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Chapter 3: Problem 1

Consider two separate objects of unequal temperature. What would you do with them and what would have to happen thereafter to enable them to reach the same common temperature? Use this idea to explain why the electromagnetic radiation enclosed in a cavity has a temperature that is the same as that of the cavity walls.

Short Answer

Expert verified
The objects would exchange heat until they reach thermal equilibrium with the same temperature. This logic is applied to explain that the radiation enclosed in a cavity is at the same temperature as the cavity walls because they both are in thermal equilibrium, exchanging energy until they reach the same temperature. A perfect black body absorbs and re-emits all incident radiation, leading to the cavity walls having the same temperature as the enclosed radiation.

Step by step solution

01

Understanding heat transfer

Heat flows from an area of higher temperature (hot object) towards an area of lower temperature (cold object). The hot object will lose energy, and the cold object will gain energy. The process continues until both objects reach thermal equilibrium, sharing a common temperature.
02

Applying the concept to enclosed radiation

With electromagnetic radiation enclosed in a cavity, a similar process happens. The walls of the cavity and the radiation inside it exchange energy until they reach an equilibrium state. This is because, according to the principles of radiation exchange, the walls absorb and emit energy at the same rate.
03

Connection with black-body radiation

In a perfect black body, all incident radiation is absorbed and, in thermal equilibrium, re-emitted with the same amount. As the cavity walls approach a perfect black body, their temperature will be equivalent to the temperature of the radiation within them due to this exchange of energy.

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Key Concepts

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

Heat Transfer
Heat transfer is the process of energy moving from a hotter object to a cooler one, guided by the second law of thermodynamics. When two objects of different temperatures come in contact, heat energy is transferred:
  • The hot object loses energy as heat is transferred away.
  • The cool object gains this energy, increasing its temperature.

Footsteps to thermal equilibrium can be seen where their temperature will stabilize at a shared value. An example of this is placing a hot cup on a cold table, where eventually both the cup and the table surface will reach the same temperature. No more heat flows once thermal equilibrium is achieved, and this balance depends on the properties of the materials involved and the surrounding conditions.
Black-Body Radiation
Black-body radiation is the phenomenon where an idealized object, referred to as a black body, absorbs all incoming radiation and re-emits energy perfectly. This concept is essential when examining thermal equilibrium:
  • A perfect black body absorbs all wavelengths of electromagnetic radiation.
  • It emits radiation solely based on its temperature and not on its surface properties.

When discussing cavities with radiation, the concept of a black body provides insights into how the walls of the cavity absorb and emit radiation equally. By achieving this balance of absorption and emission at equal rates, the cavity walls can reach thermal equilibrium with the radiative energy inside, regardless of the initial state of temperature disparity.
Electromagnetic Radiation
Electromagnetic radiation is energy emitted in the form of waves, covering a spectrum that includes visible light, infrared, and other common types. When discussing objects and cavities:
  • The radiation can transfer energy between the walls of the cavity and the enclosed space.
  • This energy exchange is a form of heat transfer occurring through radiation.

Such radiation processes explain how even in a vacuum or without direct contact, energy can still move from one object to another, achieving temperature uniformity. As the radiation bounces within the cavity, it interacts with the walls, facilitating the shifts of energy necessary to eventually balance temperature through these electromagnetic exchanges.

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Most popular questions from this chapter

In the Compton effect, we choose the electron to be at the origin and the initial photon's direction of motion to be in the \(+x\) direction. (a) We may also choose the xy-plane so that it contains the velocities of the outgoing electron and photon. Why? (b) The incoming photon's wavelength \(\lambda\) is assumed to be known. The unknowns after the collision are the outgoing photon's wavelength and direction, \(\Lambda^{\prime}\) and \(\theta,\) and the speed and direction of the electron, \(u_{e}\) and \(\phi .\) With only three equations \(-t w_{0}\) components of momentum conservation and one of energy - we can't find all four. Equation \((3-8)\) gives \(\lambda^{\prime}\) in terms of \(\theta .\) Our lack of knowledge of \(\theta\) after the collision (without an experiment) is directly related to a lack of knowledge of something before the collision. What is it? (lmagine the two objects are hard spheres.) (c) Is it reasonable to suppose that we could know this? Explain.

At what wavelength does the human body emit the maximum electromagnetic radiation? Use Wien's law from Exercise 14 and assume a skin temperature of \(70^{\circ} \mathrm{F}\).

An object moving to the right at \(0.8 c\) issouck head-on by a photon of wavelength \(\lambda\) moving to the left. The An object moving to the right at \(0.8 c\) is souck head-on by a photon of wavelength \(\lambda\) moving to the left. The object absorbs the photon (i.e., the photon disappears) and is afterward moving to the right at \(0.6 c\). (a) Determine the ratio of the object's mass after the collision to its mass before the collision. (Note: The object is not a "fundamental particle." and its mass is therefore subject lo change.) (b) Does kinetic energy inc rease or decrease?

You are conducting a photoelectric effect experiment by shining light of \(500 \mathrm{nm}\) wavelength a a piece of metal and determining the stopping potential. If, unbeknownst to you, your 500 nm light source actually contained a small amount of ultraviolet light, would it throw off your results by a small amount or by quite a bit? Explain.

An electron moving to the lefi at \(0.8 c\) collides with an incoming photon moving to the right. Afuer the collision, the elactron is moving to the right at \(0.6 c\) and an outgoing photon moves to the lefi. What was the wavelength of the incoming photon?
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