{
"metadata": {
"name": "",
"signature": "sha256:e30b9c00a7a64c549fe856050903690b0947bb9d968fe683f359ed69004ad2d0"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8 : Transmission of Heat"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.1 Page No : 462"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Input data\n",
"l1 = 10. # Length of the copper rod in cm\n",
"l2 = 4. # Length of the iron rod in cm\n",
"K1 = 0.9 # The thermal conductivity of copper\n",
"\n",
"# Calculations\n",
"K2 = (l2**2 / l1**2) * K1 # The Thermal conductivity of iron\n",
"\n",
"# Output\n",
"print 'The thermal conductivity of iron is K2 = %3.3f ' % (K2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The thermal conductivity of iron is K2 = 0.144 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.2 Page No : 469"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Input data\n",
"K = 0.2 # The thermal conductivity of the plate\n",
"d = 0.2 # The thickness of the plate in cm\n",
"A = 20. # The area of the plate in cm**2\n",
"T = 100. # The temperature difference in degree centigrade\n",
"t = 60. # The given time in seconds\n",
"\n",
"# Calculations\n",
"# The quantity of heat that will flow through the plate in one minute in cal\n",
"Q = (K * A * T * t) / d\n",
"\n",
"# Output\n",
"print 'The quantity of heat that will flow through the plate in one minute is Q = %3.4g cal ' % (Q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The quantity of heat that will flow through the plate in one minute is Q = 1.2e+05 cal \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.3 Page No : 473"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Input data\n",
"l = 30. # The length of the bar in cm\n",
"A = 5. # The uniform area of cross section of a bar in cm**2\n",
"ta = 200. # The temperature maintained at the end A in degree centigrade\n",
"tc = 0. # The temperature maintained at the end C in degree centigrade\n",
"Kc = 0.9 # The thermal conductivity of copper\n",
"Ki = 0.12 # The thermal conductivity of iron\n",
"\n",
"# Calculations\n",
"# The temperature after the steady state is reached in degree centigrade\n",
"T = ((Kc * A * ta) + (Ki * A * tc)) / ((Kc + Ki) * A)\n",
"# The rate of flow of heat along the bar when the steady state is reached\n",
"# in cal/sec\n",
"Q = (Kc * A * (ta - T)) / (l / 2)\n",
"\n",
"# Output\n",
"print 'The rate of flow of heat along the bar when the steady state is reached is Q = %3.2f cal/s ' % (Q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The rate of flow of heat along the bar when the steady state is reached is Q = 7.06 cal/s \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4 Page No : 477"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Input data\n",
"d1 = 1.75 # The thickness of the wood in cm\n",
"d2 = 3. # The thickness of the cork in cm\n",
"t2 = 0. # The temperature of the inner surface of the cork in degree centigrade\n",
"t1 = 12. # The temperature of the outer surface of the wood in degree centigrade\n",
"K1 = 0.0006 # The thermal conductivity of wood\n",
"K2 = 0.00012 # The thermal conductivity of cork\n",
"\n",
"# Calculations\n",
"# The temperature of the interface in degree centigrade\n",
"T = (((K1 * t1) / d1) + ((K2 * t2) / d2)) / ((K1 / d1) + (K2 / d2))\n",
"\n",
"# Output\n",
"print 'The temperature of the interface is T = %3.2f degree centigrade ' % (T)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The temperature of the interface is T = 10.75 degree centigrade \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.5 Page No : 483"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Input data\n",
"x1 = 3. # The thickness of the ice layer on the surface of a pond in cm\n",
"x = 1. # The increase in the thickness of the ice when the temperature is maintained at -20 degree centigrade in mm\n",
"# The increased thickness of the ice layer on the surface of a pond in cm\n",
"x2 = x1 + (x / 10)\n",
"T = -20 # The temperature of the surrounding air in degree centigrade\n",
"d = 0.91 # The density of ice at 0 degree centigrade in g/cm**3\n",
"L = 80. # The latent heat of ice in cal/g\n",
"K = 0.005 # The thermal conductivity of ice\n",
"\n",
"# Calculations\n",
"# The time taken to increase its thickness by 1 mm in sec\n",
"t = ((d * L) / (2 * K * (-T))) * (x2**2 - x1**2)\n",
"t1 = t / 60 # The time taken to increase its thickness by 1 mm in min\n",
"\n",
"# Output\n",
"print 'The time taken to increase its thickness by 1 mm is t = %3.2f s' % (t)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The time taken to increase its thickness by 1 mm is t = 222.04 s\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.6 Page No : 485"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Input data\n",
"x1 = 10. # The thickness of the ice layer on the surface of a pond in cm\n",
"x = 5. # The increase in the thickness of the ice when the temperature is maintained at -10 degree centigrade in cm\n",
"# The increased thickness of the ice layer on the surface of a pond in cm\n",
"x2 = x1 + (x)\n",
"T = -10 # The temperature of the surrounding air in degree centigrade\n",
"d = 0.90 # The density of ice at 0 degree centigrade in g/cm**3\n",
"L = 80. # The latent heat of ice in cal/g\n",
"K = 0.005 # The thermal conductivity of ice\n",
"\n",
"# Calculations\n",
"# The time taken to increase its thickness by 5 cm in sec\n",
"t = ((d * L) / (2 * K * (-T))) * (x2**2 - x1**2)\n",
"# The time taken to increase its thickness by 5 cm in hours\n",
"t1 = t / (60. * 60)\n",
"\n",
"# Output\n",
"print 'The time taken to increase its thickness by 5 cm is t = %3.0g s (or) %3.0f hours' % (t, t1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The time taken to increase its thickness by 5 cm is t = 9e+04 s (or) 25 hours\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.7 Page No : 490"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# input data\n",
"# The temperature maintained on one sphere (black body radiat(or) in K\n",
"T1 = 300.\n",
"# The temperature maintained on another sphere (black body radiat(or) in K\n",
"T2 = 200.\n",
"s = 5.672 * 10**-8 # Stefans constant in M.K.S units\n",
"\n",
"# Calculations\n",
"# The net rate of energy transfer between the two spheres in watts/m**2\n",
"R = s * (T1**4 - T2**4)\n",
"\n",
"# output\n",
"print 'The net rate of energy transfer between the two spheres is R = %3.2f watts/m^2' % (R)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The net rate of energy transfer between the two spheres is R = 368.68 watts/m^2\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8 Page No : 495"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"# Input data\n",
"T1 = 400. # The given temperature of a black body in K\n",
"T2 = 4000. # The given temperature of a black body in K\n",
"s = 5.672 * 10**-8 # Stefans constant in M.K.S units\n",
"\n",
"# Calculations\n",
"R1 = s * T1**4 # The radiant emittance of a black body at 400 k in watts/m**2\n",
"# The radiant emittance of a black body at 4000 k in kilo-watts/m**2\n",
"R2 = (s * T2**4) / 1000\n",
"\n",
"# Output\n",
"print 'The Radiant emittance of a black body at a temperature of ,\\n (i) 400 K is R = %3.0f watts/m^2 \\n (ii) 4000 K is R = %3.0f kilo-watts/m^2' % (R1, R2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Radiant emittance of a black body at a temperature of ,\n",
" (i) 400 K is R = 1452 watts/m^2 \n",
" (ii) 4000 K is R = 14520 kilo-watts/m^2\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.9 Page No : 500"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Input data\n",
"e = 0.35 # The relative emittance of tungsten\n",
"A = 10.**-3 # The surface area of a tungsten sphere in m**2\n",
"T1 = 300. # The temperature of the walls in K\n",
"T2 = 3000. # The temperature to be maintained by the sphere in K\n",
"s = 5.672 * 10**-8 # Stefans constant in M.K.S units\n",
"\n",
"# Calculations\n",
"# The power input required to maintain the sphere at 3000 K in watts\n",
"R = s * A * e * (T2**4 - T1**4)\n",
"\n",
"# Output\n",
"print 'The power input required to maintain the sphere at 3000 K is R = %3.0f watts' % (R)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The power input required to maintain the sphere at 3000 K is R = 1608 watts\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.10 Page No : 507"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Input data\n",
"e = 0.1 # The relative emittance of an aluminium foil\n",
"T1 = 300. # The temperature of one sphere in K\n",
"T2 = 200. # The temperature of another sphere in K\n",
"s = 5.672 * 10**-8 # Stefans constant in M.K.S units\n",
"\n",
"# Calculations\n",
"# The temperature of the foil after the steady state is reached in K\n",
"x = (((T1**4 + T2**4) / 2)**(1. / 4))\n",
"# The rate of energy transfer between one of the spheres and foil in watts/m**2\n",
"R = e * s * (T1**4 - x**4)\n",
"\n",
"# Output\n",
"print '1)The temperature of the foil after the steady state reached is x = %3.1f K \\\n",
"\\n2)The rate of energy transfer between the sphere and the foil is R = %3.1f watts/m^2' % (x, R)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"1)The temperature of the foil after the steady state reached is x = 263.9 K \n",
"2)The rate of energy transfer between the sphere and the foil is R = 18.4 watts/m^2\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.11 Page No : 513"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Input data\n",
"A = 5. * 10**-5 # The surface area of the filament in m**2\n",
"e = 0.85 # The relative emittance of the filament\n",
"s = 5.672 * 10**-8 # Stefans constant in M.K.S units\n",
"t = 60. # The time in seconds\n",
"T = 2000. # The temperature of the filament of an incandescent lamp in K\n",
"\n",
"# Calculations\n",
"E = A * e * s * t * (T**4) # The energy radiated from the filament in joules\n",
"\n",
"# Output\n",
"print 'The energy radiated from the filament is E = %3.0f joules ' % (E)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The energy radiated from the filament is E = 2314 joules \n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.12 Page No : 520"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Input data\n",
"E = 1.53 * 10**5 # The energy radiated from an iron furnace in calories per hour\n",
"A = 10.**-4 # The cross section area of an iron furnace in m**2\n",
"e = 0.8 # The relative emittance of the furnace\n",
"t = 3600. # The time in seconds\n",
"s = 1.36 * 10**-8 # Stefans constant in cal/m**2-s-K**4\n",
"\n",
"# Calculations\n",
"T = ((E) / (A * e * s * t))**(1. / 4) # The temperature of the furnace in K\n",
"\n",
"# Output\n",
"print 'The temperature of the furnace is T = %3.0f K ' % (T)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The temperature of the furnace is T = 2500 K \n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.13 Page No : 524"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Input data\n",
"S = 2.3 # Solar constant in cal/cm**2/minute\n",
"r = 7. * 10**10 # The radius of the sun in cm\n",
"R = 1.5 * 10**13 # The distance between the sun and the earth in cm\n",
"s = 1.37 * 10**-12 # Stefans constant in cal/cm**2/s\n",
"\n",
"# Calculations\n",
"E = (S / 60) * (R / r)**(2) # The energy radiated from the sun in cal/s\n",
"T = (E / s)**(1. / 4) # The black body temperature of the sun in K\n",
"\n",
"# Output\n",
"print 'The black body temperature of the sun is T = %3.0f K ' % (T)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The black body temperature of the sun is T = 5987 K \n"
]
}
],
"prompt_number": 14
}
],
"metadata": {}
}
]
}