A spherical communications satellite 2-m in diameter is placed in orbit around the earth. The satellite generates 1000 W of internal power from a small nuclear generator. If the surface of the satellite has an emittance of 0.3 and is shaded from solar radiation by the earth, estimate the surface temperature. What is the temperature if the satellite with an absorptivity of 0.2 is in an orbit in which it is exposed to solar radiation? Assume the sun is a blackbody and irradiation striking the satellite is 1366 W/m2 and state your assumptions.
GIVEN
• Spherical satellite
• Diameter (D) = 2 m
• Heat generation = 1000 W
• Emittance (?) = 0.3
• Absorptivity of satellite (?)=0.2
• Solar irradiation(G)=1366 W/m2
FIND
• The surface temperature (Ts)
• Surface temperature of satellite
ASSUMPTIONS
• The satellite radiates to space which behaves as a blackbody enclosure at 0 K
• The system is in steady state
SKETCH
PROPERTIES AND CONSTANTS
The Stefan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)
the rate of the heat transfer from a gray body in a blackbody enclosure is
Considering single body radiation T2=0
Solving this for the surface temperature
For steady state the rate of heat transfer must equal the rate of internal generation, therefore the
surface temperature is
The amount of radiation absorbed by the satellite is given by
Total radiation from satellite under steady state is
the rate of the heat transfer from a gray body in a blackbody enclosure is
Considering single body radiation T2=0
Solving this for the surface temperature
For steady state the rate of heat transfer must equal the total amount of energy through generation and
irradiation, therefore the surface temperature is
You might also like to view...
The following formulas are supposed to describe the speed of a sphere sinking in a thick fluid. C is a unitless constant,
is the fluid’s density in kg/m3, A is the sphere’s cross-sectional area, m is its mass, and is the gravitational field strength in N/kg. Which could be right?
A. = CA g
B. = Cmg/ A
C. = (Cmg/ A)2
D. = (Cmg/ A)1/2
E. None of these can be correct.
A mixture of ethanol and gasoline is called
a. ethaline. b. gasanine. c. gasohol. d. gethanine.
Graphical Interpretation of Work: A force acts on an object, causing it to move parallel to the force. The graph in the figure shows this force as a function of the position of the object. How much work does the force do as the object moves from 0 m to 4 m?
A. 20 J B. 30 J C. 0 J D. 40 J E. 70 J
The intensity of sunlight falling on the earth is about 1.4 kW/m2 (before any gets absorbed by our atmosphere). At what rate does the sun emit light energy?
(The earth-sun distance = 1.5 × 108 km and the earth's radius = 6.4 × 103 km.) A) 4.0 × 1026 W B) 3.2 × 1022 W C) 7.2 × 1014 W D) 7.6 × 108 W