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Chapter 12: Problem 65

What is a graybody? How does it differ from a blackbody? What is a diffuse gray surface?

Short Answer

Expert verified
Answer: The main difference between a blackbody and a graybody is that a graybody emits and absorbs radiation less efficiently compared to a blackbody due to its lower emissivity value. A blackbody has an emissivity of 1, while a graybody's emissivity lies between 0 and 1. A diffuse gray surface is a specific type of graybody that reflects and emits radiation uniformly in all directions, following Lambert's cosine law. The primary characteristics of a diffuse gray surface are constant emissivity for all directions and wavelengths, governed by Lambert's cosine law, and even emission and reflection of radiation independently of the angle of incidence.

Step by step solution

01

Blackbody Definition

A blackbody is an ideal hypothetical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. In addition, a blackbody emits radiation based on its temperature following Planck's Law of Blackbody Radiation. A perfect blackbody has an emissivity of 1, which means it emits and absorbs radiation at the maximum possible rate for any given temperature.
02

Graybody Definition

A graybody is a more realistic object that does not absorb or emit radiation as efficiently as a blackbody. The emissivity of a graybody lies between 0 and 1, which indicates that it absorbs and emits radiation less efficiently than a perfect blackbody. The energy emitted by a graybody depends on its emissivity as well as its temperature.
03

Comparing Blackbody and Graybody

While blackbodies absorb and emit radiation at the maximum rate possible for their temperature, graybodies do not. A graybody will emit a fraction of the radiation emitted by a blackbody due to its lower emissivity value. The relationship between the emissivities of blackbodies and graybodies can be represented by the equation: \(P_{gray} = e \cdot P_{black}\), where \(P_{gray}\) is the power radiated by the graybody, \(e\) is the emissivity of the graybody, and \(P_{black}\) is the power radiated by a blackbody at the same temperature.
04

Diffuse Gray Surface Definition

A diffuse gray surface is a surface that reflects and emits radiation uniformly in all directions. It meets two criteria: firstly, its emissivity is constant for all directions and wavelengths, and secondly, it follows Lambert's cosine law which states that the intensity of radiation emitted is proportional to the cosine of the angle between the direction of emission and the surface normal. In simple terms, a diffuse gray surface emits and reflects radiation evenly and independently of the angle of incidence.
05

Diffuse Gray Surface Characteristics

The main characteristics of a diffuse gray surface are: 1. Constant emissivity for all directions and wavelengths. 2. Lambert's cosine law governs the emission and reflection of radiation. 3. It emits and reflects radiation evenly and independently of the angle of incidence. In summary, a graybody is an object that emits and absorbs radiation less efficiently than a blackbody due to its lower emissivity. A diffuse gray surface is a specific type of graybody that reflects and emits radiation uniformly in all directions, following Lambert's cosine law.

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Most popular questions from this chapter

The variation of the spectral absorptivity of a surface is as given in Fig. P12-78. Determine the average absorptivity and reflectivity of the surface for radiation that originates from a source at \(T=2500 \mathrm{~K}\). Also, determine the average emissivity of this surface at \(3000 \mathrm{~K}\).

Determine the rate of net heat gain (or loss) through a 9 -ft-high, 15 -ft- wide, fixed \(\frac{1}{8}\)-in single-glass window with aluminum frames on the west wall at 3 PM solar time during a typical day in January at a location near \(40^{\circ} \mathrm{N}\) latitude when the indoor and outdoor temperatures are \(70^{\circ} \mathrm{F}\) and \(20^{\circ} \mathrm{F}\), respectively.

How is the intensity of emitted radiation defined? For a diffusely emitting surface, how is the emissive power related to the intensity of emitted radiation?

Define the properties emissivity and absorptivity. When are these two properties equal to each other?

The reflectivity of aluminum coated with lead sulfate is \(0.35\) for radiation at wavelengths less than \(3 \mu \mathrm{m}\) and \(0.95\) for radiation greater than \(3 \mu \mathrm{m}\). Determine the average reflectivity of this surface for solar radiation \((T \approx 5800 \mathrm{~K})\) and radiation coming from surfaces at room temperature \((T \approx 300 \mathrm{~K})\). Also, determine the emissivity and absorptivity of this surface at both temperatures. Do you think this material is suitable for use in solar collectors?
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