Ask Question
21 July, 18:59

A computer chip inside an orbiting satellite heats up during operation. Since there is no air in the satellite the only cooling will be by radiation. The chip is 1.50 cm wide by 2.50 cm long with a negligible thickness; it has an emissivity of 0.600; and dissipates 0.420 Watts during usage (assume that the chip radiates heat evenly from both the top and bottom surfaces). Assuming the inside of the satellite is held at a constant temperature of - 100°C; calculate the surface temperature of the chip in °C

+1
Answers (1)
  1. 21 July, 19:53
    0
    89.967°C

    Explanation:

    According to Stefan-Boltzmann's law,

    E = μΩA (Ts⁴ - Ti⁴)

    Where,

    Emissitivity, μ = 0.6,

    Stefan-boltzmann's constant, Ω = 5.67 x 10^-8 W/m²K⁴

    Surface area, A = 1.5 x 2.5 x 10-⁴ = 3.75 x 10-⁴ m²

    Satellite temperature, Ti = - 100°C = 173K

    Power dissipated, E = 0.42 W

    Since we're evaluating the temperature for both the top and bottom surfaces,

    E = 2 x μΩA (Ts⁴ - Ti⁴)

    0.42 = 2 x 0.6 x 3.75 x 10-⁴ x 5.67 x 10^-8 x (Ts⁴ - 173⁴)

    0.0165 x 10^-12 = Ts⁴ - 8.957 x 10^8

    Ts⁴ = 173.57 x 10^8

    Taking 4th root of both sides,

    Ts = 362.97 K

    Ts = (362.97 - 273) °C

    Ts = 89.967°C
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A computer chip inside an orbiting satellite heats up during operation. Since there is no air in the satellite the only cooling will be by ...” in 📘 Engineering if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers