summaryrefslogtreecommitdiff
path: root/Engineering_Physics/Chapter_8.ipynb
diff options
context:
space:
mode:
Diffstat (limited to 'Engineering_Physics/Chapter_8.ipynb')
-rw-r--r--Engineering_Physics/Chapter_8.ipynb332
1 files changed, 296 insertions, 36 deletions
diff --git a/Engineering_Physics/Chapter_8.ipynb b/Engineering_Physics/Chapter_8.ipynb
index 40606862..be4820c5 100644
--- a/Engineering_Physics/Chapter_8.ipynb
+++ b/Engineering_Physics/Chapter_8.ipynb
@@ -1,6 +1,7 @@
{
"metadata": {
- "name": "Chapter 8"
+ "name": "",
+ "signature": "sha256:a97623c1294ef4fbd99f1423addadcfc2341e13ca402c26d0b2a69dd71e1782a"
},
"nbformat": 3,
"nbformat_minor": 0,
@@ -11,25 +12,44 @@
"cell_type": "heading",
"level": 1,
"metadata": {},
- "source": "Conducting materials"
+ "source": [
+ "Conducting materials"
+ ]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.1, Page number 231"
+ "source": [
+ "Example number 8.1, Page number 231"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the electrical resistivity\n\n#Variable declaration\nm=9.1*10**-31; #mass of the electron in kg\nn=2.533*10**28; #concentration of electrons per m^3\ne=1.6*10**-19;\ntow_r=3.1*10**-14; #relaxation time in sec\n\n#Calculation\nrho=m/(n*(e**2*tow_r));\n\n#Result\nprint(\"electrical resistivity in ohm metre is\",rho);",
+ "input": [
+ " \n",
+ "#Variable declaration\n",
+ "m=9.1*10**-31; #mass of the electron in kg\n",
+ "n=2.533*10**28; #concentration of electrons per m^3\n",
+ "e=1.6*10**-19;\n",
+ "tow_r=3.1*10**-14; #relaxation time in sec\n",
+ "\n",
+ "#Calculation\n",
+ "rho=m/(n*(e**2*tow_r));\n",
+ "\n",
+ "#Result\n",
+ "print(\"electrical resistivity in ohm metre is\",rho);"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('electrical resistivity in ohm metre is', 4.526937967219795e-08)\n"
+ "text": [
+ "('electrical resistivity in ohm metre is', 4.526937967219795e-08)\n"
+ ]
}
],
"prompt_number": 1
@@ -38,19 +58,39 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.2, Page number 231"
+ "source": [
+ "Example number 8.2, Page number 231"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the band gap of semiconductor\n\n#importing modules\nimport math\n\n#Variable declaration\ns=3.75*10**3; #slope\nk=1.38*10**-23;\n\n#Calculation\nEg=2*k*s;\nEg=Eg/(1.6*10**-19); #converting J to eV\nEg=math.ceil(Eg*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint(\"band gap of semiconductor in eV is\",Eg);",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "s=3.75*10**3; #slope\n",
+ "k=1.38*10**-23;\n",
+ "\n",
+ "#Calculation\n",
+ "Eg=2*k*s;\n",
+ "Eg=Eg/(1.6*10**-19); #converting J to eV\n",
+ "Eg=math.ceil(Eg*10**3)/10**3; #rounding off to 3 decimals\n",
+ "\n",
+ "#Result\n",
+ "print(\"band gap of semiconductor in eV is\",Eg);"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('band gap of semiconductor in eV is', 0.647)\n"
+ "text": [
+ "('band gap of semiconductor in eV is', 0.647)\n"
+ ]
}
],
"prompt_number": 3
@@ -59,19 +99,43 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.3, Page number 231"
+ "source": [
+ "Example number 8.3, Page number 231"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the probability of occupation of electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nT=989; #temperature in C\nk=1.38*10**-23;\n#let E-EF be E\nE=0.5; #occupied level of electron in eV\n\n#Calculation\nT=T+273; #temperature in K\nE=E*1.6*10**-19; #converting eV to J\n#let fermi=dirac distribution function f(E) be f\nf=1/(1+math.exp(E/(k*T)));\nf=math.ceil(f*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint(\"probability of occupation of electrons is\",f);",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=989; #temperature in C\n",
