Equilibrium Temperature of a Spherical Black Body Satellite

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The discussion centers on calculating the equilibrium temperature of a spherical black body satellite with a radius of 0.3 m and electronics generating 3900 Watts. The initial approach used the Stefan-Boltzmann law but yielded an incorrect result. A key insight was provided, emphasizing the need to calculate power per unit area by dividing the total power by the satellite's surface area. This adjustment allowed for the correct application of the formula, leading to a successful resolution of the problem. The conversation highlights the importance of understanding the relationship between total power and surface area in thermal calculations.
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b) Real satellites are complicated objects (see photo above). To simplify the problem, suppose the satellite is a spherical black body with a 0.3 m radius. Suppose the satellite's electronics generated 3900 Watts. What would be the equilibrium temperature, Teq, of the satellite?

Okeedoke, so I started with the equation T=oT^4. So...

3900 J=(5.67x10^-8 W/m^2K^4)T^4

T=(3900 J/(5.67x10^-8 W/m^2 K^4))^(1/4)

Which gives me an incorrect answer... any hints in the right direction?
 
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CaptainJames said:
b) Real satellites are complicated objects (see photo above). To simplify the problem, suppose the satellite is a spherical black body with a 0.3 m radius. Suppose the satellite's electronics generated 3900 Watts. What would be the equilibrium temperature, Teq, of the satellite?

Okeedoke, so I started with the equation T=oT^4. So...

3900 J=(5.67x10^-8 W/m^2K^4)T^4

T=(3900 J/(5.67x10^-8 W/m^2 K^4))^(1/4)

Which gives me an incorrect answer... any hints in the right direction?
You are given the total power but you need the power/unit area. On the Left side, divide the power by the surface area and equate that to the right side.

AM
 
Ah! Thanks a bunch, I got it.
 

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