Thermal Radiation – Chapter 12 Study Guide & Concept Breakdown | Heat & Mass Transfer 6th Edition Çengel & Ghajar (SI Units) | 2025/2026

12-1




Solutions Manual for
Heat and Mass Transfer: Fundamentals & Applications
6th Edition in SI Units
Yunus A. Çengel, Afshin J. Ghajar
McGraw-Hill, 2020




Chapter 12
FUNDAMENTALS OF THERMAL RADIATION




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, 12-2
Electromagnetic and Thermal Radiation

12-1C Electromagnetic waves are characterized by their frequency v and wavelength  . These two properties in a medium
are related by   c / v where c is the speed of light in that medium.



12-2C Thermal radiation is the radiation emitted as a result of vibrational and rotational motions of molecules, atoms and
electrons of a substance, and it extends from about 0.1 to 100 m in wavelength. Unlike the other forms of electromagnetic
radiation, thermal radiation is emitted by bodies because of their temperature.



12-3C Microwaves in the range of 10 2 to 105 m are very suitable for use in cooking as they are reflected by metals,
transmitted by glass and plastics and absorbed by food (especially water) molecules. Thus the electric energy converted to
radiation in a microwave oven eventually becomes part of the internal energy of the food with no conduction and convection
thermal resistances involved. In conventional cooking, on the other hand, conduction and convection thermal resistances slow
down the heat transfer, and thus the heating process.



12-4C Visible light is a kind of electromagnetic wave whose wavelength is between 0.40 and 0.76 m. It differs from the
other forms of electromagnetic radiation in that it triggers the sensation of seeing in the human eye.



12-5C Light (or visible) radiation consists of narrow bands of colors from violet to red. The color of a surface depends on its
ability to reflect certain wavelength. For example, a surface that reflects radiation in the wavelength range 0.63-0.76 m
while absorbing the rest appears red to the eye. A surface that reflects all the light appears white while a surface that absorbs
the entire light incident on it appears black. The color of a surface at room temperature is not related to the radiation it emits.



12-6C Because the snow reflects almost all of the visible and ultraviolet radiation, and the skin is exposed to radiation both
from the sun and from the snow.



12-7C Infrared radiation lies between 0.76 and 100 m whereas ultraviolet radiation lies between the wavelengths 0.01 and
0.40 m. The human body does not emit any radiation in the ultraviolet region since bodies at room temperature emit
radiation in the infrared region only.



12-8C Radiation in opaque solids is considered surface phenomena since only radiation emitted by the molecules in a very
thin layer of a body at the surface can escape the solid.




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, 12-3
8
12-9 A cordless telephone operates at a frequency of 8.510 Hz. The wavelength of these telephone waves is to be
determined.
Analysis The wavelength of the telephone waves is
c 2.998108 m/s
   0.353 m  353 mm
v 8.5 108 Hz(1/s)




12-10 Electricity is generated and transmitted in power lines at a frequency of 50 Hz. The wavelength of the electromagnetic
waves is to be determined.
Analysis The wavelength of the electromagnetic waves is
c 2.998  108 m/s Power lines
   5.996  10 6 m
v 50 Hz(1/s)




12-11 The speeds of light in air, water, and glass are to be determined.
Analysis The speeds of light in air, water and glass are
c 0 3.0 108 m/s
Air: c   3.0  10 8 m/s
n 1
c 0 3.0 108 m/s
Water: c   2.26  10 8 m/s
n 1.33
c 0 3.0 108 m/s
Glass: c   2.0  10 8 m/s
n 1.5




12-12 A radio station is broadcasting radiowaves at a wavelength of 150 m. The frequency of these waves is to be
determined.
Analysis The frequency of the waves is determined from
c c 2.998  108 m/s
 
 v    2.00  10 6 Hz
v  150 m




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you are a student using this Manual, you are using it without permission.

, 12-4
9
12-13 A microwave oven operates at a frequency of 2.210 Hz. The wavelength of these microwaves and the energy of each
microwave are to be determined.
Analysis The wavelength of these microwaves is
c 2.998 108 m/s
   0.136 m  136 mm
v 2.2  10 9 Hz(1/s)
Microwave
Then the energy of each microwave becomes oven
hc (6.62510 34 Js)(2.998108 m/s)
e  hv    1.46  10 24 J
 0.136 m




12-14 The photon energies of a radio wave and a γ-ray, and the photon energy ratio of the γ-ray to the radio wave are to be
determined.
Assumptions 1 The medium is air and index of refraction is unity.
Properties The speed of light in a medium with a refraction index of 1 is c = 2.9979 × 108 m/s. The Planck’s constant is h =
6.626069 × 10−34 J∙s.
Analysis The photon energy of an electromagnetic wave is
hc
e

The photon energy of the radio wave is
hc (6.626069 10 34 J  s)(2.9979  108 m/s)
e radio    1.986  10 26 J
 10 7 μm
The photon energy of the γ-ray is
hc (6.626069 10 34 J  s)(2.9979  108 m/s)
e -ray    1.986  10 12 J
 10 7
μm
The photon energy ratio of the γ-ray to the radio wave is
e -ray  radio 10 7 μm
  7  1014
e radio  -ray 10 μm
Discussion There is 1014 times more energy in a γ-ray wave than a radio wave.




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you are a student using this Manual, you are using it without permission.