diff options
Diffstat (limited to 'Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/ch5.ipynb')
| -rwxr-xr-x | Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/ch5.ipynb | 1003 |
1 files changed, 1003 insertions, 0 deletions
diff --git a/Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/ch5.ipynb b/Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/ch5.ipynb new file mode 100755 index 00000000..6c739f7e --- /dev/null +++ b/Heat_and_Thermodynamics_by__Brijlal_and_N._Subrahmanyam/ch5.ipynb @@ -0,0 +1,1003 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:2d895fa6539cb401c1ac187f55507dc2067d26b87e5503473e832266dbcbd295" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 5 : Nature of Heat" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.1 Page No : 159" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "v = 480. # The velocity of a lead bullet in m/s\n", + "Sp = 0.03 # Specific heat of lead cal/g-K\n", + "\n", + "# Calculations\n", + "m = 10. # Let us assume the mass of bullet in gms\n", + "V = v * 100 # The velocity of the bullet in cm/s\n", + "W = (1. / 2) * m * (V**2) # The work done in ergs\n", + "J = 4.2 * 10**7 # The mechanical equivalent of heat in ergs/calorie\n", + "H = W / J # The amount of heat produced in cals\n", + "H1 = H / 2 # Half of the heat energy is used to raise the temperature of the bullet in cals\n", + "t = H1 / (m * Sp) # The rise in the temperature in degree centigrade\n", + "\n", + "# Output\n", + "print 'The rise in the temperature is t = %3.2f degree centigrade ' % (t)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rise in the temperature is t = 457.14 degree centigrade \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.2 Page No : 162" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "t = 1. # The increase in the temperature of a piece of aluminium in degree centigrade\n", + "a = 6. * 10**23 # The number of atoms present in 27 g of aluminium in atoms\n", + "Sp = 0.22 # The specific heat of aluminium in cal/g-K\n", + "m = 27. # The amount of aluminium in g\n", + "J = 4.2 * 10**7 # The mechanical equivalent of heat in ergs/calorie\n", + "\n", + "# Calculations\n", + "H = m * Sp * t # Heat required to raise the temperature of 27 gms of aluminium by 1 degree centigrade in cals\n", + "E = m * Sp * J # Energy gained by atoms of aluminium in ergs\n", + "E1 = E / a # Increase in energy per atom of aluminium in ergs\n", + "\n", + "# Output\n", + "print 'The increase in energy per atom of aluminium is %3.4g ergs ' % (E1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The increase in energy per atom of aluminium is 4.158e-16 ergs \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.3 Page No : 168" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "h = 50. # The height from which water falls in metres\n", + "m = 100. # Let us assume the mass of the water in gms\n", + "g = 980. # Gravitational constant in gms/s**2\n", + "J = 4.2 * 10**7 # The mechanical equivalent of heat in ergs/calorie\n", + "\n", + "# Calculations\n", + "h1 = h * 100 # The height from which water falls in cm\n", + "W = m * g * h1 # The work done in ergs\n", + "t = W / (J * m) # The rise in temperature of water in degree centigrade\n", + "\n", + "# Output\n", + "print 'The rise in temperature of water is t = %3.3f degree centigrade ' % (t)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rise in temperature of water is t = 0.117 degree centigrade \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.4 Page No : 174" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "v = 1. # The volume of oxygen at N.T.P in cm**3\n", + "d = 13.6 # The density of mercury in g/cm**3\n", + "r = 4.62 * 10**4 # The R.M.S velocity of oxygen molecules at 0 degree centigrade in cm/s\n", + "m = 52.8 * 10**-24 # Mass of one molecule of oxygen in g\n", + "g = 980. # Gravitational constant in gms/s**2\n", + "\n", + "# Calculations\n", + "P = 76. * g * d # The pressure in dynes/cm**2\n", + "n = ((3 * P) / (m * r**2)) # Number of molecules in 1 cc of oxygen at N.T.P\n", + "\n", + "# Output\n", + "print 'The number of molecules in 1 c.c of oxygen at N.T.P is n = %3.4g ' % (n)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of molecules in 1 c.c of oxygen at N.T.P is n = 2.696e+19 \n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5 