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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9:Statistical Mechanics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:9.1,Page no:299"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"k= 8.617*10**(-5) #Boltzmann constant, eV/K\n",
"To=273.0 #initial temperature, K\n",
"E1= -13.6 #energy of ground state, eV\n",
"E2= -3.4 #energy of first excited state, eV\n",
"dE= E2-E1 #difference in energy levels\n",
"g1=2.0 #number of energy states for E1\n",
"g2=8.0 #number of energy states for E2\n",
"\n",
"#Calculation\n",
"J= dE/(k*To) \n",
"Nratio1= (g2/g1)*math.exp(-J) #ratio of number of atoms in level 2 and level 1 at To\n",
"T1=10273.0 #K\n",
"J1= J*To/T1 \n",
"Nratio2= (g2/g1)*math.exp(-J1) #at T1\n",
"\n",
"#Result\n",
"print\"(a).The ratio at 273 K is:%.3g\"%Nratio1,\"(Approx)\"\n",
"print\"(b).The ratio at 10273 k is:%.g \"%Nratio2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a).The ratio at 273 K is:1.97e-188 (Approx)\n",
"(b).The ratio at 10273 k is:4e-05 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:9.4,Page no:305"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration \n",
"Moxygen= 16.0 #atomic mass,u\n",
"Mo2= 32.0 #Molecular mass, u\n",
"u= 1.66*(10**(-27)) #atomic mass unit, kg\n",
"Moxygen= Mo2*u #mass, kg\n",
"t= 273 #temperature, K\n",
"k= 1.38*10**(-23) #Boltzmann constant, J/K\n",
"\n",
"#Calculation\n",
"Vrms= math.sqrt(3*k*t/Moxygen) # m/s\n",
"\n",
"#Result\n",
"print\"The rms velocity of oxygen is: \",round(Vrms),\"m/s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The rms velocity of oxygen is: 461.0 m/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:9.5,Page no:314"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration \n",
"V= 1.00 #volume, cm**3\n",
"V= V*10**(-6) #converting to m**3\n",
"dI= 2.404 #standard value of definite Integral used\n",
"k= 8.617*10**(-5) #Boltzmann constant, eV/K\n",
"h= 4.13*(10**(-15)) #Planck's constant, eV.s\n",
"T= 1000 #temperature, K\n",
"c= 3 *(10**8) #speed of light, m/s\n",
"\n",
"#Calculation\n",
"#Part (a)\n",
"N= 8*(math.pi)*V*dI*((k*T/(h*c))**3)\n",
"#Part(b)\n",
"Sig= 5.670*10**(-8) #Stefan's constant, W/m**2.K**4 , refer to Page 317\n",
"Ephoton= Sig*(c**2)*(h**3)*T/(2.405*(2*(math.pi)*(k**3))) #J\n",
"e_to_J=6.23*10**18*Ephoton #Converting to eV \n",
"\n",
"#Result\n",
"print\"(a),The number of photons is:%.3g\"%N\n",
"print\"(b)The average energy of the photons is:%.3g\"%Ephoton,\"J=\",round(e_to_J,3),\"eV\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a),The number of photons is:2.03e+10\n",
"(b)The average energy of the photons is:3.72e-20 J= 0.232 eV\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:9.6,Page no:317"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration \n",
"T= 2.7 #blackbody temperature, K\n",
"Lambda= 2.898*10**(-3)/T #using wein's displacement law, Eqn 9.40, m\n",
"\n",
"#Calculation\n",
"Lambda= Lambda*10**(3) #converting to mm\n",
"\n",
"#Result\n",
"print\"The wavelength for maximum radiation is: \",Lambda,\"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelength for maximum radiation is: 1.07333333333 mm\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:9.7,Page no:317"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration \n",
"Rearth= 1.5*10**(11) #radius of earth, m\n",
"r= 1.4 #rate of arrival of sunlight, kW/m**2\n",
"\n",
"#Calculation\n",
"P= (r*10**3)*4*(math.pi)*(Rearth**2) #total power reaching Earth\n",
"Rsun= 7*10**(8) #radius of Sun, m\n",
"r2= P/(4*(math.pi)*(Rsun**2)) #radiation rate of Sun, W/m**2\n",
"emissivity=1 #for blackbody\n",
"Sig= 5.670*10**(-8) #Stefan's constant, W/m**2.K**4\n",
"T= (r2/(emissivity*Sig))**(1.0/4.0) \n",
"\n",
"#Result\n",
"print\"The surface temperature of Sun is:%.2g\"%T,\"K\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The surface temperature of Sun is:5.8e+03 K\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:9.8,Page no:325"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"u= 1.66*(10**(-27)) #atomic mass unit, kg\n",
"density= 8.94*10**(3) # kg/m**3\n",
"M= 63.5 #atomic mass of copper, u\n",
"\n",
"#Calculation\n",
"Edensity= density/(M*u) #electron density, electrons/m**3\n",
"h= 6.63*(10**(-34)) #Planck's constant, J.s\n",
"Me= 9.1*(10**(-31)) #mass of electron, kg\n",
"Efermi= h**2/(2*Me)*((3*Edensity)/(8*(math.pi)))**(2.0/3.0) # J\n",
"e_to_J=6.23*10**18*Efermi #Converting to eV \n",
"\n",
"#Result\n",
"print\"The fermi energy is:%.3g\"%Efermi,\"J or\",round(e_to_J,2),\"eV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The fermi energy is:1.13e-18 J or 7.04 eV\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
|
