.28,Page No:5.43"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "critical field =4.8751e+05 A/m\n",
- " Note: calculation mistake in texttbook in calculating Hc\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Hc0 = 700000; #critical field at 0 K\n",
- "T = 4; #temperature in K\n",
- "Tc = 7.26; #temperature in K\n",
- " \n",
- " \n",
- "#calculation\n",
- "Hc = Hc0*(1-(T/float(Tc))**2); #critical field n A/m\n",
- "\n",
- "\n",
- "#result\n",
- "print'critical field =%3.4e'%Hc,'A/m';\n",
- "print' Note: calculation mistake in texttbook in calculating Hc';\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.29,Page No:5.44"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "critical current =153.15 A\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Hc0 = 8*10**4; #critical field \n",
- "T = 4.5; #temperature in K\n",
- "Tc = 7.2; #temperature in K\n",
- "D = 1*10**-3; #diameter in m\n",
- "\n",
- " \n",
- "#calculation\n",
- "Hc = Hc0*(1-(T/float(Tc))**2);\n",
- "r = D/float(2); #radius in m\n",
- "Ic = 2*math.pi*r*Hc; #critical current in A\n",
- "\n",
- "#result\n",
- "print'critical current =%3.2f'%Ic,'A';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.30,Page No:5.44"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 28,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "critical field =0.0217 tesla\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Hc0 = 0.0306; #critical field at 0 K\n",
- "T = 2; #temperature in K\n",
- "Tc = 3.7; #temperature in K\n",
- " \n",
- " \n",
- "#calculation\n",
- "Hc = Hc0*(1-(T/float(Tc))**2); #critical field in tesla\n",
- "\n",
- "\n",
- "#result\n",
- "print'critical field =%3.4f'%Hc,'tesla';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.31,Page No:5.44"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "transition temperature =16.00 K\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "HcT = 1.5*10**5; # critical field for niobium at 0 K\n",
- "Hc0 = 2*10**5; # critical field for nobium at 0 K\n",
- "T = 8; # temperature in K\n",
- " \n",
- "\n",
- "#calculation\n",
- "Tc = T/((1-(HcT/float(Hc0)))**0.5); #transition temperature in K\n",
- " \n",
- "\n",
- "#result\n",
- "print'transition temperature =%3.2f'%Tc,'K';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.32,Page No:5.45"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 30,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "transition temperature =14.47 K\n",
- " critical field =2.50 T\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Hc1 = 0.176; #critical fields\n",
- "Hc2 = 0.528; #critical fields\n",
- "T1 = 14; #temperature in K\n",
- "T2 = 13; #temperature in K\n",
- "T3 = 4.2; #temperature in K\n",
- "\n",
- "#formula\n",
- "#Hcn =Hc*((1-((T/Tc)**4)))\n",
- "#calculation\n",
- "Tc =(((((Hc2*(T1**2))-(Hc1*(T2**2)))/float(Hc2-Hc1)))**(1/float(2))); #transition temperature in K\n",
- "Hc0 = Hc1/(1-((T1/float(Tc))**2)); #critical field in T\n",
- "Hc2 = Hc0*(1-((T3/float(Tc))**2)); #critical field in T\n",
- "\n",
- "\n",
- "#result\n",
- "print'transition temperature =%3.2f '%Tc,'K';\n",
- "print' critical field =%3.2f '%Hc2,'T';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.33,Page No:5.46"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "critical current =99.274328 A\n",
- "Note: calculation mistake in textbook in calculation of I\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Hc = 7900; #magnetic field in A/m\n",
- "r = 2.0*10**-3; #radius of super condutor in m\n",
- " \n",
- " \n",
- "#calculation\n",
- "I = 2*math.pi*r*Hc; #critical current in A\n",
- " \n",
- "#result\n",
- "print'critical current =%4f'%I,'A';\n",
- "print'Note: calculation mistake in textbook in calculation of I';\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.34,Page No:5.46"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 32,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "current =137 Amp\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "d = 10**-3; #diameter in m\n",
- "Bc = 0.0548; # Bc in T\n",