+ "k=1.38*10**-23;\n",
+ "#let E-EF be E\n",
+ "E=0.5; #occupied level of electron in eV\n",
+ "\n",
+ "#Calculation\n",
+ "T=T+273; #temperature in K\n",
+ "E=E*1.6*10**-19; #converting eV to J\n",
+ "#let fermi=dirac distribution function f(E) be f\n",
+ "f=1/(1+math.exp(E/(k*T)));\n",
+ "f=math.ceil(f*10**3)/10**3; #rounding off to 3 decimals\n",
+ "\n",
+ "#Result\n",
+ "print(\"probability of occupation of electrons is\",f);"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('probability of occupation of electrons is', 0.011)\n"
+ "text": [
+ "('probability of occupation of electrons is', 0.011)\n"
+ ]
}
],
"prompt_number": 4
@@ -80,19 +144,36 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.4, Page number 232"
+ "source": [
+ "Example number 8.4, Page number 232"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the drift velocity of free electrons\n\n#Variable declaration\nmew_e=0.0035; #mobility of electrons in m^2/Vs\nE=0.5; #electric field strength in V/m\n\n#Calculation\nvd=mew_e*E;\nvd=vd*10**3;\n\n#Result\nprint(\"drift velocity of free electrons in m/sec is\",vd,\"*10**-3\");\n\n#answer given in the book is wrong",
+ "input": [
+ " \n",
+ "mew_e=0.0035; #mobility of electrons in m^2/Vs\n",
+ "E=0.5; #electric field strength in V/m\n",
+ "\n",
+ "#Calculation\n",
+ "vd=mew_e*E;\n",
+ "vd=vd*10**3;\n",
+ "\n",
+ "#Result\n",
+ "print(\"drift velocity of free electrons in m/sec is\",vd,\"*10**-3\");\n",
+ "\n",
+ "#answer given in the book is wrong"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('drift velocity of free electrons in m/sec is', 1.75, '*10**-3')\n"
+ "text": [
+ "('drift velocity of free electrons in m/sec is', 1.75, '*10**-3')\n"
+ ]
}
],
"prompt_number": 1
@@ -101,19 +182,51 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.5, Page number 232"
+ "source": [
+ "Example number 8.5, Page number 232"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the mobility of electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nA=6.022*10**23; #avagadro number\ne=1.6*10**-19;\nrho=1.73*10**-8; #resistivity of Cu in ohm metre\nw=63.5; #atomic weight \nd=8.92*10**3; #density in kg/m^3\n\n#Calculation\nd=d*10**3;\nsigma=1/rho;\nsigmaa=sigma/10**7;\nsigmaa=math.ceil(sigmaa*10**3)/10**3; #rounding off to 3 decimals\nn=(d*A)/w;\nmew=sigma/(n*e); #mobility of electrons\nmew=mew*10**3;\nmew=math.ceil(mew*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint(\"electrical conductivity in ohm-1 m-1\",sigmaa,\"*10**7\");\nprint(\"concentration of carriers per m^3\",n);\nprint(\"mobility of electrons in m^2/Vsec is\",mew,\"*10**-3\");",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "A=6.022*10**23; #avagadro number\n",
+ "e=1.6*10**-19;\n",
+ "rho=1.73*10**-8; #resistivity of Cu in ohm metre\n",
+ "w=63.5; #atomic weight \n",
+ "d=8.92*10**3; #density in kg/m^3\n",
+ "\n",
+ "#Calculation\n",
+ "d=d*10**3;\n",
+ "sigma=1/rho;\n",
+ "sigmaa=sigma/10**7;\n",
+ "sigmaa=math.ceil(sigmaa*10**3)/10**3; #rounding off to 3 decimals\n",
+ "n=(d*A)/w;\n",
+ "mew=sigma/(n*e); #mobility of electrons\n",
+ "mew=mew*10**3;\n",
+ "mew=math.ceil(mew*10**4)/10**4; #rounding off to 4 decimals\n",
