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Chapter 9: Problem 3

Consider a hot boiled egg in a spacecraft that is filled with air at atmospheric pressure and temperature at all times. Will the egg cool faster or slower when the spacecraft is in space instead of on the ground? Explain.

Short Answer

Expert verified
Answer: The hot boiled egg will cool faster in space compared to on Earth. This is mainly due to increased heat loss through radiation and the reduced effectiveness of convection in the microgravity environment of space.

Step by step solution

01

Identify the modes of heat transfer

There are three main modes of heat transfer that can contribute to the cooling of the egg: conduction, convection, and radiation.
02

Analyze conduction

Conduction is the transfer of heat within a material due to the movement of particles. In the case of the egg, heat will be conducted through the shell and into the surrounding air. As this process relies on the egg being in contact with a material (like air), its effectiveness would be the same inside a spacecraft in space and on Earth since the problem states that the spacecraft is filled with air at atmospheric pressure and temperature at all times.
03

Analyze convection

Convection is the transfer of heat through the movement of fluids (like gases or liquids) due to differences in temperature. In the Earth's atmosphere, the hot air surrounding the egg will rise while cooler air replaces it, creating a continuous flow that helps to cool the egg. However, in space, where gravity is significantly reduced or even absent, the buoyancy-driven mechanism that causes convection on Earth does not work, and this method of heat transfer becomes less effective.
04

Analyze radiation

Radiation is the transfer of heat through the emission of electromagnetic waves, such as infrared radiation. An object, like the hot egg, emits thermal radiation in all directions, which does not rely on the presence of any material, unlike conduction or convection. Therefore, radiation will be present both on Earth and in space. However, in space, the surrounding environment's temperature is much lower than on Earth, which means the temperature difference between the egg and its environment is higher, causing the egg to radiate more heat away.
05

Compare heat transfer modes in space and on Earth

Comparing the effectiveness of the three heat transfer modes, we can conclude the following: - Conduction is equally effective in space and on Earth. - Convection is less effective in space than on Earth due to the lack of gravity-driven buoyancy. - Radiation is more effective in space than on Earth due to the larger temperature difference between the egg and its environment.
06

Draw a conclusion

As radiation is more effective in space while conduction remains the same, and convection is less effective, we can conclude that the hot boiled egg will cool faster when the spacecraft is in space instead of on the ground. The faster cooling is primarily due to increased heat loss through radiation and the reduced effectiveness of convection in the microgravity environment of space.

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Most popular questions from this chapter

Show that the thermal resistance of a rectangular enclosure can be expressed as \(R=L_{c} /(A k \mathrm{Nu})\), where \(k\) is the thermal conductivity of the fluid in the enclosure.

A vertical \(1.5\)-m-high and \(3.0\)-m-wide enclosure consists of two surfaces separated by a \(0.4-\mathrm{m}\) air gap at atmospheric pressure. If the surface temperatures across the air gap are measured to be \(280 \mathrm{~K}\) and \(336 \mathrm{~K}\) and the surface emissivities to be \(0.15\) and \(0.90\), determine the fraction of heat transferred through the enclosure by radiation. Answer: \(0.30\)

When is natural convection negligible and when is it not negligible in forced convection heat transfer?

Consider a horizontal \(0.7\)-m-wide and \(0.85\)-m-long plate in a room at \(30^{\circ} \mathrm{C}\). Top side of the plate is insulated while the bottom side is maintained at \(0^{\circ} \mathrm{C}\). The rate of heat transfer from the room air to the plate by natural convection is (a) \(36.8 \mathrm{~W}\) (b) \(43.7 \mathrm{~W}\) (c) \(128.5 \mathrm{~W}\) (d) \(92.7 \mathrm{~W}\) (e) \(69.7 \mathrm{~W}\) (For air, use \(k=0.02476 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=0.7323, v=\) \(\left.1.470 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\right)\)

What does the effective conductivity of an enclosure represent? How is the ratio of the effective conductivity to thermal conductivity related to the Nusselt number?
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