- " \n",
- " \n",
- "#calculation\n",
- "u0 = 4*math.pi*10**-7; #permiability m**2\n",
- "r = d/float(2); #radius in m\n",
- "Ic = (2*math.pi*r*Bc)/float(u0); #current in Amp\n",
- "\n",
- "#result\n",
- "print'current =%3.2d '%Ic,'Amp';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.35,Page No:5.52"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 33,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "penetration depth=11.33 nm\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "D =8.5*10**3; #density in kg/m**3\n",
- "W =93; #atomic weight \n",
- "m =9.1*10**-31; #mass of electron in kilograms\n",
- "e =2*1.6*10**-19; #charge of electron in coulombs\n",
- "N =6.023*10**26; #avagadro number in (lb-mol)−1\n",
- "\n",
- "\n",
- "#calculation\n",
- "u0 =4*math.pi*10**-7;\n",
- "ns =(D*N)/float(W); #in per m**3\n",
- "lamdaL =(m/float(u0*ns*e**2))**(1/float(2)); #London's penetration depth in nm\n",
- "\n",
- "#result\n",
- "print'penetration depth=%3.2f'%(lamdaL*10**9),'nm';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.36,Page No:5.52"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "penetration depth=467.9 Å\n",
- " Note: calculation mistake in textbook in calculating lamdaT\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Tc =7.2; #temperature in K\n",
- "lamda =380; #penetration depth in Å\n",
- "T =5.5; #temperature in K\n",
- " \n",
- "\n",
- "#calculation\n",
- "\n",
- "lamdaT=lamda*((1-((T/float(Tc))**4))**(-1/float(2))); #penetration depth in Å\n",
- " \n",
- "#result\n",
- "print'penetration depth=%3.1f'%lamdaT,'Å';\n",
- "print' Note: calculation mistake in textbook in calculating lamdaT';"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.37,Page No:5.53"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 35,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "critical temperature =8.48 K\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "lamda1 = 16; #penetration depth in nm\n",
- "lamda2 = 96; #penetration depth in nm\n",
- "T1 = 2.18; #temperature in K\n",
- "T2 = 8.1; # temperature in K\n",
- "\n",
- "#formula\n",
- "#lamdaT =lamda0*((1-((T/Tc)**4))**(-1/4))\n",
- "#calculation\n",
- "Tc = ((((lamda2*(T2**4))-(lamda1*(T1**4)))/float(lamda2-lamda1))**(1/float(4))); #critical temperature in K\n",
- "\n",
- "\n",
- "#result\n",
- "print'critical temperature =%3.2f '%Tc,'K';\n",
- " "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.38,Page No:5.55"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 36,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "wavelength=0.41 mm\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "Eg =30.5*1.6*10**-23; #energy gap in eV\n",
- "h =6.6*10**-34; #planck's constant in (m**2)*kg/s\n",
- "c =3.0*10**8; #velocity of light in m\n",
- " \n",
- "\n",
- "#formula\n",
- "#Eg=h*v\n",
- "#calculation\n",
- "v = Eg/float(h); #velocity in m\n",
- "lamda = c/float(v); #wavelength in m\n",
- "\n",
- "#result\n",
- "print'wavelength=%2.2f'%(lamda*10**3),'mm';\n",
- " "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example 5.39,Page No:5.55"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 37,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "region of electromagnetic spectrum=1.14e-03 m\n"
- ]
- }
- ],
- "source": [
- "import math\n",
- "\n",
- "#variable declaration\n",
- "k =1.38*10**-23;\n",
- "Tc =4.2; #tempetrature in K\n",
- "h =6.6*10**-34; #planck's constant in (m**2)*kg/s\n",
- "c =3*10**8; # velocity of light in m\n",
- " \n",
- " \n",
- "#calculation\n",
- "Eg = (3*k*Tc); #energy gap in eV\n",
- "lamda = h*c/float(Eg); #wavelngth in m\n",
- "\n",
- "#result\n",
- "print'region of electromagnetic spectrum=%3.2e'%lamda,'m';"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 2",
- "language": "python",
- "name": "python2"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 2
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython2",
- "version": "2.7.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}
generated by cgit (git 2.34.1) at 2024-12-20 10:59:08 +0000