Question

Sputnik 1, the first satellite launched into space by the Russians in 1957, is a 2-shel aluminum alloy (2024-T6) sphere. The highly polished outer shell (seeing deep space) is 585 mm in diameter, and has thickness of 1 mm (ID 583 mm). The inside shell is 2 mm thick. There is a contact resistance between the two shells of value Ric 100 m2 K/W Inside the shell, there is a radio unit that is uniformly dissipating thermal energy of Ignore the effects of the antennas. Hint: You can use a radiation heat transfer coefficient hr = εσ Qadio = 1 W Inner Shell Tsur = 0 K

Answer 1

Given Inner shell, inner dia = 583 - 2 times 2 D_i = 579 mm Now, the contact resistance, R��_t, c = 100 m^2 k/w and Q_radio = 1 w we know that, Q_radio = A_c times 6 times epsilon times (T^4_shell - T^4_sur) = A_c times h_r times T_shell (Because 6 epsilon T^3_shell = hr T_sur = 0) Now we know, shell resistance, R��_t, c = 1/A_c hr Therefore Q_radio = T_shell/R��_t, c rightarrow T_shell/100 = 1 Therefore T_shel = 100 k Ans