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Chapter 1: Problem 50

Define emissivity and absorptivity. What is Kirchhoff's law of radiation?

Short Answer

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Question: Define emissivity, absorptivity, and explain Kirchhoff's law of radiation. Answer: Emissivity (\(\epsilon\)) is a measure of how effectively a material emits thermal radiation compared to a perfect blackbody radiator. Absorptivity (\(\alpha\)) represents the fraction of incident electromagnetic radiation absorbed by a material compared to the total incident radiation. Kirchhoff's law of radiation states that, for an object in thermal equilibrium, the emissivity and absorptivity are equal at the same temperature and wavelength (i.e., \(\epsilon = \alpha\)). This law implies that good absorbers are also good emitters, while poor absorbers are poor emitters.

Step by step solution

01

Definition of Emissivity

Emissivity, represented by the symbol \(\epsilon\), is a measure of how effectively a material emits thermal radiation as compared to a perfect blackbody radiator. It is a dimensionless quantity with values ranging from 0 to 1. A higher value of emissivity indicates more effective emission of thermal radiation by the material.
02

Definition of Absorptivity

Absorptivity, represented by the symbol \(\alpha\), is the fraction of incident electromagnetic radiation absorbed by a material compared to the total incident radiation. It is also a dimensionless quantity, with values ranging from 0 to 1. A higher value of absorptivity indicates more effective absorption of incident radiation by the material.
03

Kirchhoff's Law of Radiation

Kirchhoff's law of radiation states that, for an object in thermal equilibrium, the emissivity and absorptivity are equal at the same temperature and wavelength. Mathematically, it is expressed as: $$\epsilon = \alpha$$ This law implies that good absorbers are also good emitters of radiation and that poor absorbers are poor emitters. This principle is essential in understanding the behavior of materials in various applications such as thermal insulation, solar panels, and radiative cooling systems.

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Most popular questions from this chapter

A 2-kW electric resistance heater submerged in 30-kg water is turned on and kept on for \(10 \mathrm{~min}\). During the process, \(500 \mathrm{~kJ}\) of heat is lost from the water. The temperature rise of water is (a) \(5.6^{\circ} \mathrm{C}\) (b) \(9.6^{\circ} \mathrm{C}\) (c) \(13.6^{\circ} \mathrm{C}\) (d) \(23.3^{\circ} \mathrm{C}\) (e) \(42.5^{\circ} \mathrm{C}\)

What is a blackbody? How do real bodies differ from blackbodies?

A room is heated by a baseboard resistance heater. When the heat losses from the room on a winter day amount to \(9000 \mathrm{~kJ} / \mathrm{h}\), it is observed that the air temperature in the room remains constant even though the heater operates continuously. Determine the power rating of the heater, in \(\mathrm{kW}\).

Consider a person standing in a room maintained at \(20^{\circ} \mathrm{C}\) at all times. The inner surfaces of the walls, floors, and ceiling of the house are observed to be at an average temperature of \(12^{\circ} \mathrm{C}\) in winter and \(23^{\circ} \mathrm{C}\) in summer. Determine the rates of radiation heat transfer between this person and the surrounding surfaces in both summer and winter if the exposed surface area, emissivity, and the average outer surface temperature of the person are \(1.6 \mathrm{~m}^{2}, 0.95\), and \(32^{\circ} \mathrm{C}\), respectively.

Define thermal conductivity and explain its significance in heat transfer.
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