/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 Consider a hot boiled egg in a s... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Conduction
Conduction is one of the primary ways heat transfers from one part of a material to another part or to a different material that is in direct contact. Imagine heat as a series of tiny particle exchanges, where higher energy particles bump into lower energy particles, transferring energy. This occurs most commonly in solids but can happen in any material where particles can collide directly.

In the context of our boiled egg, conduction occurs through the egg's shell to the air surrounding it. Since the spacecraft is filled with air at atmospheric pressure, this mode of heat transfer will be consistent whether the egg is on Earth or in outer space. The particles in the air around the egg will continue to collide with the particles in the eggshell, allowing heat to conduct away from the egg at the same rate in both locations.
  • Conduction needs a medium through which heat can be transferred via direct contact.
  • In our example, conduction happens similarly in the spacecraft and on the ground as long as air is present.
Convection
Convection is a fascinating form of heat transfer that involves the movement of fluids, which can be either liquids or gases. This movement occurs due to changes in temperature causing variations in density, thereby creating currents of moving fluid.

Picture this: On Earth, a hot boiled egg warms the air around it. This warmer, less dense air rises and is replaced by cooler air, which in turn is warmed by the egg. This cycle induces airflow, effectively transferring heat away from the surface of the egg.

However, in space, this process is significantly disrupted due to reduced gravity. Without gravity, this buoyancy-driven flow doesn’t happen as efficiently. Less movement of air means slower heat exchange through convection, making this process less effective in space compared to Earth's environment.
  • Convection relies on fluid movement, driven by temperature differences.
  • Gravity plays a critical role in facilitating convection.
  • In space, reduced gravity limits convection effectiveness.
Radiation
Radiation is a unique form of heat transfer because it does not require any medium to move through. Instead, heat is transferred through electromagnetic waves, typically in the infrared spectrum. Imagine standing in sunlight and feeling the warmth on your skin; this warmth is delivered via radiation.

For our boiled egg, radiation is always working to emit heat energy into the environment, whether on Earth or in space. Yet, in space, where the ambient temperature is exceptionally lower than on Earth, the contrast in temperature between the hot egg and its cold surrounding causes the egg to radiate more heat energy.

This means that the egg can potentially cool faster in space through radiation, as the greater the temperature difference, the more intense the radiative heat loss. Unlike convection, radiation doesn't rely on gravity or direct contact, making it a potent mode of heat transfer in diverse environments, including the vacuum of space.
  • Radiation requires no medium, unlike conduction and convection.
  • Temperature differences affect the rate of radiation.
  • In space, higher radiation effectiveness aids faster cooling.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Under what conditions does natural convection enhance forced convection, and under what conditions does it hurt forced convection?

A solar collector consists of a horizontal aluminum tube of outer diameter \(5 \mathrm{~cm}\) enclosed in a concentric thin glass tube of \(7 \mathrm{~cm}\) diameter. Water is heated as it flows through the aluminum tube, and the annular space between the aluminum and glass tubes is filled with air at \(1 \mathrm{~atm}\) pressure. The pump circulating the water fails during a clear day, and the water temperature in the tube starts rising. The aluminum tube absorbs solar radiation at a rate of \(20 \mathrm{~W}\) per meter length, and the temperature of the ambient air outside is \(30^{\circ} \mathrm{C}\). Approximating the surfaces of the tube and the glass cover as being black (emissivity \(\varepsilon=1\) ) in radiation calculations and taking the effective sky temperature to be \(20^{\circ} \mathrm{C}\), determine the temperature of the aluminum tube when equilibrium is established (i.e., when the net heat loss from the tube by convection and radiation equals the amount of solar energy absorbed by the tube). For evaluation of air properties at \(1 \mathrm{~atm}\) pressure, assume \(33^{\circ} \mathrm{C}\) for the surface temperature of the glass cover and \(45^{\circ} \mathrm{C}\) for the aluminum tube temperature. Are these good assumptions?

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?

A 4-m-long section of a 5-cm-diameter horizontal pipe in which a refrigerant flows passes through a room at \(20^{\circ} \mathrm{C}\). The pipe is not well insulated and the outer surface temperature of the pipe is observed to be \(-10^{\circ} \mathrm{C}\). The emissivity of the pipe surface is \(0.85\), and the surrounding surfaces are at \(15^{\circ} \mathrm{C}\). The fraction of heat transferred to the pipe by radiation is \(\begin{array}{lllll}\text { (a) } 0.24 & \text { (b) } 0.30 & \text { (c) } 0.37 & \text { (d) } 0.48 & \text { (e) } 0.58\end{array}\) (For air, use \(k=0.02401 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=0.735, v=\) \(1.382 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\) )

A 0.5-m-long thin vertical copper plate is subjected to a uniform heat flux of \(1000 \mathrm{~W} / \mathrm{m}^{2}\) on one side, while the other side is exposed to air at \(5^{\circ} \mathrm{C}\). Determine the plate midpoint temperature for \((a)\) a highly polished surface and \((b)\) a black oxidized surface. Hint: The plate midpoint temperature \(\left(T_{L / 2}\right)\) has to be found iteratively. Begin the calculations by using a film temperature of \(30^{\circ} \mathrm{C}\).

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.