| 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.
E(watts/m2) = 5.70 x 10-8 T4 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) |
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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). 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?
4. Using the graph "Wien's Displacement Law1" below, determine the wavelength of maximum intensity at which a human body radiates electromagnetic energy. |
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5. a) Using the graph to the left, determine the radiative flux of a surface of 1m2 whose temperature is 6000K. 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) 6. Using the graph "Wien's Displacement Law" below, determine the wavelength of maximum intensity at which the sun radiates electromagnetic energy. |
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For thermal electromagnetic radiation, that is radiation from objects due to their temperature,
the wavelength of maximum intensity is given by
 where the wavelength is in metres (m) and the temperature is in Kelvins(K). 1This law, discovered by Wilhelm Wien(1864-1928) showed that the higher the temperature of an object, the shorter the wavelength of its most intense radiation. Wilhelm Wien was awarded the Noble prize in physics in 1911 for his work in optics and radiation. |
Transparency Master |
For those inexperienced with log/log plots, two values, 2x10-7 and 3x10-7 are labeled 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).
b) Using the Stefan-Boltzmann law, calculate the radiative flux. |
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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). b) Using the Stefan-Boltzmann law, calculate the radiative flux. |