# [50 points] Consider two concentric spherical shells. The inner shell has a constant temperature of T;...

###### Question:

[50 points] Consider two concentric spherical shells. The inner shell has a constant temperature of T; = 100 °C. The outer shell has a constant temperature of T, = 25 °C. Let both shells act as perfect black bodies. Let the outer shell has a diameter D. = 1 m. Note: Due to physical constraints, it is always the case that: fi-jA; = fj-iAj, where fi- is the fraction of radiation from surface i that strikes surface j, and Aį is the area of surface i. a. [10 Points) Find a formula for the net heat flow between the shells in the case where they are separated by perfect vacuum. No need to plug in numbers. b. [10 Points] Find a formula for the net heat flow between the shells in the case where they are separated from one another by an opaque layer of polystyrene foam. No need to plug in numbers. W c. [10 Points] The polystyrene foam has a thermal conductivity kg = 0.035 For m. what inner shell diameter(s), Di, do the situations in (a) and (b) yield the same heat flow between the shells? d. [15 Points] Over what range of inner diameters is heat transfer faster for conduction? Over what range of inner diameters is heat transfer faster for radiation? Show your work. e. [5 Points] If you were designing a thermos, which insulator would be better: vacuum or polystyrene foam? Why?

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