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diff --git a/Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/chA.ipynb b/Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/chA.ipynb new file mode 100755 index 00000000..40c49ef7 --- /dev/null +++ b/Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/chA.ipynb @@ -0,0 +1,2565 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:df5fbd8c032abd96a18eaa179ff1b33448892f4e62b9b9800c35cefba3950007" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Appendix Examples" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.1 Page No : 557" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 300. # The given temperature in K\n", + "R = 8.31 # Universal gas constant in J/mole-K\n", + "\n", + "# Calculations\n", + "# The total random kinetic energy of one gram mole of oxygen in J\n", + "U = (3. / 2) * R * T\n", + "\n", + "# Output\n", + "print 'The total random kinetic energy of one gram mole of oxygen is U = %3.0f J ' % (U)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total random kinetic energy of one gram mole of oxygen is U = 3740 J \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.2 Page No : 560" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "a = 0.245 # Van der Waals constant in atoms-litre**2-mole**-2\n", + "b = 2.67 * 10**-2 # Van der Waals constant in litre-mole**-1\n", + "R = 8.314 * 10**7 # Universal gas constant in ergs/mole-K\n", + "\n", + "# Calculations\n", + "# Van der Waals constant in dynes-cm**4-mole**-2\n", + "a1 = a * 76 * 13.6 * 980 * 10**6\n", + "b1 = b * 10**3 # Van der Waals constant in cm**3mole**-1\n", + "Tc = (8. / 27) * (a1 / b1) * (1 / R) # The critical temperature in K\n", + "Tc1 = Tc - 273 # The critical temperature in degree centigrade\n", + "\n", + "# Output\n", + "print 'The critical temperature is Tc = %3.2f K (or) %3.2f degree centigrade ' % (Tc, Tc1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The critical temperature is Tc = 33.12 K (or) -239.88 degree centigrade \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.3 Page No : 565" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t = 0. # The given temperature in degree centigrade\n", + "E = 5.64 * 10**-21 # The mean kinetic energy of molecules of hydrogen in J\n", + "R = 8.32 # Universal gas constant in J/mole-K\n", + "\n", + "# Calculations\n", + "T = t + 273 # The given temperature in K\n", + "N = (3. / 2) * (R / E) * (T) # Avogadros number\n", + "\n", + "# Output\n", + "print 'The Avogadro number is N = %3.4g ' % (N)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Avogadro number is N = 6.041e+23 \n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.4 Page No : 570" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "d = 2. * 10**-8 # The diameter of the molecule of a gas in cm\n", + "k = 1.38 * 10**-23 # Boltzmanns constant in J/K\n", + "T = 273. # The temperature at NTP in K\n", + "pi = 3.14 # The mathematical constant of pi\n", + "\n", + "# Calculations\n", + "d1 = d / 100 # The diameter of the molecule of a gas in m\n", + "P = 0.76 * 13.6 * 9.8 * 1000 # The pressure at NTP\n", + "n = P / (k * T) # The number of molecules per cubic meter\n", + "l = 1. / (pi * d1**2 * n) # The mean free path in m\n", + "\n", + "# Output\n", + "print 'The mean free path at NTP is %3.4g m ' % (l)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mean free path at NTP is 2.961e-07 m \n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.6 Page No : 577" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "n = 3. * 10**25 # The number of molecules per cubic metre\n", + "d = 3.6 * 10**-10 # The diameter of oxygen molecule in m\n", + "M = 32. # Molecular weight of oxygen\n", + "N = 6.023 * 10**26 # Avogadro number\n", + "k = 1.38 * 10**-23 # Boltzmans constant in J/K\n", + "T = 273. # The temperature at NTP in K\n", + "pi = 3.14 # The mathematical constant of pi\n", + "\n", + "# Calculations\n", + "m = M / N # The mass of oxygen atom in kg\n", + "# Average speed of oxygen molecule at 273K in m/s\n", + "V = ((8 * k * T) / (pi * m))**(1. / 2)\n", + "c = pi * d**2 * V * n # The collision frequency of the molecules\n", + "l = 1. / (pi * d**2 * n) # The mean free path in m\n", + "\n", + "# Output\n", + "print '(a)The collision frequency of the molecules is %3.2g collisions/second \\n (b)The mean free path is %3.4g m ' % (c, l)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)The collision frequency of the molecules is 5.2e+09 collisions/second \n", + " (b)The mean free path is 8.191e-08 m \n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.7 Page No : 580" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "d = 9000. # The density of copper in kg/m**3\n", + "w = 63.5 # The atomic weight of copper in kg\n", + "N = 6.023 * 10**26 # Avogadros number\n", + "pi = 3.14 # Mathematical constant of pi\n", + "h = 6.624 * 10**-34 # Planks constant in Js\n", + "\n", + "# Calculations\n", + "V = w / d # The volume of copper in m**3\n", + "Ef = ((h**2 / (8. * 9. * 10**-31)) * ((3 / pi) * (N / V)) **\n", + " (2. / 3)) / (1.6 * 10**-19) # The fermi energy in eV\n", + "# The pressure at absolute zero for copper in N/m**2\n", + "P = (2. / 3) * (N / V) * Ef\n", + "\n", + "# Output\n", + "print '(a)The Fermi energy is E = %3.3f eV \\n (b)The pressure at absolute zero for copper is P = %3.6g N/m^2 ' % (Ef, P)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)The Fermi energy is E = 7.163 eV \n", + " (b)The pressure at absolute zero for copper is P = 4.07656e+29 N/m^2 \n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.8 Page No : 586" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "p1 = 80. # The initial pressure of a gas in cm of Hg\n", + "p2 = 60. # The final pressure of a gas in cm of Hg\n", + "v2 = 1190. # The final volume occupied by a gas in cc\n", + "v1 = 1000. # The initial volume occupied by a gas in cc\n", + "\n", + "# Calculations\n", + "g = (math.log10(p1 / p2)) / (math.log10(v2 / v1)) # The adiabatic index\n", + "\n", + "# Output\n", + "print 'The adiabatic index is %3.3f ' % (g)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The adiabatic index is 1.654 \n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.9 Page No : 589" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "t = 27. # The given temperature in degree centigrade\n", + "R = 8.3 # Universal gas constant in J/deg mole\n", + "\n", + "# Calculations\n", + "T = t + 273 # The given temperature in K\n", + "v1 = 1. # Let the original volume be in cc\n", + "v2 = 2. * v1 # The final volume in cc\n", + "W = R * T * math.log(v2 / v1) # The work done in J\n", + "\n", + "# Output\n", + "print 'The work done is W = %3.1f J ' % (W)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The work done is W = 1725.9 J \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.10 Page No : 594" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t1 = 27. # The initial temperature of the gas in degree centigrade\n", + "T1 = t1 + 273 # The initial temperature of the gas in K\n", + "g = 1.5 # The adiabatic index\n", + "p = 8. # The ratio of final pressure to the initial