At our distance from the Sun, the intensity of solar radiation is 1 370 W/m 2 . The temperature of the Earth is affected by the greenhouse effect of the atmosphere. This phenomenon describes the effect of absorption of infrared light emitted by the surface so as to make the surface temperature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius r with no atmosphere at the same distance from the Sun as the Earth. Assume its emissivity is the same for all kinds of electromagnetic waves and its temperature is uniform over its surface. (a) Explain why the projected area over which it absorbs sunlight is πr 2 and the surface area over which it radiates is 4 πr 2 . (b) Compute its steady-state temperature. Is it chilly?
At our distance from the Sun, the intensity of solar radiation is 1 370 W/m 2 . The temperature of the Earth is affected by the greenhouse effect of the atmosphere. This phenomenon describes the effect of absorption of infrared light emitted by the surface so as to make the surface temperature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius r with no atmosphere at the same distance from the Sun as the Earth. Assume its emissivity is the same for all kinds of electromagnetic waves and its temperature is uniform over its surface. (a) Explain why the projected area over which it absorbs sunlight is πr 2 and the surface area over which it radiates is 4 πr 2 . (b) Compute its steady-state temperature. Is it chilly?
Solution Summary: The author explains that the projected area over which sunlight absorbs is pir2 and the surface area — the spherical object radiates infrared light outward in
At our distance from the Sun, the intensity of solar radiation is 1 370 W/m2. The temperature of the Earth is affected by the greenhouse effect of the atmosphere. This phenomenon describes the effect of absorption of infrared light emitted by the surface so as to make the surface temperature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius r with no atmosphere at the same distance from the Sun as the Earth. Assume its emissivity is the same for all kinds of electromagnetic waves and its temperature is uniform over its surface. (a) Explain why the projected area over which it absorbs sunlight is πr2 and the surface area over which it radiates is 4πr2. (b) Compute its steady-state temperature. Is it chilly?
Interaction between an electric field and a magnetic field.
The outer surface of a spacecraft in space has an emissivity of 0.8 and a solar absorptivity of 0.3. If solar radiation is incident on the spacecraft at a rate of 950 W/m2, determine the surface temperature of the spacecraft when the radiation emitted equals the solar energy absorbed.
Betelgeuse, a bright red star in the constellation Orion, has a luminosity that is 100,000 times that of the Sun. However, the surface temperature of Betelgeuse is only 3000 K. Assuming that the emissivity of stars is 1, What is the radius of Betelgeuse?
The thermal conductivities of human tissues vary greatly. Fat and skin have conductivities of about 0.20 W/m · K and 0.020 W/m · K respectively, while other tissues inside the body have conductivities of about 0.50 W/m · K. Assume that between the core region of the body and the skin surface lies a skin layer of 1.0 mm, fat layer of 0.50 cm, and 3.2 cm of other tissues.
(a) Find the R-factor for each of these layers, and the equivalent R-factor for all layers taken together, retaining two digits.
Rskin
m2 · K/W
Rfat
m2 · K/W
Rtissue
m2 · K/W
R
m2 · K/W
(b) Find the rate of energy loss when the core temperature is 37°C and the exterior temperature is 0°C. Assume that both a protective layer of clothing and an insulating layer of unmoving air are absent, and a body area of 2.0 m2. W
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