In the thermos shown in Fig. P8.42, 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 q1is by radiation only (since the space is evacuated). Heat transfer between the middle layer and outside shell q2is by convection in a small space. Heat transfer from the outside shell to the air q3 is by natural convection. The heat flux from each region of the thermos must be equal-that is,

q₁= q₂= q_3. Find the temperatures T₁and T₂at steady state. T₀is 450C and T₃= 25C.

q₁= 10-9[(T₀ + 273)4- (T₁+ 273)4]

q₂= 4(T₁- T₂)

q₃= 1.3(T₂- T₃)^4/3