In the thermos shown in Figure

In the thermos shown in Figure, the innermost compartment is separated from the middle container by a vacuum. There is a final shell around the thermos. This final shell is separated from the middle layer by a thin layer of air. The outside of the final shell comes in contact with room air. Heat transfer from the inner compartment to the next layer q₁ is by radiation only (since the space is evacuated). Heat transfer between the middle layer and outside shell q₂ is by convection in a small space. Heat transfer from the outside shell to air q₃ is by natural convection. The heat flux from each region of the thermos must be equal-that is, q₁ = q₂ = q₃. Find the temperature T₁ and T₂ at steady state. T₀ is 450^oC and T₃ = 25^oC.

q₁ = 10^–9 [(T₀ + 273)⁴ – (T₁ + 273)⁴]

q₂ = 4(T₁ – T₂)

q₃ = 1.3(T₂ – T₃)^4/3

 

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