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Diffstat (limited to 'Engineering_Physics/Chapter15_1.ipynb')
| -rw-r--r-- | Engineering_Physics/Chapter15_1.ipynb | 191 |
1 files changed, 170 insertions, 21 deletions
diff --git a/Engineering_Physics/Chapter15_1.ipynb b/Engineering_Physics/Chapter15_1.ipynb index cfabc2c6..feff19f4 100644 --- a/Engineering_Physics/Chapter15_1.ipynb +++ b/Engineering_Physics/Chapter15_1.ipynb @@ -1,6 +1,7 @@ { "metadata": { - "name": "Chapter15" + "name": "", + "signature": "sha256:16c7c597c3247782caaceb2ade68420e223aff8e960ccd80320d3e5521140cc3" }, "nbformat": 3, "nbformat_minor": 0, @@ -11,25 +12,48 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": "15: Thermal Properties " + "source": [ + "15: Thermal Properties " + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 15.1, Page number 323" + "source": [ + "Example number 15.1, Page number 323" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the Debye temperature\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nk = 1.38*10**-23; #Boltzmann constant(J/K)\nh = 6.626*10**-34; #Planck's constant(Js)\nf_D = 64*10**11; #Debye frequency for Al(Hz)\n\n#Calculation\ntheta_D = h*f_D/k; #Debye temperature(K)\ntheta_D = math.ceil(theta_D*10)/10; #rounding off the value of theta_D to 1 decimal\n\n#Result\nprint \"The Debye temperature of aluminium is\",theta_D, \"K\"", + "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" + "text": [ + "The Debye temperature of aluminium is 307.3 K\n" + ] } ], "prompt_number": 2 @@ -38,19 +62,45 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 15.2, Page number 323" + "source": [ + "Example number 15.2, Page number 323" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the lattice specific heat\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nN = 6.02*10**26; #Avogadro's number(per kmol)\nk = 1.38*10**-23; #Boltzmann constant(J/K)\nh = 6.626*10**-34; #Planck's constant(Js)\nf_D = 40.5*10**12; #Debye frequency for Al(Hz)\nT = 30; #Temperature of carbon(Ks)\n\n#Calculation\ntheta_D = h*f_D/k; #Debye temperature(K)\nC_l = 12/5*math.pi**4*N*k*(T/theta_D)**3; #Lattice specific heat of carbon(J/k-mol/K)\nC_l = math.ceil(C_l*10**3)/10**3; #rounding off the value of C_l to 3 decimals\n\n#Result\nprint \"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", + "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" + "text": [ + "The lattice specific heat of carbon is 7.132 J/k-mol/K\n" + ] } ], "prompt_number": 3 @@ -59,19 +109,41 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 15.3, Page number 323" + "source": [ + "Example number 15.3, Page number 323" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To show that the frequency falls in the infrared region\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nk = 1.38*10**-23; #Boltzmann constant(J/K)\nh = 6.626*10**-34; #Planck's constant(Js)\ntheta_E = 1990; #Einstein temperature of Cu(K)\n\n#Calculation\nf_E = k*theta_E/h; #Einstein frequency for Cu(K)\n\n#Result\nprint \"The Einstein frequency for Cu is\",f_E, \"Hz\"\nprint \"The frequency falls in the near infrared region\"", + "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\nThe frequency falls in the near infrared region\n" + "text": [ + "The Einstein frequency for Cu is 4.14458194989e+13 Hz\n", + "The frequency falls in the near infrared region\n" + ] } ], "prompt_number": 4 @@ -80,19 +152,48 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 15.4, Page number 323" + "source": [ + "Example number 15.4, Page number 323" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the electronic and lattice heat capacities\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\nN = 6.02*10**23; #Avogadro's number(per mol)\nT = 0.05; #Temperature of Cu(K)\nE_F = 7; #Fermi energy of Cu(eV)\nk = 1.38*10**-23; #Boltzmann constant(J/K)\nh = 6.626*10**-34; #Planck's constant(Js)\ntheta_D = 348; #Debye temperature of Cu(K)\n\n#Calculation\nC_e = math.pi**2*N*k**2*T/(2*E_F*e); #Electronic heat capacity of Cu(J/mol/K)\nC_V = (12/5)*math.pi**4*(N*k)*(T/theta_D)**3; #Lattice heat capacity of Cu(J/mol/K)\n\n#Result\nprint \"The electronic heat capacity of Cu is\",C_e, \"J/mol/K\"\nprint \"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", + "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\nThe lattice heat capacity of Cu is 5.76047891492e-09 J/mol/K\n" + "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 @@ -101,19 +202,41 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 15.5, Page number 324" + "source": [ + "Example number 15.5, Page number 324" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the heat capacity\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nT = 1; #For simplicity assume temperature to be unity(K)\nR = 1; #For simplicity assume molar gas constant to be unity(J/mol/K)\ntheta_E = T; #Einstein temperature(K)\n\n#Calculation\nC_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)\nC_V = C_V/3;\nC_V = math.ceil(C_V*10**3)/10**3; #rounding off the value of C_V to 3 decimals\n\n#Result\nprint \"The Einstein lattice specific heat is\",C_V, \"X 3R\"", + "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" + "text": [ + "The Einstein lattice specific heat is 0.921 X 3R\n" + ] } ], "prompt_number": 6 @@ -122,19 +245,45 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 15.6, Page number 324" + "source": [ + "Example number 15.6, Page number 324" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the molar electronic heat capacity\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\nv = 2; #Valency of Zn atom\nN = v*6.02*10**23; #Avogadro's number(per mol)\nT = 300; #Temperature of Zn(K)\nE_F = 9.38; #Fermi energy of Zn(eV)\nk = 1.38*10**-23; #Boltzmann constant(J/K)\nh = 6.626*10**-34; #Planck's constant(Js)\n\n#Calculation\nN = v*6.02*10**23; #Avogadro's number(per mol)\nC_e = math.pi**2*N*k**2*T/(2*E_F*e); #Electronic heat capacity of Zn(J/mol/K)\nC_e = math.ceil(C_e*10**4)/10**4; #rounding off the value of C_e to 4 decimals\n\n#Result\nprint \"The molar electronic heat capacity of zinc is\",C_e, \"J/mol/K\"", + "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" + "text": [ + "The molar electronic heat capacity of zinc is 0.2262 J/mol/K\n" + ] } ], "prompt_number": 8 @@ -142,7 +291,7 @@ { "cell_type": "code", "collapsed": false, - "input": "", + "input": [], "language": "python", "metadata": {}, "outputs": [] |