| The electromagnetic power emitted by a surface is very sensitive to the temperature of the surface. In fact it depends upon the temperature to the fourth power!
The electromagnetic radiative power emitted by a surface can be easily determined
using the Stefan-Boltzmann1,2 equation.
The constant 5.70 x 10-8 J m-2 s-1 K-4 is called the Stefan-Boltzmann constant 1 Ludwig Boltzmann (1844-1906)
|
 |
1. a) Using the graph to the left, determine the radiative flux emitted by a surface of one square metre whose temperature is 310K (body temperature). About 550 W/m2 b) The total surface area of an adult human is about 2m2. How much energy is radiated from the human body? 1100 W/m2 2. a) Using the graph to the left determine the radiative flux emitted by a surface of one square metre whose temperature is 290K ( environmental room temperature). |
| 3. Based on your results in questions (1) and (2), what is the
net radiative heat loss from the human body?
300 W/m2. This is quite close to the actual value for a human whose entire body is at 310K (37oC) in an environment at 290K (17oC); generally the temperature of the skin and limbs is slightly lower. Also, clothing slightly reduces radiative losses. 4. Using the graph "Wien's Displacement Law" below, determine
the wavelength of maximum intensity at which a human body radiates electromagnetic energy. |
 |
5. a) Using the graph to the left, determine the radiative flux of a surface of 1m2 whose temperature is 6000K. About 7.3x107 W/m2 b) Given that 6000K is approximately the surface temperature of the sun, and the sun's radius is 6.96x108m, calculate the total flux radiated by the sun (called the solar luminosity) 7.4x107 W/m2 x surface area of the sun or 4.4 x1026 watts. About 20% too high, but quite good for this approximation. 6. Using the graph "Wien's Displacement Law" below, determine
the wavelength of maximum intensity at which the sun radiates electromagnetic energy.
|
|
For thermal electromagnetic radiation, that is radiation from objects, due to their temperature,
the wavelength of maximum intensity of the electromagnetic radiation depends upon an object's temperature according a law discovered by Wilhelm Wien (1864-1928).
Wilhelm Wien was awarded the Noble prize in physics in 1911 for his work in optics and radiation.
His famous law, now known by physicists as Wien's Displacement Law is written as
 where the wavelength is in metres (m) and the temperature in Kelvins(K). |
Transparency Master |
For those inexperienced with log/log plots, two values, 2x10-7 and 3x10-7 are labelled to assist you.
7. Determine the characteristic electromagnetic emission (i.e. radio, infrared, microwave, etc.) of objects whose temperatures are 1000K, 10,000K and
80,000K respectively. Use the graph to the left to find the wavelength and the
electromagnetic spectrum chart to characterize the radiation.
8. The spectrum of a star is taken. It is found that its maximum brightness occurs at exactly 1x10-7m. What is its temperature? |
| 9. a) Using Wien's Displacement Law calculate the temperature (in K) of a star whose
maximum wavelength is 3.6x10-9m (i.e. an x-ray star).
8.0x105K b) Using the Stefan-Boltzmann law, calculate the radiative flux. 2.4x1016W/m2 |
10. a) Using Wien's Displacement Law calculate the temperature (in K) of a star whose maximum wavelength is 2.2x10-6m (i.e. an infrared star). 1.3x103K b) Using the Stefan-Boltzmann law, calculate the radiative flux. 1.7x105W/m2 |
ASSESSMENTThe chart that follows identifies four levels of achievement for assessing students' communication of information and ideas. Levels 1 and 2 describe performance that is approaching the standard for the grade; level 3 describes the standard for the grade; and level 4 describes performance that is above the standard. In numerical terms, all four levels are at passing level for the grade. Level 1 corresponds to a mark of 50%-59%; level 2, 60%-69%; level 3, 70%-79%; and level 4, 80%-100% . Student performance that is not approaching or is significantly below the standard would receive a failing grade. |
|||
|
Understanding of Basic Concepts
The student: |
|||
|
Level 1
|
Level 2
|
Level 3
|
Level 4
|
| demonstrates limited understanding of the relationship between electromagnetic radiative power emitted by a surface and the temperature of the surface by solving problems related to radiative flux with limited accuracy | demonstrates some understanding of the relationship between electromagnetic radiative power emitted by a surface and the temperature of the surface by solving problems related to radiative flux with some accuracy | demonstrates considerable understanding of the relationship between electromagnetic radiative power emitted by a surface and the temperature of the surface by solving problems related to radiative flux with general accuracy | demonstrates thorough understanding of the relationship between electromagnetic radiative power emitted by a surface and the temperature of the surface by solving problems related to radiative flux with a high degree of accuracy |
|
Inquiry
The student: |
|||
|
Level 1
|
Level 2
|
Level 3
|
Level 4
|
| interprets and uses graphs relating to electromagnetic radiative power emitted by a surface with limited competence making major errors/omissions | interprets and uses graphs relating to electromagnetic radiative power emitted by a surface with moderate competence making several minor errors/omissions | interprets and uses graphs relating to electromagnetic radiative power emitted by a surface with considerable competence making few minor errors/omissions | interprets and uses graphs relating to electromagnetic radiative power emitted by a surface with a high degree of competence making practically no errors/omissions |
|
Communication of Information and Ideas
The student: |
|||
|
Level 1
|
Level 2
|
Level 3
|
Level 4
|
| uses scientific terminology, symbols, conventions, and SI units with limited accuracy and effectiveness | uses scientific terminology, symbols, conventions, and SI units with some accuracy and effectiveness | uses scientific terminology, symbols, conventions, and SI units with considerable accuracy and effectiveness | uses scientific terminology, symbols, conventions, and SI units with a high degree of accuracy and effectiveness |