Page No : 177" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "t = -100 # The given temperature in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t + 273 # The given temperature in K\n", + "m1 = 1. # number of hydrogen molecules\n", + "m2 = 16. # number of oxygen molecules\n", + "m = m2 / m1 # Number of oxygen molecules to the hydrogen molecules\n", + "T2 = (T1 * m) - 273 # The temperature in degree centigrade\n", + "\n", + "# Output\n", + "print 'The temperature at which the oxygen molecules have the same root mean square velocity as that of hydrogen molecules is T2 = %3.0f degree centigrade ' % (T2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature at which the oxygen molecules have the same root mean square velocity as that of hydrogen molecules is T2 = 2495 degree centigrade \n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.6 Page No : 180" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "t = 27. # The given temperature in degree centigrade\n", + "d = 13.6 # The density of mercury in g/cm**3\n", + "g = 980. # Gravitational constant in gms/s**2\n", + "m1 = 16. # number of oxygen molecules\n", + "D = 0.000089 # The density of hydrogen at N.T.P in g/cc\n", + "T = 273. # The temperature at N.T.P in K\n", + "\n", + "# Calculations\n", + "P = 76. * g * d # The pressure in dynes/cm**2\n", + "p = m1 * D # The density of oxygen at N.T.P in g/cc\n", + "C = ((3 * P) / (p))**(1. / 2) # The RMS velocity of oxygen molecule in cm/s\n", + "T1 = t + T # The given temperature in K\n", + "# The RMS velocity of the molecules at 27 degree centigrade in cm/s\n", + "C1 = C * (T1 / T)**(1. / 2)\n", + "\n", + "# Output\n", + "print 'The RMS velocity of the oxygen molecules at 27 degree centigrade is C1 = %3.4g cm/s ' % (C1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The RMS velocity of the oxygen molecules at 27 degree centigrade is C1 = 4.843e+04 cm/s \n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.7 Page No : 186" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "d = 13.6 # The density of mercury in g/cm**3\n", + "g = 980. # Gravitational constant in gms/s**2\n", + "m = 3.2 # Mass of oxygen in gms\n", + "t = 27. # The given temperature in degree centigrade\n", + "p = 76. # The pressure in cm of Hg\n", + "R = 8.31 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "\n", + "# Calculations\n", + "P = p * g * d # The given pressure in dynes/cm**2\n", + "T = t + 273 # The given temperature in K\n", + "V = (T * R) / P # Volume per g mol of oxygen in cc per g mol\n", + "m1 = 32. # Molecular weight of Oxygen\n", + "V1 = V * (m / m1) # Volume of 3.2 g of oxygen in cc\n", + "\n", + "# Output\n", + "print 'The Volume occupied by 3.2 gms of Oxygen is V = %3.0f cc ' % (V1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Volume occupied by 3.2 gms of Oxygen is V = 2461 cc \n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.9 Page No : 193" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "v = 1. # The volume of an Ideal gas at N.T.P in m**3\n", + "d = 13.6 # The density of mercury in g/cm**3\n", + "g = 980. # Gravitational constant in gms/s**2\n", + "p = 76. # The pressure in cm of Hg\n", + "R = 8.31 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "N = 6.023 * 10**23 # The Avogadro number\n", + "T = 273. # The temperature at N.T.P in K\n", + "\n", + "# Calculations\n", + "P = p * g * d # The given pressure in dynes/cm**2\n", + "x = (P * N * 10**6) / (R * T) # Number of molecules in one cubic metre volume\n", + "\n", + "# Output\n", + "print 'The number of molecules in one cubic metre of an ideal gas at N.T.P is x = %3.4g ' % (x)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of molecules in one cubic metre of an ideal gas at N.T.P is x = 2.689e+25 \n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.10 Page No : 196" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "v = 1. # The volume of an ideal gas in litre\n", + "d = 13.6 # The density of mercury in g/cm**3\n", + "g = 980. # Gravitational constant in gms/s**2\n", + "p = 76. # The pressure in cm of Hg\n", + "R = 8.31 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "N = 6.023 * 10**23 # The Avogadro number\n", + "T = 273. # The temperature at N.T.P in K\n", + "t = 136.5 # The given temperature in degree