Two parallel plates of infinite extent perpendicular to the page are situated relative to each other as shown in the figure. The upper plate is at 300°C and the lower plate is at 100°C. Determine the net rate of radiation heat transfer from the upper and lower plate assuming the environment is at a temperature below 100°C. Assume that both the lower surface of the upper plate and the upper surface of the lower plate are black.
GIVEN
• The planet Mars revolving around the sun
• Diameter of Mars (Dm) = 6600 km
• Distance from the sun (Rms) = 225 × 106 km
• Diameter of the sun (Ds) =1,384,000 km FIND
(a) The equilibrium temperature of Mars (Tm)
(b) Tm assuming that the albedo of Mars = 0.15
ASSUMPTIONS
• Both Mars and the sun act as blackbodies
• The sun has an equivalent blackbody temperature (Ts) of 5600 K
PROPERTIES AND CONSTANTS
The Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)
The energy from the sun that is incident on Mars can be calculated by integrating
where ?1 and ? 2 are the angles shown in Figure 11.28. For this case, since Dm << Rms and Ds << Rms, the following approximations can be used cos ? 1 and cos ? 2 = 1, r = Rms.
Also Eb1 = ? Ts4
Case (a)
If Mars behaves as a blackbody, it will absorb all the sun’s energy incident on it. For equilibrium, the energy radiated by Mars must equal the incident solar energy
Solving for the temperature of Mars
Case (b)
For an albedo of 0.15, Mars absorbs only 85% of the incident solar radiation, therefore
You might also like to view...
Comets with orbits that take them through the inner solar system shed sand- to pebble-size particles that then follow the comet around its orbit. How do these particles affect Earth?
A) They are the particles that produce meteor showers. B) They are the particles that produce the lights of auroras. C) They have been implicated in mass extinctions, including the extinction of the dinosaurs. D) On rare occasions, they can blanket our entire atmosphere with dust.
Why Bode's law was never considered a law of physics?
a. Because it is not testable. b. Because it is not consistent. c. Because it turned out not to be true. d. Because it had no scientific basis. e. Because it wasn't invented by Bode.
How do we think the "hot Jupiters" around other stars were formed?
A) They formed as jovian planets close to the star in the same orbits that they are seen today. B) They formed as dense, rocky planets close to the star in the same orbits that they are seen today. C) They formed as jovian planets beyond the frost line and then migrated inward. D) Many planets were formed around the star but coalesced into a single planet close in. E) They spun off from the young star when it was rapidly rotating.
In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much heat is exchanged with the gas during this process?
A) 0.00 J B) 25 J C) 50 J D) -25 J E) -50 J