+ "\n",
+ "#Result\n",
+ "print(\"electrical conductivity in ohm-1 m-1\",sigmaa,\"*10**7\");\n",
+ "print(\"concentration of carriers per m^3\",n);\n",
+ "print(\"mobility of electrons in m^2/Vsec is\",mew,\"*10**-3\");"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('electrical conductivity in ohm-1 m-1', 5.781, '*10**7')\n('concentration of carriers per m^3', 8.459250393700786e+28)\n('mobility of electrons in m^2/Vsec is', 4.2708, '*10**-3')\n"
+ "text": [
+ "('electrical conductivity in ohm-1 m-1', 5.781, '*10**7')\n",
+ "('concentration of carriers per m^3', 8.459250393700786e+28)\n",
+ "('mobility of electrons in m^2/Vsec is', 4.2708, '*10**-3')\n"
+ ]
}
],
"prompt_number": 16
@@ -122,19 +235,42 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.6, Page number 232"
+ "source": [
+ "Example number 8.6, Page number 232"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the fermi energy\n\n#importing modules\nimport math\n\n#Variable declaration\nn=18.1*10**28; #concentration of electrons per m^3\nh=6.62*10**-34; #planck constant in Js\nme=9.1*10**-31; #mass of electron in kg\n\n#Calculation\nX=h**2/(8*me);\nE_F0=X*(((3*n)/math.pi)**(2/3));\nE_F0=E_F0/(1.6*10**-19); #converting J to eV\n\n#Result\nprint(\"Fermi energy in eV is\",E_F0);\n\n#answer given in the book is wrong",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=18.1*10**28; #concentration of electrons per m^3\n",
+ "h=6.62*10**-34; #planck constant in Js\n",
+ "me=9.1*10**-31; #mass of electron in kg\n",
+ "\n",
+ "#Calculation\n",
+ "X=h**2/(8*me);\n",
+ "E_F0=X*(((3*n)/math.pi)**(2/3));\n",
+ "E_F0=E_F0/(1.6*10**-19); #converting J to eV\n",
+ "\n",
+ "#Result\n",
+ "print(\"Fermi energy in eV is\",E_F0);\n",
+ "\n",
+ "#answer given in the book is wrong"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('Fermi energy in eV is', 3.762396978021977e-19)\n"
+ "text": [
+ "('Fermi energy in eV is', 3.762396978021977e-19)\n"
+ ]
}
],
"prompt_number": 18
@@ -143,19 +279,41 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.7, Page number 233"
+ "source": [
+ "Example number 8.7, Page number 233"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the concentration of free electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nE_F0=5.5; #fermi energy in eV\nh=6.63*10**-34; #planck constant in Js\nme=9.1*10**-31; #mass of electron in kg\n\n#Calculation\nE_F0=E_F0*1.6*10**-19; #converting eV to J\nn=((2*me*E_F0)**(3/2))*((8*math.pi)/(3*h**3));\n\n#Result\nprint(\"concentration of free electrons per unit volume of silver per m^3 is\",n);\n\n#answer given in the book is wrong\n",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "E_F0=5.5; #fermi energy in eV\n",
+ "h=6.63*10**-34; #planck constant in Js\n",
+ "me=9.1*10**-31; #mass of electron in kg\n",
+ "\n",
+ "#Calculation\n",
+ "E_F0=E_F0*1.6*10**-19; #converting eV to J\n",
+ "n=((2*me*E_F0)**(3/2))*((8*math.pi)/(3*h**3));\n",
+ "\n",
+ "#Result\n",
+ "print(\"concentration of free electrons per unit volume of silver per m^3 is\",n);\n",
+ "\n",
+ "#answer given in the book is wrong\n"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('concentration of free electrons per unit volume of silver per m^3 is', 4.603965704817037e+52)\n"
+ "text": [
+ "('concentration of free electrons per unit volume of silver per m^3 is', 4.603965704817037e+52)\n"
+ ]
}
],
"prompt_number": 19
@@ -164,19 +322,42 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.8, Page number 233"