centigrade\n", + "p1 = 3. # The given atmospheric pressure in atm pressure\n", + "\n", + "# Calculations\n", + "T1 = T + t # The given temperature in K\n", + "P = p * g * d # The given pressure in dynes/cm**2\n", + "x = (p1 * P * N * 10**3) / (R * T1) # Number of molecules in one litre volume\n", + "\n", + "# Output\n", + "print 'The number of molecules in one litre of an ideal gas volume is x = %3.4g ' % (x)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of molecules in one litre of an ideal gas volume is x = 5.378e+22 \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.11 Page No : 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "v = 1. # The volume of a gas in cc\n", + "d = 13.6 # The density of mercury in g/cm**3\n", + "p2 = 10.**-7 # The pressure in cm of Hg\n", + "g = 980. # Gravitational constant in gms/s**2\n", + "p1 = 76. # The pressure in cm of Hg\n", + "R = 8.31 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "N = 6.023 * 10**23 # The Avogadro number\n", + "T = 273. # The temperature at N.T.P in K\n", + "n1 = 2.7 * 10**19 # The number of molecules per cc of gas at N.T.P\n", + "t2 = 0. # The given temperature in degree centigrade\n", + "t3 = 39. # The given temperature in degree centigrade\n", + "\n", + "# Calculations\n", + "P1 = p1 * g * d # The given pressure in dynes/cm**2\n", + "P2 = p2 * g * d # The given pressure in dynes/cm**2\n", + "# The number of molecules per cc of the gas at 0 degree centigrade\n", + "n2 = n1 * (P2 / P1)\n", + "T2 = t2 + 273 # The given temperature in K\n", + "T3 = t3 + 273 # The given temperature in K\n", + "# The number of molecules per cc of the gas at 398 degree centigrade\n", + "n3 = n2 * (T2 / T3)\n", + "\n", + "# Output\n", + "print 'The number of molecules per cc of the gas , \\n (1)at 0 degree centigrade and 10^-6 mm pressure of mercury is n2 = %3.4g \\n (2)at 39 degree centigrade and 10^-6 mm pressure of mercury is n3 = %3.4g' % (n2, n3)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of molecules per cc of the gas , \n", + " (1)at 0 degree centigrade and 10^-6 mm pressure of mercury is n2 = 3.553e+10 \n", + " (2)at 39 degree centigrade and 10^-6 mm pressure of mercury is n3 = 3.109e+10\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.12 Page No : 208" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 300. # The given temperature in K\n", + "R = 8.3 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "\n", + "# Calculations\n", + "# The total random kinetic energy per gram -molecule of oxygen in joules\n", + "E = ((3. / 2) * (R * T)) / 10**7\n", + "\n", + "# Output\n", + "print 'The total random kinetic energy of one gm-molecule of oxygen at 300 K is K.E = %3.0f joules' % (E)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total random kinetic energy of one gm-molecule of oxygen at 300 K is K.E = 3735 joules\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.13 Page No : 213" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 300. # The given temperature in K\n", + "k = 1.38 * 10**-16 # Boltzmann constant in erg/molecule-deg\n", + "\n", + "# Calculations\n", + "E = (3. / 2) * k * T # The average Kinetic energy of a molecule in ergs\n", + "\n", + "# Output\n", + "print 'The Average Kinetic energy of a molecule of a gas at 300 K is K.E = %3.4g ergs ' % (E)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Average Kinetic energy of a molecule of a gas at 300 K is K.E = 6.21e-14 ergs \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.14 Page No : 220" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "R = 8.32 # Universal gas constant in joules/mole-K\n", + "t = 727. # The given temperature in degree centigrade\n", + "N = 6.06 * 10**23 # The Avogadro number\n", + "\n", + "# Calculations\n", + "T = 273. + t # The given temperature in K\n", + "k = R / N # Boltzmann constant in joules/mol-K\n", + "E = (3. / 2) * k * T # Mean translational kinetic energy per molecule in joules\n", + "\n", + "# Output\n", + "print 'The mean translational kinetic energy per molecule is K.E = %3.4g joule ' % (E)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mean translational kinetic energy per molecule is K.E = 2.059e-20 joule \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.15 Page No : 224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 