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Chapter 12: Problem 3

What is thermal radiation? How does it differ from the other forms of electromagnetic radiation?

Short Answer

Expert verified
Answer: The primary differences between thermal radiation and other forms of electromagnetic radiation are the source and characteristics of the emitted radiation. Thermal radiation is produced by objects due to their temperature and the random motion of charged particles within them, while other forms of electromagnetic radiation result from various mechanisms such as atomic transitions, radioactive decay, or electric-generating devices. Additionally, thermal radiation typically consists of a continuous range of wavelengths with the peak wavelength determined by the object's temperature, whereas specific forms of electromagnetic radiation have distinct wavelengths or frequency ranges, and their intensities depend on factors like the source's power or transition probabilities in case of atomic emissions.

Step by step solution

01

Define Thermal radiation

Thermal radiation refers to the emission of electromagnetic waves by all objects that have a temperature above absolute zero (0 Kelvin). This radiation is in the form of electromagnetic waves and is a direct result of the random motion of charged particles (such as electrons) within the object.
02

Electromagnetic Spectrum

Electromagnetic radiation can be classified into various categories based on its wavelength or frequency. The electromagnetic spectrum includes radio waves, microwaves, infrared (IR) radiation, visible light, ultraviolet (UV) radiation, X-rays, and gamma rays. While thermal radiation lies mostly in the infrared range of the electromagnetic spectrum, it can also extend into the visible and ultraviolet ranges, depending on the temperature of the object.
03

Differences between Thermal Radiation and Other Electromagnetic Radiations

The primary differences between thermal radiation and other forms of electromagnetic radiation are the source and characteristics of the emitted radiation: 1. Source: Thermal radiation is produced by objects due to their temperature and the random motion of charged particles within them. In contrast, other forms of electromagnetic radiation result from various mechanisms, such as atomic transitions (UV, visible light, X-rays), radioactive decay (gamma rays), or electric-generating devices (radio waves, microwaves). 2. Wavelengths and intensities: Thermal radiation typically consists of a continuous range of wavelengths, with the peak wavelength (and intensity) determined by the object's temperature, as described by Wien's Displacement Law and Planck's Law. On the other hand, specific forms of electromagnetic radiation have distinct wavelengths or frequency ranges (e.g., radio waves have longer wavelengths than microwaves), and their intensities depend on factors like the source's power or the transition probabilities in case of atomic emissions. Understanding the differences between thermal radiation and other types of electromagnetic radiation is essential for studying various physical phenomena, such as heat transfer, atmospheric radiation, and remote sensing.

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Key Concepts

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

Electromagnetic Spectrum
The electromagnetic spectrum encompasses all types of electromagnetic radiation, which differ in wavelength and frequency. Electromagnetic waves are synchronized oscillations of electric and magnetic fields that travel through space at the speed of light. The spectrum is broadly categorized based on wavelength, starting with long radio waves, up through microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and ending with the high-energy, short-wavelength gamma rays.

Each category exhibits distinct properties and interacts with matter in unique ways. For instance, visible light enables us to see the world around us, while ultraviolet radiation can lead to chemical reactions, such as the production of vitamin D in our skin. The relevance of the electromagnetic spectrum to thermal radiation lies closely with infrared waves, where much of the thermal radiation is situated. This is because objects at common temperatures on Earth emit most of their energy in this range. However, as the temperature increases, the peak emission can shift to visible or even ultraviolet wavelengths.
Wien's Displacement Law
Wien's Displacement Law provides insight into the relationship between the temperature of an object and the peak wavelength of the radiation it emits. This law is mathematically expressed as
\[ \lambda_{\text{max}} = \frac{b}{T} \]
where \( \lambda_{\text{max}} \) is the peak wavelength, \( T \) is the absolute temperature of the object, and \( b \) is Wien's displacement constant, approximately equal to \( 2.897 \times 10^{-3} m \cdot K \).

The implication of Wien's Displacement Law is that hotter objects emit peak radiation at shorter wavelengths. For example, as an object heats up from room temperature to a red glow, its peak emission moves from the infrared part of the spectrum into the visible light range. Applying this law helps us predict the color of a heated object, such as a star, and is fundamental in the field of astrophysics and thermal imaging.
Planck's Law
Planck's Law offers a comprehensive description of the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature. This law is vital in understanding thermal radiation. It is given by the formula:
\[ I(\lambda, T) = \frac{2\pi h c^2}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda kT}} - 1} \]
where \( I(\lambda, T) \) is the spectral radiance, \( \lambda \) is the wavelength, \( T \) is the absolute temperature, \( h \) is the Planck constant, \( c \) is the speed of light in a vacuum, and \( k \) is the Boltzmann constant.

This equation indicates that radiation emitted by an object is not uniform across all wavelengths; instead, it has a distinct distribution determined by the object's temperature. The higher the temperature, the greater the intensity and the shorter the peak wavelength of emitted radiation. Planck's Law underpins the science of quantum mechanics and is critical for advancements in fields like thermography, climate science, and astronomy.

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Most popular questions from this chapter

Consider a surface at \(-5^{\circ} \mathrm{C}\) in an environment at \(25^{\circ} \mathrm{C}\). The maximum rate of heat that can be emitted from this surface by radiation is (a) \(0 \mathrm{~W} / \mathrm{m}^{2}\) (b) \(155 \mathrm{~W} / \mathrm{m}^{2}\) (c) \(293 \mathrm{~W} / \mathrm{m}^{2}\) (d) \(354 \mathrm{~W} / \mathrm{m}^{2}\) (e) \(567 \mathrm{~W} / \mathrm{m}^{2}\)

A microwave oven is designed to operate at a frequency of \(2.2 \times 10^{9} \mathrm{~Hz}\). Determine the wavelength of these microwaves and the energy of each microwave.

For a surface, how is radiosity defined? For diffusely emitting and reflecting surfaces, how is radiosity related to the intensities of emitted and reflected radiation?

Consider a surface at \(500 \mathrm{~K}\). The spectral blackbody emissive power at a wavelength of \(50 \mu \mathrm{m}\) is (a) \(1.54 \mathrm{~W} / \mathrm{m}^{2} \cdot \mu \mathrm{m}\) (b) \(26.3 \mathrm{~W} / \mathrm{m}^{2} \cdot \mu \mathrm{m}\) (c) \(108.4 \mathrm{~W} / \mathrm{m}^{2} \cdot \mu \mathrm{m}(d) 2750 \mathrm{~W} / \mathrm{m}^{2} \cdot \mu \mathrm{m}(e) 8392 \mathrm{~W} / \mathrm{m}^{2} \cdot \mu \mathrm{m}\)

By what properties is an electromagnetic wave characterized? How are these properties related to each other?
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