pressure\n", + "\n", + "# Calculations\n", + "T2 = ((p)**((g - 1) / g)) * T1 # The final temperature of the gas in K\n", + "T21 = T2 - 273 # The final temperature of the gas in degree centigrade\n", + "\n", + "# Output\n", + "print 'The final temperature of the gas is T2 = %3.0f K (or) %3.0f degree centigrade ' % (T2, T21)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The final temperature of the gas is T2 = 600 K (or) 327 degree centigrade \n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.11 Page No : 600" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "n = 0.3 # The efficiency of a carnot engine\n", + "t = 27. # The temperature of the sinkk in degree centigrade\n", + "n1 = 0.5 # The increased efficiency of a carnot engine\n", + "\n", + "# Calculations\n", + "T2 = t + 273 # The temperature of the sinkk in K\n", + "T1 = T2 / (1 - n) # The temperature of the source for 0.3 efficiency in K\n", + "T11 = T2 / (1 - n1) # The temperature of the source for 0.5 efficiency in K\n", + "T = T11 - T1 # The increase in temperature in K\n", + "\n", + "# Output\n", + "print 'The increase in temperature is T = %3.2f K ' % (T)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in temperature is T = 171.43 K \n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.12 Page No : 602" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "T1 = 2100. # One of the operating temperature in K\n", + "T2 = 700. # One of the another operating temperature in K\n", + "n1 = 40. # The actual efficiency of the engine in percent\n", + "\n", + "# Calculations\n", + "n = (1 - (T2 / T1)) * 100 # The efficiency of the engine in percent\n", + "# The percentage of actual efficiency to the maximum possible efficiency\n", + "# in percent\n", + "n2 = (n1 / n) * 100\n", + "\n", + "# Output\n", + "print 'The percentage of actual efficiency to the maximum possible efficiency is %3.0f percent ' % (n2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The percentage of actual efficiency to the maximum possible efficiency is 60 percent \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.13 Page No : 609" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "T1 = 600. # The working temperature of the engine in K\n", + "T2 = 300. # The another working temperature of the engine in K\n", + "n = 52. # Efficiency of the engine claimed by the inventor in percent\n", + "\n", + "# Calculations\n", + "n1 = (1 - (T2 / T1)) * 100 # The carnot efficiency of the engine in percent\n", + "\n", + "# Output\n", + "print 'The efficiency of the engine claimed by inventor is n = %3.0f percent\\nThe carnot efficiency of the engine is n = %3.0f percent \\n (The efficiency claimed is more than the carnots engine efficiency \\n No engine can have efficiency more than carnots efficiency \\n Hence the claim is invalid)' % (n, n1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The efficiency of the engine claimed by inventor is n = 52 percent\n", + "The carnot efficiency of the engine is n = 50 percent \n", + " (The efficiency claimed is more than the carnots engine efficiency \n", + " No engine can have efficiency more than carnots efficiency \n", + " Hence the claim is invalid)\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.14 Page No : 612" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "H1 = 10.**4 # The heat absorbed by a carnots engine in calories\n", + "t1 = 627. # The temperature from a reservoir in degree centigrade\n", + "t2 = 27. # The temperature of the sinkk in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of the reservoir in K\n", + "T2 = t2 + 273 # The temperature of the sinkk in K\n", + "n = (1 - (T2 / T1)) * 100 # The efficiency of the engine in percent\n", + "H2 = H1 * (T2 / T1) # The heat rejected to the sinkk in calories\n", + "W = (H1 - H2) * 4.2 # The work done by the engine in J\n", + "\n", + "# Output\n", + "print 'The efficiency of the engine is n = %3.2f percent The work done by the engine is W = %3.2g J ' % (n, W)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The efficiency of the engine is n = 66.67 percent The work done by the engine is W = 2.8e+04 J \n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.15 Page No : 619" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "w = 100. # The given power of an engine in kW\n", + "t1 = 117. # The operating temperature of an engine in degree centigrade\n", + "t2 = 17. # The another operating temperature of an engine in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The operating temperature of an engine in K\n", + "T2 = t2 + 273 # The another operating temperature of an engine in K\n", + "W = w * 1000 # The given power of an engine in J/s\n", + "n = (1 - (T2 / T1)) * 100 # The efficiency of an engine in percent\n", + "H = (T1 / T2) # The amount of heat absorbed to the amount of heat rejected\n", + "H2 = W / (H - 1) # The amount of heat rejected per second in J/s\n", + "H1 = H * H2 # The amount of heat absorbed per second in J/s\n", + "\n", + "# Output\n", + "print '(i)The amount of heat absorbed is %3.0g J/s \\n (ii)The amount of heat rejected is %3.0g J/s \\n (iii)The efficiency of the engine is %3.1f percent ' % (H1, H2, n)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i)The amount of heat absorbed is 4e+05 J/s \n", + " (ii)The amount of heat rejected is 3e+05 J/s \n", + " (iii)The efficiency of the engine is 25.6 percent \n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.16 Page No : 626" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "m1 = 10. # The mass of water at 60 degree centigrade in g\n", + "m2 = 30. # The mass of water at 20 degree centigrade in g\n", + "t1 = 60. # The temperature of 10 g water in degree centigrade\n", + "t2 = 20. # The temperature of 30 g water in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of 10g water in K\n", + "T2 = t2 + 273 # The temperature of 30g water in K\n", + "T = ((m1 * T1) + (m2 * T2)) / (m1 + m2) # The final temperature of water in K\n", + "# The change in entropy of 10g water from 333 to 303 K in cal/K\n", + "s1 = m1 * math.log(T / T1)\n", + "# The change in entropy of 30g water from 293 to 303 K in cal/K\n", + "s2 = m2 * math.log(T / T2)\n", + "s = s1 + s2 # The total gain in the entropy of the system in cal/K\n", + "\n", + "# Output\n", + "print 'The change in entropy is %3.4f cal/K ' % (s)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The change in entropy is 0.0627 cal/K \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.17 Page No : 629" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# input data\n", + "m = 10. # The given amount of water in kg\n", + "t1 = 100. # The temperature of water in degree centigrade\n", + "L = 540. # The latent heat of vapourisation of steam in cal\n", + "\n", + "# Calculations\n", + "m1 = m * 1000 # The given amount of water in g\n", + "T1 = t1 + 273 # The temperature of water in K\n", + "S = (m1 * L) / T1 # The increase in entropy in cal/K\n", + "\n", + "# Output\n", + "print 'The increase in entropy is %3.0f cal/K ' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in entropy is 14477 cal/K \n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.18 Page No : 634" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "m = 50. # The given amount of water in g\n", + "t1 = 10. # The initial temperature of water in degree centigrade\n", + "t2 = 90. # The final temperature of water in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The initial temperature of water in K\n", + "T2 = t2 + 273 # The final temperature of water in K\n", + "S = m * math.log(T2 / T1) # The increase in entropy in cal/K\n", + "\n", + "# Output\n", + "print 'The increase in entropy is %3.3f cal/K ' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in entropy is 12.448 cal/K \n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.19 Page No : 640" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "m = 10. # The given amount of ice in g\n", + "T1 = 273. # The initial temperature of ice in K\n", + "T2 = 373. # The final temperature of steam in K\n", + "L1 = 80. # The latent heat of ice in cal/g\n", + "L2 = 540. # The latent heat of vapourisation of steam in cal\n", + "\n", + "# Calculations\n", + "s1 = (m * L1) / T1 # Increase in entropy from ice at 273K to water at 273K in cal/K\n", + "# Increase in entropy from water at 273K to water at 373K in cal/K\n", + "s2 = (m) * math.log(T2 / T1)\n", + "# Increase in entropy from water at 373K to steam at 373K in cal/K\n", + "s3 = (m * L2) / T2\n", + "s = s1 + s2 + s3 # The total increase in entropy in cal/K\n", + "\n", + "# Output\n", + "print 'The total increase in entropy is %3.2f cal/K ' % (s)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total increase in entropy is 20.53 cal/K \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.20 Page No : 645" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "m = 1. # The given amount of nitrogen in g\n", + "t1 = 50. # The initial temperature of nitrogen in degree centigrade\n", + "t2 = 100. # The final temperature of nitrogen in degree centigrade\n", + "Cv = 0.18 # Molar specific heat of nitrogen\n", + "w = 28. # Molecular weight of nitrogen\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The initial temperature of nitrogen in K\n", + "T2 = t2 + 273 # The final temperature of nitrogen in K\n", + "S = (Cv / w) # The Specific heat of nitrogen\n", + "s = m * S * math.log(T2 / T1) # The change in entropy in cal/K\n", + "\n", + "# Output\n", + "print 'The change in entropy is %3.4g cal/K ' % (s)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The change in entropy is 0.0009252 cal/K \n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.21 Page No : 650" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "p = 135.2 # The given increase in the pressure in atmospheres\n", + "V = -0.091 # The given increase in the specific volume when 1g of water freezes into ice in cm**3\n", + "L = 80. # Latent heat of fusion of ice in cal/gram\n", + "T = 273. # The temperature of ice in K\n", + "\n", + "# Calculations\n", + "L1 = L * 4.18 * 10**7 # The latent heat of fusion of ice in ergs/g\n", + "P = p * 1.013 * 10**6 # The given increase in the pressure in dynes/cm**2\n", + "# The temperature at which ice will freeze in degree centigrade\n", + "t = (P * T * V) / L1\n", + "t1 = t + 273 # The temperature at which ice will freeze in K\n", + "\n", + "# Calculations\n", + "print 'The temperature at which ice will freeze is %3.0f degree centigrade (or) %3.0f K ' % (t, t1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature at which ice will freeze is -1 degree centigrade (or) 272 K \n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.22 Page No : 655" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "m = 1. # The given amount of water in kg\n", + "s = 1000. # The specific heat of water in cal/kg-K\n", + "T1 = 273. # The initial temperature of water in K\n", + "T2 = 373. # The temperature of the heat reservoir in K\n", + "\n", + "# Calculations\n", + "S = m * s * math.log(T2 / T1) # The increase in entropy in cal/K\n", + "\n", + "# Output\n", + "print 'The increase in the entropy of water is %3.0f cal/K' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in the entropy of water is 312 cal/K\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.23 Page No : 661" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# input data\n", + "m = 0.0273 # The given amount of ice in kg\n", + "L = 80. # The latent heat of fusion of ice in cal/gram\n", + "T = 273. # The temperature of ice in K\n", + "\n", + "# Calculations\n", + "L1 = L * 1000 # The latent heat of fusion of ice in cal/kg\n", + "S = (m * L1 * 4.2) / T # The change in entropy in J/K\n", + "\n", + "# Output\n", + "print 'The change in entropy is %3.1f J/K' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The change in entropy is 33.6 J/K\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.24 Page No : 667" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "t1 = 27. # The given initial temperature in degree centigrade\n", + "p = 50. # The reduce in the pressure in atmospheres\n", + "a = 13.2 * 10**-2 # Van der Waals constant in Nm**4mole**-2\n", + "b = 31.2 * 10**-6 # Van der Waals constant in mole**-1m**3\n", + "R = 8.3 # Universal gas constant in JK**-1(mole)**-1\n", + "Cp = 3.5 # The specific heat at constant pressure\n", + "M = 32. # Molecular weight of oxygen\n", + "\n", + "# Calculations\n", + "T = t1 + 273 # The given initial temperature in K\n", + "P = p * 0.76 * 13.6 * 1000 * 9.8 # The reduce in the pressure in N/m**2\n", + "# The drop in the temperature in K\n", + "T1 = ((P) / (4.2 * M * Cp * R)) * (((2 * a) / (R * T)) - b)\n", + "\n", + "# Output\n", + "print 'The drop in the temperature is %3.4f K ' % (T1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The drop in the temperature is 0.0971 K \n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.25 Page No : 674" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 300. # The temperature of the metallic copper disc in K\n", + "Cp = 24.5 # The specific heat at constant pressure in J/mol K\n", + "a = 50.4 * 10**-6 # The coefficient of thermal expansion in K**-1\n", + "K = 7.78 * 10**-12 # Isothermal compressibility in N/m**2\n", + "V = 7.06 * 10**-6 # The specific volume in m**3/mol\n", + "\n", + "# Calculations\n", + "C = (T * V * a**2) / K # The change in specific heats in J/mol K\n", + "Cv = Cp - C # The specific heat at constant volume in J/mol K\n", + "\n", + "# Output\n", + "print 'The specific heat at constant volume is Cv = %3.4f J/mol-K ' % (Cv)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The specific heat at constant volume is Cv = 23.8085 J/mol-K \n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.26 Page No : 676" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "p = 50. # The reduced pressure in atmospheres\n", + "t = 27. # The initial temperature of the gas in degree centigrade\n", + "a = 1.32 * 10**12 # Van der Waal constant a in cm**4 dynes/mole**2\n", + "b = 31.2 # Van der Waal constant b in cm**3/mole\n", + "Cp = 7. # The specific heat at constant pressure in cal/mole-K\n", + "\n", + "# Calculations\n", + "P = p * 76 * 13.6 * 980 # The reduced pressure in dynes/cm**2\n", + "Cp1 = Cp * 4.2 * 10**7 # The specific heat at constant pressure in