300. # The given temperature in K\n", + "M = 28. # Molecular weight of nitrogen in g\n", + "R = 8.3 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "\n", + "# Calculations\n", + "E = (3. / 2) * R * T # The total random kinetic energy of nitrogen in ergs\n", + "# The total random kinetic energy of one gram of nitrogen at 300 K in joule\n", + "E1 = E / (M * 10**7)\n", + "\n", + "# Output\n", + "print 'The total random kinetic energy of one gram of nitrogen at 300 K is K.E = %3.1f joule ' % (E1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total random kinetic energy of one gram of nitrogen at 300 K is K.E = 133.4 joule \n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.16 Page No : 228" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 200. # The given temperature in K\n", + "m = 2. # Given mass of Helium in g\n", + "M = 4. # Molecular weight of helium in g\n", + "R = 8.3 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "\n", + "# Calculations\n", + "# The energy for 2 g of helium in joules\n", + "E = (m * (3. / 2) * (R * T) / (M)) / 10**7\n", + "\n", + "# Output\n", + "print 'The total random kinetic energy of 2 g of helium at 200 K is K.E = %3.0f joules' % (E)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total random kinetic energy of 2 g of helium at 200 K is K.E = 1245 joules\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.17 Page No : 233" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 300. # The given temperature in K\n", + "R = 8.3 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "M = 221. # The molecular weight of mercury\n", + "\n", + "# Calculations\n", + "# The root mean square velocity of a molecule of mercury vapour at 300 K\n", + "# in cm/s\n", + "C = ((3 * R * T) / (M))**(1. / 2)\n", + "\n", + "# Output\n", + "print 'The root mean square velocity of a molecule of mercury vapour at 300 K is C = %3.4g cm/s ' % (C)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The root mean square velocity of a molecule of mercury vapour at 300 K is C = 1.839e+04 cm/s \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.18 Page No : 239" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "T = 300. # The given temperature in K\n", + "M = 32. # Molecular weight of oxygen\n", + "R = 8.3 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "\n", + "# Calculations\n", + "# Total random kinetic energy of 1 g molecule of oxygen in ergs\n", + "E = (3. / 2) * R * T\n", + "# The required speed of one gram molecule of oxygen in cm/s\n", + "v = ((E) * (2 / M))**(1. / 2)\n", + "\n", + "# Output\n", + "print 'The required speed of one gram molecule of oxygen is v = %3.2g cm/s ' % (v)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required speed of one gram molecule of oxygen is v = 4.8e+04 cm/s \n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.19 Page No : 242" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "v = 8. # The speed of the earths first satellite in km/s\n", + "R = 8.3 * 10**7 # The Universal gas constant in ergs/g mol-K\n", + "M = 2. # Molecular weight of hydrogen\n", + "\n", + "# Calculations\n", + "V = v * 10**5 # The speed of the earths first satellite in cm/s\n", + "T = (M * V**2) / (3 * R) # The temperature at which it becomes equal in K\n", + "\n", + "# Output\n", + "print 'The temperature at which the r.m.s velocity of a hydrogen molecule will be equal to the speed of earths first satellite is T = %3.4g K' % (T)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature at which the r.m.s velocity of a hydrogen molecule will be equal to the speed of earths first satellite is T = 5141 K\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.20 Page No : 248" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "t1 = 0. # The given temperature in degree centigrade\n", + "\n", + "# Calculations\n", + "T1 = t1 + 273 # The given temperature in K\n", + "# The temperature at which the r.m.s velocity of a gas be half its value\n", + "# at 0 degree centigrade in K\n", + "T2 = (1. / 2)**2 * T1\n", + "T21 = T2 - 273 # The required temperature in degree centigrade\n", + "\n", + "# Output\n", + "print 'The required temperature is T2 = %3.2f K (or) %3.2f degree centigrade ' % (T2, T21)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required temperature is T2 = 68.25 