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Chapter 13: Problem 76

The reflectance and emittance of a perfectly black body are respectively (a) 0,1 (b) 1,0 (c) \(0.5,0.5\) (d) 0,0

Short Answer

Expert verified
Option (a): Reflectance = 0, Emittance = 1.

Step by step solution

01

Understanding Black Body

A perfectly black body is an idealized physical body that absorbs all incident electromagnetic radiation. A perfect black body's reflectance is 0 because it reflects no radiation.
02

Emittance of Black Body

A perfectly black body also emits radiation at its thermal equilibrium. By definition, the emittance of a perfect black body is 1, since it is the most efficient emitter.
03

Analyzing Options

Let's evaluate the options: - **Option (a):** Reflectance = 0, Emittance = 1 (matches our criteria) - **Option (b):** Reflectance = 1, Emittance = 0 (reflectance is incorrect for a black body) - **Option (c):** Reflectance = 0.5, Emittance = 0.5 (does not match criteria for either) - **Option (d):** Reflectance = 0, Emittance = 0 (emittance is incorrect for a black body)
04

Selecting Correct Answer

The correct answer is option (a), where the reflectance is 0 and the emittance is 1, aligning with the properties of a perfectly black body.

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Key Concepts

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

Reflectance
Reflectance is a measure of how much electromagnetic radiation is reflected by a surface when it encounters a material. Imagine a mirror, which would have high reflectance, reflecting much of the light that hits it. In contrast, a perfectly black body, which we discussed in the context of the exercise, reflects none of the incident light, hence has a reflectance of 0.

This concept is crucial in understanding how different materials interact with light and other forms of electromagnetic waves. A black body's zero reflectance means it absorbs all the incident radiation without reflecting any.

  • A perfect reflector (like a mirror) would have a reflectance of 1, meaning it reflects all incoming light.
  • Ordinary materials may have partial reflectance, where some light is absorbed and some is reflected.
Emittance
Emittance refers to the ability of a material to emit energy in the form of electromagnetic radiation. A perfectly black body is considered an ideal emitter, with an emittance rate of 1. This means it efficiently emits all of the absorbed energy.

Think of emittance as a body naturally radiating heat when it is in thermal equilibrium. If a material is a better emitter, it can effectively release the absorbed energy, maintaining its thermal balance.

  • High emittance means the material is very effective at emitting absorbed energy.
  • A perfectly black body at thermal equilibrium will emit the maximum possible radiation, making it an ideal model for studying thermal radiation.
Understanding emittance helps in determining how objects cool down by losing energy in the form of heat or light.
Electromagnetic Radiation
Electromagnetic radiation is a type of energy that travels through space at the speed of light. It includes a wide range of waves like visible light, infrared, ultraviolet, X-rays, and more.

The nature of electromagnetic radiation is characterized by its wavelength and frequency, determining its potential interactions with matter. For instance, visible light interacts in ways that can be seen, while other types of radiation might be absorbed or emitted without visible evidence.

  • Black bodies play a significant role in studying electromagnetic radiation as they ideally absorb and emit across this entire spectrum.
  • Understanding electromagnetic radiation is key to exploring how energy is transferred between systems, which is important for fields such as astronomy, climate science, and engineering.
Recognizing the relationship between black bodies and electromagnetic radiation helps illuminate how energy is conserved and transformed in various systems.

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Most popular questions from this chapter

When a bimetallic strip is heated, it (a) does not bend at all (b) gets twisted in the form of an helix (c) bend in the form of an arc with the more expandable metal outside (d) bends in the form of an arc with the more expandable metal inside

A liquid is filled in a container which is kept in a room whose temperature is \(20^{\circ} \mathrm{C}\). When temperature of liquid is \(80^{\circ} \mathrm{C}\), it emits heat at the rate of \(45 \mathrm{cals}^{-1}\), When temperature of liquid falls to \(40^{\circ} \mathrm{C}\), its rate of heat loss will be (a) \(15 \mathrm{cals}^{-1}\) (b) \(30 \mathrm{cals}^{-1}\) (c) \(45 \mathrm{cal} \mathrm{s}^{-1}\) (d) \(60 \mathrm{cal}^{-1}\)

A flask of volume \(10^{3} \mathrm{cc}\) is completely filled with mercury at \(0^{\circ} \mathrm{C}\). The coefficient of cubical expansion of mercury is \(1.80 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\) and that of glass is \(1.4 \times 10^{-6} \mathrm{C}^{-1}\). If the flask is now placed in boiling water at \(100^{\circ} \mathrm{C}\), how much mercury will overflow? (a) \(7 \mathrm{cc}\) (b) \(1.4 \mathrm{cc}\) (c) \(21 \mathrm{cc}\) (d) \(28 \mathrm{cc}\)

A cylinder of radius \(r\) and thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of linear radius \(r\) and outer radius \(2 r\), whose thermal conductivity is \(K_{2}\). There is no loss of heat across cylindrical surfaces, when the ends of the combined system are maintained at temperatures \(T_{1}\) and \(T_{2}\). The effective thermal conductivity of the system, in the steady state is (a) \(\frac{K_{1} K_{1}}{K_{1}+K_{2}}\) (b) \(K_{1}+K_{2}\) (c) \(\frac{K_{1}+3 K_{2}}{4}\) (d) \(\frac{3 K_{1}+K_{2}}{4}\)

The volume of a metal sphere increases by \(0.24 \%\) when its temperature is raised by \(40^{\circ} \mathrm{C}\). The coefficient of linear expansion of the metal is ... \({ }^{\circ} \mathrm{C}\). (a) \(2 \times 10^{-5} \mathrm{per}^{\circ} \mathrm{C}\) (b) \(6 \times 10^{-5}\) per \(^{\circ} \mathrm{C}\) (c) \(2.1 \times 10^{-5} \mathrm{per}^{\circ} \mathrm{C}\) (d) \(1.2 \times 10^{-5} \mathrm{per}^{\circ} \mathrm{C}\)
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