ergs/mole-K\n", + "T = t + 273 # The initial temperature of the gas in K\n", + "R = 8.31 * 10**7 # The real gas constant in ergs/mole-K\n", + "# The drop in temperature in K or degree centigrade\n", + "dT = (P / Cp1) * (((2 * a) / (R * T)) - b)\n", + "\n", + "# Output\n", + "print 'The drop in temperature produced by adiabatic throttling process is %3.3f K (or) %3.3f degree centigrade ' % (dT, dT)\n", + "\n", + "# Error . There is a change in the result compared to the textbook because\n", + "# the final calculations did in the textbook went wrong , so the final\n", + "# result varied from the textbook\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The drop in temperature produced by adiabatic throttling process is 12.868 K (or) 12.868 degree centigrade \n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.27 Page No : 678" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "t = 0. # The initial temperature of mercury in degree centigrade\n", + "p = 1. # The initial pressure of mercury in atmospheres\n", + "Cp = 28. # The specific heat at constant pressure in J/mol K\n", + "V = 1.47 * 10**-5 # The given specific volume in m**3/mol\n", + "b = 1.81 * 10**-6 # The given volume expansivity in K**-1\n", + "k = 3.89 * 10**-11 # The given compressibility in pa**-1\n", + "\n", + "# Calculations\n", + "T = t + 273 # The initial temperature of mercury in K\n", + "# The specific heat at constant volume in J/mol K\n", + "Cv = Cp - ((T * V * b**2) / k)\n", + "g = Cp / Cv # The adiabatic index\n", + "\n", + "# Output\n", + "print 'The adiabatic index is %3.0f ' % (g)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The adiabatic index is 1 \n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.28 Page No : 681" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "K = 24. * 10**-3 # The coefficient of thermal conductivity of an oxygen molecule in J/m.s.K\n", + "Cv = 20.9 * 10**3 # The specific heat at constant volume in J/kilo.mole.K\n", + "k = 1.38 * 10**-23 # The boltzmanns constant in J/K\n", + "m = 5.31 * 10**-26 # The mass of an oxygen molecule in kg\n", + "T = 273. # The temperature of the molecule in K\n", + "pi = 3.142 # Mathematical constant of pi\n", + "\n", + "# Calculations\n", + "C = ((3 * k * T) / m)**(1. / 2) # The velocity of the molecule in m\n", + "r = (((3 * k * T * m)**(1. / 2) * Cv) / (3. * 2.**(1. / 2) * pi * K)\n", + " )**(1. / 2) # The radius of an oxygen molecule in m\n", + "\n", + "# Output\n", + "print 'The radius of an oxygen molecule is %3.4g m ' % (r)\n", + "\n", + "# Error . There is a change in the result compared to the textbook because\n", + "# the final calculations did in the textbook went wrong , so the final\n", + "# result varied from the textbook\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The radius of an oxygen molecule is 1.265e-09 m \n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.29 Page No : 687" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "b = 0.3 # The given wiens constant in cm-K\n", + "l = 5500. # The given wavelength in A units\n", + "\n", + "# Calculations\n", + "L = l * 10**-8 # The given wavelength in cm\n", + "T = b / L # The temperature of the sun in K\n", + "\n", + "# Output\n", + "print 'The temperature of the sun is %3.0f K ' % (T)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature of the sun is 5455 K \n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.30 Page No : 692" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "R = 1. * 10**4 # The rate at which black body loses thermal energy in watts/m**2\n", + "s = 5.672 * 10**-8 # Stefans constant in SI units\n", + "\n", + "# Calculations\n", + "T = (R / s)**(1. / 4) # The temperature of the black body in K\n", + "\n", + "# Output\n", + "print 'The temperature of the black body is %3.0f K' % (T)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature of the black body is 648 K\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.31 Page No : 697" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "T = 6174. # The temperature of the black body in K\n", + "l = 4700. # The wavelength of the black body emitting in amstrong units\n", + "l1 = 1.4 * 10**-5 # The wavelength to be emitted by the black body in m\n", + "\n", + "# Calculations\n", + "L = l * 10**-10 # The wavelength of the black body emitted at 6174 K in m\n", + "L1 = l1 # The wavelength to be emitted by the black body in m\n", + "T1 = (L * T) / L1 # The temperature to be maintained by the black body in K\n", + "\n", + "# Output\n", + "print 'The temperature to be maintained by the black body is %3.2f K ' % (T1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature to be maintained by the black body is 207.27 K \n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.32 Page No : 701" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "T = 5800. # The temperature of the sun in K\n", + "\n", + "# Calculations\n", + "r = 7. * 10**8 # The radius of the sun in m\n", + "pi = 3.142 # The mathematical constant of pi\n", + "A = 4. * pi * r**2 # The surface area of the sun in m**2\n", + "s = 5.672 * 10**-8 # Stefans constant in SI units\n", + "U = A * s * T**4 # The total energy emitted by sun per second in J\n", + "r1 = 1.5 * 10**11 # The distance of the earths atmosphere from the sun in m\n", + "# Energy reaching the top of earths atmosphere in kW/m**2\n", + "R = (U / (4 * pi * r1**2)) / 1000\n", + "\n", + "# Output\n", + "print 'The total radiant energy emitted by sun per second is %3.4g J \\\n", + "\\nThe rate at which energy is reaching earths atmosphere is %3.1f kW/m^2 ' % (U, R)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total radiant energy emitted by sun per second is 3.953e+26 J \n", + "The rate at which energy is reaching earths atmosphere is 1.4 kW/m^2 \n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.33 Page No : 706" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "n = 5. # The molecules of ozone in grams\n", + "t = 27. # The temperature of ozone in degree centigrade\n", + "R = 8.3 # The universal gas constant in J/g-mol/K\n", + "\n", + "# Calculations\n", + "T = t + 273 # The temperature of ozone in K\n", + "U = n * ((3. / 2) * R * T) # The energy of ozone in J\n", + "\n", + "# Output\n", + "print 'The energy of 5 gms molecules of ozone at 27 degree centigrade is %3.6g J ' % (U)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy of 5 gms molecules of ozone at 27 degree centigrade is 18675 J \n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.34 Page No : 708" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t = -1 # The pressure required to lower the melting point of ice in K\n", + "l = 79.6 # The latent heat of ice in cal/g\n", + "V1 = 1. # The specific volumes of water at 0 degree centigrade in cm**2\n", + "V2 = 1.091 # The specific volumes of ice at 0 degree centigrade in cm**2\n", + "p = 1.013 * 10**6 # One atmospheric pressure in dyne/cm**2\n", + "\n", + "# Calculations\n", + "T = 273. # The temperature of water in K\n", + "L = l * 4.18 * 10**7 # The latent heat of ice in ergs/g\n", + "p1 = (L * t) / (T * (V1 - V2)) # The obtained pressure in dynes/cm**2\n", + "P = p1 / p # The obtained pressure in atmospheres\n", + "P1 = P + 1 # The required pressure in atmospheres\n", + "\n", + "# Output\n", + "print 'The pressure required is %3.2f atmospheres ' % (P1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The pressure required is 133.21 atmospheres \n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.35 Page No : 710" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t1 = 127. # The temperature of the black body in degree centigrade\n", + "t2 = 27. # The temperature of the walls maintained in degree centigrade\n", + "s = 5.672 * 10**-8 # Stefans constant in SI units\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of the black body in K\n", + "T2 = t2 + 273 # The temperature of the walls maintained in K\n", + "R = s * (T1**4 - T2**4) # The net amount of energy lost by body in W/m**2\n", + "\n", + "# Output\n", + "print 'The net amount of energy lost by body per sec per unit area is %3.1f watts/m^2' % (R)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The net amount of energy lost by body per sec per unit area is 992.6 watts/m^2\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.36 Page No : 713" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t2 = 7. # The low temperature of reservoir in degree centigrade\n", + "n1 = 50. # The efficiency of the carnots engine in percentage\n", + "n2 = 70. # The increased efficiency of the carnots engine in percentage\n", + "\n", + "# Calculations\n", + "T2 = t2 + 273 # The low temperature of the reservoir in K\n", + "T1 = T2 / (1 - (n1 / 100)) # The temperature of the source reservoir in K\n", + "# The temperature to be maintained by the source reservoir in K\n", + "T11 = T2 / (1 - (n2 / 100))\n", + "T = T11 - T1 # The increase in temperature of the source in K or degree centigrade\n", + "\n", + "# Output\n", + "print 'The increase in temperature of the source is %3.1f K (or) %3.1f degree centigrade ' % (T, T)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in temperature of the source is 373.3 K (or) 373.3 degree centigrade \n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.37 Page No : 717" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "T1 = 6174. # The temperature of the black body in K\n", + "l1 = 4700. # The wavelength emitted by the black body in amstrong units\n", + "l2 = 1400. # The wavelength to be emitted by the black body in amstrong units\n", + "\n", + "# Calculations\n", + "T2 = (l1 * T1) / l2 # The temperature to be maintained by the black body in K\n", + "\n", + "# Output\n", + "print 'The temperature to be maintained by the black body is %3.0f K ' % (T2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature to be maintained by the black body is 20727 K \n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.38 Page No : 723" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "e = 8.5 * 10**28 # The given energy density of electrons in copper in electrons/m**3\n", + "k = 1.38 * 10**-23 # The boltzmann constant in J/K\n", + "h = 6.62 * 10**-34 # Planks constant in J.s\n", + "m = 9.1 * 10**-31 # The given mass of electrons in kg\n", + "pi = 3.14 # The mathematical constant of pi\n", + "\n", + "# Calculations\n", + "E = (((3 * e) / pi)**(2. / 3)) * (h**2) * (1. / 8) * \\\n", + " (1 / m) # The fermi energy for copper in J\n", + "EF = E / (1.6 * 10**-19) # The fermi energy for copper in eV\n", + "\n", + "# Output\n", + "print 'The fermi energy for copper at absolute zero is %3.3f eV ' % (EF)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The fermi energy for copper at absolute zero is 7.056 eV \n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.39 Page No : 725" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t1 = 100. # The temperature of the source in degree centigrade\n", + "t2 = 0. # The temperature of the sinkk in degree centigrade\n", + "P = 100. # The power of the engine in watts (or) J/s\n", + "l = 80. # The latent heat of ice in cal/g\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of the source in K\n", + "T2 = t2 + 273 # The temperature of the sinkk in K\n", + "L = l * 4.2 * 10**3 # The latent heat of ice in ergs/kg\n", + "W = P * 60 # The amount of work done in one minute in J\n", + "H2 = (W * T2) / (T1 - T2) # The amount of heat at the sinkk in J\n", + "m = (H2 / L) # The amount of ice melts in kg\n", + "\n", + "# Output\n", + "print 'The amount of ice that will melt in one minute is %3.5f kg ' % (m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The amount of ice that will melt in one minute is 0.04875 kg \n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.40 Page No : 730" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "C1 = 1.84 # The RMS speed of molecules of hydrogen at NTP in km/s\n", + "p1 = 2. # The molecular weight of hydrogen\n", + "p2 = 32. # The molecular weight of oxygen\n", + "\n", + "# Calculations\n", + "C2 = C1 * (p1 / p2)**(1. / 2) # The RMS speed of oxygen at NTP in km/s\n", + "C21 = C2 * 1000 # The RMS speed of oxygen at NTP in m/s\n", + "\n", + "# Output\n", + "print 'The RMS speed of oxygen at NTP is %3.2f km/s (or) %3.0f m/s ' % (C2, C21)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The RMS speed of oxygen at NTP is 0.46 km/s (or) 460 m/s \n" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.41 Page No : 737" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t = 101. # The temperature at which water boils in degree centigrade\n", + "p = 787. # The pressure maintained at water boils in mm of Hg\n", + "t1 = 100. # Normal boiling point of water in degree centigrade\n", + "T = t1 + 273 # Normal boiling point of water in K\n", + "p1 = 760. # The normal maintained pressure in mm of Hg\n", + "V2 = 1601. # The specific volume of water evaporation in cm**3\n", + "V1 = 1. # The specific volume of water in cm**3\n", + "\n", + "# Calculations\n", + "V = V2 - V1 # The change in specific volume in cm**3\n", + "dT = t - t1 # The change in temperature in degree centigrade or K\n", + "dP = (p - p1) / 10 # The change in pressure in cm of Hg\n", + "L = (T * dP * 13.6 * 980 * V) / dT # Latent heat of steam in ergs/g\n", + "L1 = L / (4.2 * 10**7) # The latent heat of steam in cal/g\n", + "\n", + "# Output\n", + "print 'The latent heat of steam is %3.4g ergs/g (or) %3.2f cal/g ' % (L, L1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The latent heat of steam is 2.148e+10 ergs/g (or) 511.34 cal/g \n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.42 Page No : 742" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "d = 7.7 * 10**3 # The density of aluminium in kg/m**3\n", + "w = 27. # The atomic weight of Al in kg/k.mol\n", + "N = 6.023 * 10**26 # The number of free electrons in Al\n", + "k = 1.38 * 10**-23 # The boltzmann constant in J/K\n", + "h = 6.62 * 10**-34 # Planks constant in J.s\n", + "m = 9.1 * 10**-31 # The given mass of electrons in kg\n", + "pi = 3.14 # The testematical constant of pi\n", + "\n", + "# Calculations\n", + "V = w / d # The volume occupied by Al in m**3/k.mol\n", + "E = (((3 * (N / V)) / pi)**(2. / 3)) * (h**2) * (1. / 8) * \\\n", + " (1 / m) # The fermi energy for aluminium in J\n", + "EF = E / (1.6 * 10**-19) # The fermi energy for aluminium in eV\n", + "# The pressure of electrons in aluminium at absolute zero in N/m**2\n", + "p = (2. / 3) * (N / V) * (E)\n", + "\n", + "# Output\n", + "print 'The fermi energy for aluminium at absolute zero is %3.3f eV \\\n", + "\\nThe pressure of electrons in aluminium at absolute zero is %3.4g N/m^2' % (EF, p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The fermi energy for aluminium at absolute zero is 11.278 eV \n", + "The pressure of electrons in aluminium at absolute zero is 2.066e+11 N/m^2\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.43 Page No : 747" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t2 = 20. # The temperature of room in degree centigrade\n", + "t1 = 37. # The skin temperature of the boy in degree centigrade\n", + "t = 10. # The given time in min\n", + "A = 3. # The surface area of the student in m**2\n", + "e = 0.9 # The emissivity of the student\n", + "\n", + "# Calculations\n", + "T2 = t2 + 273 # The temperature of the room in K\n", + "T1 = t1 + 273 # The skin temperature of the boy in K\n", + "t1 = t * 60 # The given time in sec\n", + "s = 5.67 * 10**-8 # Stefans constant in W/m**2-K**4\n", + "R = e * A * s * (T1**4 - T2**4) # Heat loss by the skin in one second in J/s\n", + "Q = R * t1 # Total heat loss by the skin in 10 minutes in J\n", + "\n", + "# Output\n", + "print 'The total heat loss by the skin in 10 minutes is %3.4g J ' % (Q)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total heat loss by the skin in 10 minutes is 1.713e+05 J \n" + ] + } + ], + "prompt_number": 45 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.44 Page No : 751" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t1 = 20. # The temperature of the air in the cylinder of a combustion engine in degree centigrade\n", + "p1 = 1. # The initial pressure of the air in atmospheres\n", + "V1 = 8. * 10**-4 # The initial volume of the air in m**3\n", + "V2 = 6. * 10**-5 # The final volume of the air in m**3\n", + "g = 1.4 # The adiabatic index\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of the air in K\n", + "p2 = p1 * (V1 / V2)**(g) # The final pressure of the gas in atmospheres\n", + "T2 = (p2 / p1) * (V2 / V1) * T1 # The final temperature of the gas in K\n", + "T21 = T2 - 273 # The final temperature of the gas in degree centigrade\n", + "\n", + "# Output\n", + "print 'The final pressure of the gas is %3.1f atmospheres \\\n", + "\\nThe final temperature of the gas is %3.1f K (or) %3.1f degree centigrade ' % (p2, T2, T21)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The final pressure of the gas is 37.6 atmospheres \n", + "The final temperature of the gas is 825.7 K (or) 552.7 degree centigrade \n" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.47 Page No : 757" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "d = 2. * 10**-10 # The molecular diameter of an ideal gas in m\n", + "t = 20. # The temperature of the gas in degree centigrade\n", + "p = 1. # The pressure of the gas in atmosphere\n", + "pi = 3.142 # The mathematical constant of pi\n", + "\n", + "# Calculations\n", + "T = t + 273 # The temperature of the gas in K\n", + "P = 1.01 * 10**5 # The pressure of the gas in N/m**2\n", + "v = 511. # The velocity of the molecules at 20 degree centigrade in m/s\n", + "k = 1.38 * 10**-23 # Boltzman constant in J/K\n", + "n = P / (k * T) # The number of molecules per m**3\n", + "l = 1. / (1.414 * pi * d**2 * n) # The mean free path in m\n", + "f = v / l # The collision frequency in per second\n", + "\n", + "# Output\n", + "print '(a)The mean free path is %3.4g m \\n (b)The collision frequency is %3.4g per second ' % (l, f)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)The mean free path is 2.253e-07 m \n", + " (b)The collision frequency is 2.268e+09 per second \n" + ] + } + ], + "prompt_number": 47 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.48 Page No : 760" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "l = 1.876 * 10**-7 # The mean free path of the gas in m\n", + "v = 511. # The average speed of the molecule in m/s\n", + "\n", + "# Calculations\n", + "f = v / l # The collision frequency in per second\n", + "\n", + "# Output\n", + "print 'The collision frequency is %3.4g per second ' % (f)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The collision frequency is 2.724e+09 per second \n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.49 Page No : 764" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "s = 1. # The specific heat of water in k cal kg C\n", + "m = 1. # The mass of ice in kg\n", + "H = 80. # The latent heat of ice in kcal/kg\n", + "H1 = 540. # The latent heat of steam in kcal/kg\n", + "T = 273. # The temperature of the ice in K\n", + "T1 = 373. # The temperature of water at 100 degree centigrade in K\n", + "\n", + "# Calculations\n", + "S1 = H / T # The increase in entropy when 1 kg of ice at 273 K is converted into water at 273 K in kcal/K\n", + "# The increase in entropy when 1 kg of water at 273 K is converted into\n", + "# water at 373 K in kcal/K\n", + "S2 = m * s * math.log(T1 / T)\n", + "S3 = H1 / T1 # The increase in entropy when 1 kg of water at 373 K is converted into steam at 373 K in kcal/K\n", + "S = S1 + S2 + S3 # The total increase in entropy in kcal/K\n", + "\n", + "# Output\n", + "print 'The total increase in entropy is %3.3f kcal/K ' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total increase in entropy is 2.053 kcal/K \n" + ] + } + ], + "prompt_number": 49 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.50 Page No : 767" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t1 = 27. # The initial temperature of the gas in degree centigrade\n", + "g = 1.4 # The adiabatic index\n", + "p1 = 1. # Let the initial pressure in atmospheres\n", + "p2 = 2. * p1 # The final pressure in atmospheres\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The initial temperature of the gas in K\n", + "# The final temperature of the gas in K\n", + "T2 = (((p2 / p1)**(g - 1)) * (T1)**g)**(1 / g)\n", + "T = T2 - T1 # The rise in temperature of a gas in K or degree centigrade\n", + "\n", + "# Output\n", + "print 'The rise in temperature is %3.1f degree centigrade ' % (T)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rise in temperature is 65.7 degree centigrade \n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.51 Page No : 770" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "V1 = 10.