K (or) -204.75 degree centigrade \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.21 Page No : 252" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "n = 1.66 * 10**-4 # The viscosity of the gas in dynes/cm**2\n", + "C = 4.5 * 10**4 # The R.M.S velocity of the molecules in cm/s\n", + "d = 1.25 * 10**-3 # The density of the gas in g/cc\n", + "N = 6.023 * 10**23 # The Avogadro number\n", + "V = 22400. # The volume of a gas at N.T.P in cc\n", + "pi = 3.142 # The mathematical constant of pi\n", + "\n", + "# Calculations\n", + "L = (3 * n) / (d * C) # The mean free path of the molecules of the gas in cm\n", + "F = (C / L) # The frequency collision in per sec\n", + "n = N / V # Number of molecules per cc\n", + "# Molecular diameter of the gas molecules in cm\n", + "D = 1. / ((1.414 * pi * n * L)**(1. / 2))\n", + "\n", + "# Output\n", + "print '(1)The mean free path of the molecules of the gas is %3.0g cm \\n (2)The frequency of collision is N = %3.0g /sec \\n (3)Molecular diameter of the gas molecules is d = %3.0g cm ' % (L, F, D)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1)The mean free path of the molecules of the gas is 9e-06 cm \n", + " (2)The frequency of collision is N = 5e+09 /sec \n", + " (3)Molecular diameter of the gas molecules is d = 3e-08 cm \n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.22 Page No : 255" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "n = 2.25 * 10**-4 # The viscosity of the gas in dynes/cm**2\n", + "C = 4.5 * 10**4 # The RMS velocity of the molecules in cm/s\n", + "d = 10.**-3 # The density of the gas in g/cc\n", + "\n", + "# Calculations\n", + "L = (3 * n) / (d * C) # The mean free path of the molecules in cm\n", + "\n", + "# Output\n", + "print 'The mean free path of the molecules is %3g cm ' % (L)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mean free path of the molecules is 1.5e-05 cm \n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.23 Page No : 261" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "d = 2. * 10**-8 # The molecular diameter in cm\n", + "n = 3. * 10**19 # The number of molecules per cc\n", + "pi = 3.14 # Mathematical constant of pi\n", + "\n", + "# Calculations\n", + "L = 1. / ((pi * (d)**2 * n)) # The mean free path of a gas molecule in cm\n", + "\n", + "# Output\n", + "print 'The mean free path of a gas molecule is %3.0g cm ' % (L)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mean free path of a gas molecule is 3e-05 cm \n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.24 Page No : 265" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Input data\n", + "p = 760. # The given pressure in mm of Hg\n", + "T = 273. # The temperature of the chamber in K\n", + "V = 22400. # The volume of the gas at N.T.P in cc\n", + "p1 = 10.**-6 # The pressure in the chamber in mm of mercury pressure\n", + "N = 6.023 * 10**23 # The Avogadro number\n", + "d = 2. * 10**-8 # Molecular diameter in cm\n", + "pi = 3.14 # Mathematical constant of pi\n", + "\n", + "# Calculations\n", + "# The number of molecules per cm**3 in the chamber in molecules/cm**3\n", + "n = (N * p1) / (V * p)\n", + "# The mean free path of the gas molecules in the chamber in cm\n", + "L = 1. / (pi * (d)**2 * n)\n", + "\n", + "# Output\n", + "print 'The mean free path of gas molecules in a chamber is %3.4g cm ' % (L)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mean free path of gas molecules in a chamber is 2.25e+04 cm \n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.25 Page No : 270" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Input data\n", + "Tc = 132. # The given temperature in K\n", + "Pc = 37.2 # The given pressure in atms\n", + "R = 82.07 # Universal gas constant in cm**3 atoms K**-1\n", + "\n", + "# Calculations\n", + "# Vander Waals constant in atoms cm**6\n", + "a = (27. / 64) * ((R)**2 * (Tc)**2) / Pc\n", + "b = ((R * Tc) / (8 * Pc)) # Vander Waals constant in cm**3\n", + "\n", + "# Output\n", + "print 'The Van der Waals constants are , \\n (1) a = %3.4g atoms cm^6 \\n (2) b = %3.2f cm^3 ' % (a, b)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Van der Waals constants are , \n", + " (1) a = 1.331e+06 atoms cm^6 \n", + " (2) b = 36.40 cm^3 \n" + ] + } + ], + "prompt_number": 24 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |