A research satellite dissipates waste thermal energy through three identical radiator…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A research satellite dissipates waste thermal energy through three identical radiator panels, each of area A=1.2m2. The panels are thin aluminum sheets coated on the space-facing side with either a white paint (Panel W) or a black paint (Panel B). Both coatings have the same absorptivity for incoming solar radiation, but the white paint has emissivity εW=0.25 while the black paint has εB=0.85. In deep space, conduction and convection to an external medium are negligible; radiation is the sole mechanism for energy exchange.
During a particular orbital segment, each panel receives a uniform solar flux of S=650Wm−2 incident perpendicular to its surface. Internally, electric components conduct Pint=400W of power to each panel’s back side, which is thermally well-coupled to the front surface.
(a) Derive a symbolic expression for the steady-state temperature T of a panel in terms of A,S,Pint,ε, and fundamental constants. State all physical principles you apply.
(b) Using your expression, determine the steady-state temperatures of Panel W and Panel B. Assume the cosmic background temperature is effectively 0K.
(c) Mission planners argue that switching all radiators to the black coating will always decrease internal component temperatures. Evaluate this claim by considering how the orbital solar flux might vary, and discuss any trade-offs involved.
(d) Suppose a micrometeoroid damages 25% of the area of one black-coated panel, removing its paint and exposing bare aluminum with emissivity 0.05. Predict qualitatively how the panel’s steady-state temperature will change. Justify your prediction with comparative reasoning.