**-3 # One litre of monoatomic perfect gas at NTP in m**3\n", + "V2 = (V1 / 2) # The final volume in m**3\n", + "g = 1.67 # The adiabatic index\n", + "\n", + "# Calculations\n", + "# The work done on the gas in J\n", + "W = (1 / (g - 1)) * ((1 / (V2)**(g - 1)) - (1 / (V1)**(g - 1)))\n", + "\n", + "# Output\n", + "print 'The work done on the gas is %3.1f J ' % (W)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The work done on the gas is 90.3 J \n" + ] + } + ], + "prompt_number": 51 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.52 Page No : 775" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T1 = 1200. # The temperature at which first engine receives heat in K\n", + "T2 = 300. # The temperature at which second engine rejects to heat reservoir in K\n", + "\n", + "# Calculations\n", + "# The temperature when the work outputs of two engines are equal in K\n", + "Tw = (T1 + T2) / 2\n", + "# The temperature when the efficiency of two engines are equal in K\n", + "Te = (T1 * T2)**(1. / 2)\n", + "\n", + "# Output\n", + "print '(a)The temperature when the work outputs of two engines are equal is %3.0f K \\n (b)The temperature when the efficiency of two engines are equal is %3.0f K ' % (Tw, Te)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a)The temperature when the work outputs of two engines are equal is 750 K \n", + " (b)The temperature when the efficiency of two engines are equal is 600 K \n" + ] + } + ], + "prompt_number": 57 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.53 Page No : 777" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "t1 = 27. # The temperature of the source in degree centigrade\n", + "t2 = -73 # The temperature of the sinkk in degree centigrade\n", + "H2 = 300. # The amount of heat released by the sinkk in cal\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of the source in K\n", + "T2 = t2 + 273 # The temperature of the sinkk in K\n", + "H1 = H2 * (T1 / T2) # The amount of heat released by the source in cal\n", + "W = H1 - H2 # The work performed per cycle in cal\n", + "W1 = W * 4.2 # The work performed per cycle in J\n", + "\n", + "# Output\n", + "print 'The work performed by the engine per cycle is %3.0f J ' % (W1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The work performed by the engine per cycle is 630 J \n" + ] + } + ], + "prompt_number": 56 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.54 Page No : 782" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "m = 3. # The rate at which ice melts in kg/hour\n", + "t = 28. # The external temperature in degree centigrade\n", + "Li = 3.3 * 10**5 # Specific latent heat of ice fusion in Jkg**-1\n", + "s = 4.2 * 10**3 # The specific heat in Jkg**-1.C\n", + "\n", + "# Calculations\n", + "Q = (m * Li) + (m * s * t) # The heat taken by the ice to melt into water in J\n", + "P = Q / 3600 # To prevent melting of ice ,the refrigerator should have the power out in J/s\n", + "\n", + "# Output\n", + "print 'The minimum power output of the motor is %3.0f watts ' % (P)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The minimum power output of the motor is 373 watts \n" + ] + } + ], + "prompt_number": 55 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.55 Page No : 788" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "Li = 3.3 * 10**5 # Specific latent heat of ice fusion in Jkg**-1\n", + "V1 = 1.090 * 10**-3 # The specific volume of one kg of ice in m**3\n", + "V2 = 10.**-3 # The specific volume of one kg of water in m**3\n", + "T = 273. # The temperature maintained in K\n", + "dP = 1.01 * 10**5 # The increase in pressure in N/m**2\n", + "\n", + "# Calculations\n", + "# The depression in the melting point of ice in K (or) degree centigrade\n", + "dT = -(dP * T * (V2 - V1)) / Li\n", + "\n", + "# Output\n", + "print 'The depression of melting point of ice is %3.2g K (or) %3.2g degree centigrade ' % (dT, dT)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The depression of melting point of ice is 0.0075 K (or) 0.0075 degree centigrade \n" + ] + } + ], + "prompt_number": 58 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.56 Page No : 791" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "dp = 100. # The change in mercury pressure in cm of Hg\n", + "v2 = 1601. # Specific volume of steam in cm**3/gram\n", + "v1 = 1. # Specific volume of water in cm**3/gram\n", + "l = 536. # Latent heat in cal/gram\n", + "t = 100. # The temperature of the steam in degree centigrade\n", + "\n", + "# calculations\n", + "dP = 1. * 13.6 * 10**3 * 9.8 # The change in mercury pressure in N/m**2\n", + "V2 = v2 * 10**-3 # Specific volume of steam in m**3/kg\n", + "V1 = v1 * 10**-3 # Specific volume of water in m**3/kg\n", + "L = l * 4.2 * 10**3 # Latent heat in J/kg\n", + "T = t + 273 # The temperature of the steam in K\n", + "# The increase in boiling point of water in K or degree centigrade\n", + "dT = (dP * T * (V2 - V1)) / L\n", + "\n", + "# Output\n", + "print 'The increase in boiling point of water is %3.2f K (or) %3.2f degree centigrade ' % (dT, dT)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in boiling point of water is 35.33 K (or) 35.33 degree centigrade \n" + ] + } + ], + "prompt_number": 59 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.57 Page No : 796" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "L = 80. # The latent heat of fusion of ice in cal/gm\n", + "Li = 3.3 * 10**5 # Specific latent heat of ice fusion in Jkg**-1\n", + "dp = 1. # The increase in pressure in atmospheres\n", + "t = 0. # The given temperature in degree centigrade\n", + "v = -0.1 # The change in specific volume in cm**3/gm\n", + "\n", + "# Calculations\n", + "dP = 0.76 * 13.6 * 10**3 * 9.8 # The increase in pressure in N/m**2\n", + "V = v * 10**-3 # The change in specific volume in m**3/kg\n", + "T = t + 273 # The given temperature in K\n", + "# The decrease in the melting point of ice with increase in the pressure\n", + "# of one atmosphere in K\n", + "dT = -(dP * T * (V)) / Li\n", + "\n", + "# Output\n", + "print 'The decrease in melting point of ice is %3.4f K (or) %3.4f degree centigrade ' % (dT, dT)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The decrease in melting point of ice is 0.0084 K (or) 0.0084 degree centigrade \n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.58 Page No : 803" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "R = 8.4 # The universal gas constant in J.mol**-1.K**-1\n", + "Cv = 21. # The spacific heat at constant volume in J.mol**-1.K**-1\n", + "P1 = 2. * 10**5 # The initial pressure of gas in N/m**2\n", + "V1 = 20. # The initial volume of the gas occupied in litres\n", + "P2 = 5. * 10**5 # The final pressure of the gas in N/m**2\n", + "V2 = 50. # The final volume of the gas occupied in litres\n", + "\n", + "# Calculations\n", + "# The ratio of final temperature to the initial temperature for perfect gas\n", + "T = (P2 * V2) / (P1 * V1)\n", + "V = V2 / V1 # The ratio of final volume to the initial volume for perfect gas\n", + "S = (Cv * math.log(T)) + (R * math.log(V)) # The change of entropy in J/K\n", + "\n", + "# Output\n", + "print 'The increase in entropy is %3.2f J/K ' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in entropy is 46.18 J/K \n" + ] + } + ], + "prompt_number": 61 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.59 Page No : 807" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "s = 4.2 * 10**3 # The specific heat of water is J/kg.C\n", + "m1 = 0.1 # The mass of water at 15 degree centigrade in kg\n", + "m2 = 0.16 # The mass of water at 40 degree centigrade in kg\n", + "t1 = 15. # The temperature of the first water in degree centigrade\n", + "t2 = 40. # The temperature of the second water in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of the first water in K\n", + "T2 = t2 + 273 # The temperature of the second water in K\n", + "T = ((m1 * T1) + (m2 * T2)) / (m1 + m2) # The final mixed temperature in K\n", + "# The change in entropy for 0.1 kg of water in J/K\n", + "s1 = m1 * s * 2.3026 * math.log10(T / T1)\n", + "# The change in entropy for 0.16 kg of water in J/K\n", + "s2 = m2 * s * 2.3026 * math.log10(T / T2)\n", + "S = s1 + s2 # The net change in the entropy of the system in J/K\n", + "\n", + "# Output\n", + "print 'The net increase in entropy is %3.2f J/K ' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The net increase in entropy is 0.89 J/K \n" + ] + } + ], + "prompt_number": 62 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.60 Page No : 811" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "m = 12.5 * 10**-3 # The amount of ice in kg\n", + "li = 80. # Latent heat of ice in cal/gram\n", + "l = 536. # Latent heat of steam in cal/gram\n", + "si = 0.5 # Specific heat of ice in cal/gram-K\n", + "sw = 1. # Specific heat of water in cal/gram-K\n", + "T1 = -24 + 273 # The initial temperature of ice in K\n", + "T2 = 0. + 273 # The final temperature of ice in K\n", + "T3 = 100. + 273 # The final temperature of water in K\n", + "\n", + "# Calculations\n", + "Li = li * 10**3 * 4.2 # The latent heat of ice in J/kg\n", + "Ls = l * 10**3 * 4.2 # The latent heat of water in J/kg\n", + "Si = si * 10**3 * 4.2 # The specific heat of ice in J/kg-K\n", + "Sw = sw * 10**3 * 4.2 # The specific heat of water in J/kg-K\n", + "# The increase in entropy of ice from 249 K to 273 K in J/K\n", + "s1 = m * Si * math.log(T2 / T1)\n", + "s2 = (m * Li) / T2 # The increase in entropy from 273 K ice to 273 K water in J/K\n", + "# The increase in entropy of water from 273 K to 373 K in J/K\n", + "s3 = m * Sw * math.log(T3 / T2)\n", + "# The increase in entropy from water at 373 K to steam at 373 K in J/K\n", + "s4 = (m * Ls) / T3\n", + "S = s1 + s2 + s3 + s4 # The total increase in entropy in J/K\n", + "\n", + "# Output\n", + "print 'The total increase in entropy is %3.2f J/K ' % (S)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total increase in entropy is 109.63 J/K \n" + ] + } + ], + "prompt_number": 63 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.61 Page No : 813" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "x1 = 20. # The initial thickness of the layer in cm\n", + "x2 = 30. # The final thickness of the layer in cm\n", + "t1 = -15 # The temperature of the surroundings in degree centigrade\n", + "L = 80. # The latent heat of ice in cal/gram\n", + "d = 0.9 # The given density of ice in g/cm**3\n", + "K = 0.005 # The coefficient of thermal conductivity in C.G.S units\n", + "\n", + "# Calculations\n", + "t = ((d * L) / (2 * K * t1)) * (x1**2 - x2**2) # The time taken in sec\n", + "\n", + "# Output\n", + "print 'The time taken for a layer of ice to increase the thickness is %3.2g sec ' % (t)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The time taken for a layer of ice to increase the thickness is 2.4e+05 sec \n" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.62 Page No : 815" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "t1 = 121. # The temperature of solid copper sphere in degree centigrade\n", + "dt1 = 2.6 # The rate of cooling of copper sphere in degree centigrade per minute\n", + "t2 = 195. # The temperature of another solid sphere in degree centigrade\n", + "t = 30. # The surrounding temperature in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The temperature of solid copper sphere in K\n", + "T2 = t2 + 273 # The temperature of another solid copper sphere in K\n", + "T0 = t + 273 # The surrounding temperature in K\n", + "R1 = 1. # Let the radius of the first sphere in m\n", + "R2 = 2. * R1 # The radius of the second sphere in m\n", + "# The rate at which solid copper sphere cools in degree centigrade per minute\n", + "dt2 = (dt1) * (R1 / R2) * ((T2**4 - T0**4) / (T1**4 - T0**4))\n", + "\n", + "# Output\n", + "print 'The rate at which solid copper sphere cools is %3.3f degree centigrade per minute ' % (dt2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rate at which solid copper sphere cools is 3.281 degree centigrade per minute \n" + ] + } + ], + "prompt_number": 65 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.63 Page No : 820" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "dt = 250. # The temperature gradient of an insulated copper rod in degree centigrade per metre\n", + "x = 0.05 # The distance between the two points in m\n", + "K = 384. # The thermal conductivity of copper in W.m**-1.K**-1\n", + "A = 1. # The surface area of the copper rod in m**2\n", + "t = 1. # The given time in seconds\n", + "\n", + "# Calculations\n", + "T = dt * x # The temperature difference in degree centigrade\n", + "# The amount of heat crossed per unit area per sec in J/s\n", + "Q = K * A * (dt) * t\n", + "\n", + "# Output\n", + "print '(1)The difference in temperature between two points seperated by 0.05m is %3.1f degree centigrade \\n (2)The amount of heat crossing per second per unit area normal to the rod is %3.2g J/s ' % (T, Q)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1)The difference in temperature between two points seperated by 0.05m is 12.5 degree centigrade \n", + " (2)The amount of heat crossing per second per unit area normal to the rod is 9.6e+04 J/s \n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.64 Page No : 826" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "T1 = 200. # The first temperature of the black body in K\n", + "T2 = 2000. # The second temperature of the black body in K\n", + "s = 5.672 * 10**-8 # Stefans constant in M.K.S units\n", + "\n", + "# Calculations\n", + "# The comparision of radiant emittance of a black body for given\n", + "# temperatures\n", + "R = (s * T1**4) / (s * T2**4)\n", + "\n", + "# Output\n", + "print 'The comparision of radiant emittance of a black body at 200 K and 2000 K is %3.0g ' % (R)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The comparision of radiant emittance of a black body at 200 K and 2000 K is 0.0001 \n" + ] + } + ], + "prompt_number": 67 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example A.65 Page No : 828" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Input data\n", + "d = 0.08 # The diameter of the black sphere in m\n", + "T = 500. # The temperature of the black sphere in K\n", + "T0 = 300. # The temperature of the surroundings in K\n", + "s = 6. * 10**-8 # The stefans constant in W m**-2 K**-4\n", + "pi = 3.14 # The mathematical constant of pi\n", + "\n", + "# Calculations\n", + "A = pi * d**2 # The area of the black sphere in m**2\n", + "e = 1. # The emittance of the black body\n", + "# The rate at which energy is radiated in J/s or watts\n", + "R = s * A * e * (T**4 - T0**4)\n", + "\n", + "# Output\n", + "print 'The rate at which energy is radiated R = %3.2f J/s (or) %3.2f watts' % (R, R)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rate at which energy is radiated R = 65.59 J/s (or) 65.59 watts\n" + ] + } + ], + "prompt_number": 68 + } + ], + "metadata": {} + } + ] +}
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