+ "source": [
+ "Example number 8.8, Page number 233"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the probability of an electron\n\n#importing modules\nimport math\n\n#Variable declaration\nEg=1.07; #energy gap of silicon in eV\nk=1.38*10**-23;\nT=298; #temperature in K\n\n#Calculation\nEg=Eg*1.6*10**-19; #converting eV to J\n#let the probability of electron f(E) be X\n#X=1/(1+exp((E-Ef)/(k*T)))\n#but E=Ec and Ec-Ef=Eg/2\nX=1/(1+math.exp(Eg/(2*k*T)))\n\n#Result\nprint(\"probability of an electron thermally excited is\",X);",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "Eg=1.07; #energy gap of silicon in eV\n",
+ "k=1.38*10**-23;\n",
+ "T=298; #temperature in K\n",
+ "\n",
+ "#Calculation\n",
+ "Eg=Eg*1.6*10**-19; #converting eV to J\n",
+ "#let the probability of electron f(E) be X\n",
+ "#X=1/(1+exp((E-Ef)/(k*T)))\n",
+ "#but E=Ec and Ec-Ef=Eg/2\n",
+ "X=1/(1+math.exp(Eg/(2*k*T)))\n",
+ "\n",
+ "#Result\n",
+ "print(\"probability of an electron thermally excited is\",X);"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('probability of an electron thermally excited is', 9.122602463573379e-10)\n"
+ "text": [
+ "('probability of an electron thermally excited is', 9.122602463573379e-10)\n"
+ ]
}
],
"prompt_number": 21
@@ -185,19 +366,47 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.9, Page number 234"
+ "source": [
+ "Example number 8.9, Page number 234"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the fermi energy and temperature\n\n#importing modules\nimport math\n\n#Variable declaration\nk=1.38*10**-23;\nm=9.1*10**-31; #mass of the electron in kg\nvf=0.86*10**6; #fermi velocity in m/sec\n\n#Calculation\nEfj=(m*vf**2)/2;\nEf=Efj/(1.6*10**-19); #converting J to eV\nEf=math.ceil(Ef*10**3)/10**3; #rounding off to 3 decimals\nTf=Efj/k;\nTf=Tf/10**4;\nTf=math.ceil(Tf*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint(\"fermi energy of metal in J is\",Efj);\nprint(\"fermi energy of metal in eV is\",Ef);\nprint(\"fermi temperature in K is\",Tf,\"*10**4\");\n",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "k=1.38*10**-23;\n",
+ "m=9.1*10**-31; #mass of the electron in kg\n",
+ "vf=0.86*10**6; #fermi velocity in m/sec\n",
+ "\n",
+ "#Calculation\n",
+ "Efj=(m*vf**2)/2;\n",
+ "Ef=Efj/(1.6*10**-19); #converting J to eV\n",
+ "Ef=math.ceil(Ef*10**3)/10**3; #rounding off to 3 decimals\n",
+ "Tf=Efj/k;\n",
+ "Tf=Tf/10**4;\n",
+ "Tf=math.ceil(Tf*10**4)/10**4; #rounding off to 4 decimals\n",
+ "\n",
+ "#Result\n",
+ "print(\"fermi energy of metal in J is\",Efj);\n",
+ "print(\"fermi energy of metal in eV is\",Ef);\n",
+ "print(\"fermi temperature in K is\",Tf,\"*10**4\");\n"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('fermi energy of metal in J is', 3.3651800000000002e-19)\n('fermi energy of metal in eV is', 2.104)\n('fermi temperature in K is', 2.4386, '*10**4')\n"
+ "text": [
+ "('fermi energy of metal in J is', 3.3651800000000002e-19)\n",
+ "('fermi energy of metal in eV is', 2.104)\n",
+ "('fermi temperature in K is', 2.4386, '*10**4')\n"
+ ]
}
],
"prompt_number": 24
@@ -206,19 +415,36 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.10, Page number 234"
+ "source": [
+ "Example number 8.10, Page number 234"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the Lorentz number\n\n#Variable declaration\nsigma=5.82*10**7; #electrical conductivity in ohm^-1m^-1\nK=387; #thermal conductivity of Cu in W/mK\nT=27; #temperature in C\n\n#Calculation\nT=T+273; #temperature in K\nL=K/(sigma*T);\n\n#Result\nprint(\"lorentz number in W ohm/K^2 is\",L);\n",
