Question

Consider a sealed 20 -cm-high electronic box whose base dimensions are 40 cm×40 cm placed in a vacuum chamber. The emissivity of the outer surface of the box is 0.95 . If the 3 electronic components in the box dissipate a total of 100 W of power and the outer surface temperature of the box is not to exceed 55 ∘C, determine the temperature at which the surrounding surfaces must be kept if this box is to be cooled by radiation alone. Assume the heat transfer from the bottom surface of the box to the stand to be negligible.

Answer 1

To determine the temperature at which the surrounding surfaces must be kept for the box to be cooled by radiation alone, we can use the Stefan-Boltzmann law.

Step-by-step explanation:

To determine the temperature at which the surrounding surfaces must be kept for the box to be cooled by radiation alone, we can use the Stefan-Boltzmann law. According to the law, the rate of heat transfer by radiation is given by:

Q = Aεσ(T4 - T'4)

where Q is the rate of heat transfer, A is the surface area of the box, ε is the emissivity of the box, σ is the Stefan-Boltzmann constant, T is the temperature of the outer surface of the box (55°C), and T' is the temperature of the surrounding surfaces that we need to find.

Simplifying the equation and plugging in the given values:

100 = (40*40*6)(0.95)(5.67x10^-8)(55^4 - T'^4)

Using this equation, we can calculate the temperature T' at which the surrounding surfaces must be kept in order to cool the box by radiation alone.