+ "input": [
+ " \n",
+ "#Variable declaration\n",
+ "sigma=5.82*10**7; #electrical conductivity in ohm^-1m^-1\n",
+ "K=387; #thermal conductivity of Cu in W/mK\n",
+ "T=27; #temperature in C\n",
+ "\n",
+ "#Calculation\n",
+ "T=T+273; #temperature in K\n",
+ "L=K/(sigma*T);\n",
+ "\n",
+ "#Result\n",
+ "print(\"lorentz number in W ohm/K^2 is\",L);\n"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('lorentz number in W ohm/K^2 is', 2.2164948453608246e-08)\n"
+ "text": [
+ "('lorentz number in W ohm/K^2 is', 2.2164948453608246e-08)\n"
+ ]
}
],
"prompt_number": 25
@@ -227,19 +453,53 @@
"cell_type": "heading",
"level": 2,
"metadata": {},
- "source": "Example number 8.11, Page number 235"
+ "source": [
+ "Example number 8.11, Page number 235"
+ ]
},
{
"cell_type": "code",
"collapsed": false,
- "input": "#To calculate the electrical conductivity, thermal conductivity and Lorentz number\n\n#importing modules\nimport math\n\n#Variable declaration\nm=9.1*10**-31; #mass of the electron in kg\ne=1.6*10**-19;\nk=1.38*10**-23;\nn=8.49*10**28; #concentration of electrons in Cu per m^3\ntow_r=2.44*10**-14; #relaxation time in sec\nT=20; #temperature in C\n\n#Calculation\nT=T+273; #temperature in K\nsigma=(n*(e**2)*tow_r)/m;\nsigmaa=sigma/10**7;\nsigmaa=math.ceil(sigmaa*10**4)/10**4; #rounding off to 4 decimals\nK=(n*(math.pi**2)*(k**2)*T*tow_r)/(3*m);\nK=math.ceil(K*100)/100; #rounding off to 2 decimals\nL=K/(sigma*T);\n\n#Result\nprint(\"electrical conductivity in ohm^-1 m^-1 is\",sigmaa,\"*10**7\");\nprint(\"thermal conductivity in W/mK is\",K);\nprint(\"Lorentz number in W ohm/K^2 is\",L);\n\n#answer for lorentz number given in the book is wrong\n",
+ "input": [
+ " \n",
+ "#importing modules\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=9.1*10**-31; #mass of the electron in kg\n",
+ "e=1.6*10**-19;\n",
+ "k=1.38*10**-23;\n",
+ "n=8.49*10**28; #concentration of electrons in Cu per m^3\n",
+ "tow_r=2.44*10**-14; #relaxation time in sec\n",
+ "T=20; #temperature in C\n",
+ "\n",
+ "#Calculation\n",
+ "T=T+273; #temperature in K\n",
+ "sigma=(n*(e**2)*tow_r)/m;\n",
+ "sigmaa=sigma/10**7;\n",
+ "sigmaa=math.ceil(sigmaa*10**4)/10**4; #rounding off to 4 decimals\n",
+ "K=(n*(math.pi**2)*(k**2)*T*tow_r)/(3*m);\n",
+ "K=math.ceil(K*100)/100; #rounding off to 2 decimals\n",
+ "L=K/(sigma*T);\n",
+ "\n",
+ "#Result\n",
+ "print(\"electrical conductivity in ohm^-1 m^-1 is\",sigmaa,\"*10**7\");\n",
+ "print(\"thermal conductivity in W/mK is\",K);\n",
+ "print(\"Lorentz number in W ohm/K^2 is\",L);\n",
+ "\n",
+ "#answer for lorentz number given in the book is wrong\n"
+ ],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
- "text": "('electrical conductivity in ohm^-1 m^-1 is', 5.8277, '*10**7')\n('thermal conductivity in W/mK is', 417.89)\n('Lorentz number in W ohm/K^2 is', 2.4473623172034308e-08)\n"
+ "text": [
+ "('electrical conductivity in ohm^-1 m^-1 is', 5.8277, '*10**7')\n",
+ "('thermal conductivity in W/mK is', 417.89)\n",
+ "('Lorentz number in W ohm/K^2 is', 2.4473623172034308e-08)\n"
+ ]
}
],
"prompt_number": 29
@@ -247,7 +507,7 @@
{
"cell_type": "code",
"collapsed": false,
- "input": "",
+ "input": [],
"language": "python",
"metadata": {},
"outputs": []
generated by cgit (git 2.34.1) at 2024-12-20 20:30:37 +0000