Cameron Miranda
There are several laws of radiation that govern the relationships between temperature, energy, and wavelength. These laws are based on the concept of a blackbody, which is a theoretical construct representing a perfect emitter and absorber of all wavelengths when in thermal equilibrium. One of the primary laws is Planck's Law, which states that all matter emits radiation at all wavelengths, but not equally. This is complemented by Wien's Law, which states that the wavelength of peak emission is inversely proportional to the temperature of the emitting object. Other laws include Kirchoff's Law, which relates emissivity and absorptance, and Lambert's Law, which describes the geometrical distribution of radiation from flat surfaces. These laws provide a foundation for understanding how radiation interacts with different surfaces and how it can be measured.
| Characteristics | Values |
|---|---|
| Everything emits and absorbs radiation | All objects emit radiation at all wavelengths |
| Includes electromagnetic radiation | |
| Plank's Law | |
| Kirchhoff's Law of Thermal Radiation | The ratio of emissive power to the coefficient of absorption is equal to a universal function of radiative wavelength and temperature |
| Planck's Law is the universal function | |
| Real objects are grey-bodies, emitting and absorbing different wavelengths selectively | |
| Emissivity is a value less than one that scales the Stefan-Boltzmann law | |
| Stefan-Boltzmann Law | The total amount of energy per unit area emitted by an object is proportional to the 4th power of the temperature |
| Lambert's Cosine Law | The radiation per unit solid angle (radiant intensity) from a flat surface varies with the cosine of the angle to the surface normal |
| Wein's Law | The peak emission of the sun occurs near 0.5 microns, on the short-wave end of the visible spectrum |
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What You'll Learn
- Planck's Law: All objects emit radiation across the electromagnetic spectrum
- Kirchhoff's Law: The ratio of emissive power to the coefficient of absorption is equal to a function of wavelength and temperature
- Stefan-Boltzmann Law: Total energy emitted per unit area is proportional to the fourth power of temperature
- Lambert's Cosine Law: Radiant intensity from a flat surface varies with the cosine of the angle to the surface normal
- Wein's Law: The sun's peak emission occurs in the visible light portion of the spectrum
Planck's Law: All objects emit radiation across the electromagnetic spectrum
In physics, Planck's Law, also known as Planck Radiation Law, states that all objects emit radiation across the electromagnetic spectrum. This means that every object, including humans, emits radiation at all wavelengths.
The law was formulated in 1900 by German physicist Max Planck to explain the spectral-energy distribution of radiation emitted by a blackbody—a hypothetical body that completely absorbs all radiant energy that falls on it, reaches some equilibrium temperature, and then re-emits that energy as quickly as it absorbs it. Planck's law is a universal function that derives from Kirchhoff's Law of Thermal Radiation.
According to Planck's Law, the wavelength of emitted radiation is inversely proportional to its frequency, or λ = c/ν. The value of Planck's constant is defined as 6.62607015 × 10^-34 joule-second. For a blackbody at temperatures up to several hundred degrees, most of the radiation is in the infrared radiation region of the electromagnetic spectrum.
The law also states that with increasing temperature, the total radiated energy of an object increases, and the peak of the emitted spectrum shifts to shorter wavelengths. This shift due to temperature is called Wien's displacement law. Planck radiation is the greatest amount of radiation that any body at thermal equilibrium can emit from its surface, regardless of its chemical composition or surface structure.
An example of Planck's Law in action is when you turn off a light bulb. While the light bulb may no longer be emitting radiation that is visible to the human eye, it is still emitting radiation at all wavelengths, likely in the form of infrared radiation.
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Kirchhoff's Law: The ratio of emissive power to the coefficient of absorption is equal to a function of wavelength and temperature
Radiation laws are mathematical ways to define the relationships between temperature, energy, and wavelength. Gustav Robert Kirchhoff, in 1860, stated that "at thermal equilibrium, the power radiated by an object is equal to the power absorbed". This is now known as Kirchhoff's Law of Thermal Radiation.
Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. It is a special case of Onsager reciprocal relations as a consequence of the time reversibility of microscopic dynamics, also known as microscopic reversibility.
Kirchhoff's law states that for a body of any arbitrary material emitting and absorbing thermal electromagnetic radiation at every wavelength in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative wavelength and temperature. In simpler terms, the emissivity function is equal to the absorptivity function. The emissivity of a source is the ratio of the radiant emittance of the source to the radiant emittance of a black body at the same temperature.
Kirchhoff's law has another corollary: the emissivity cannot exceed one (because the absorptivity cannot, by conservation of energy), so it is not possible to thermally radiate more energy than a black body, at equilibrium.
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Stefan-Boltzmann Law: Total energy emitted per unit area is proportional to the fourth power of temperature
The Stefan-Boltzmann law, also known as Stefan's law, describes the intensity of thermal radiation emitted by matter in terms of its temperature. It is named after Josef Stefan, who empirically derived the relationship, and Ludwig Boltzmann, who derived the law theoretically.
The law states that the total energy emitted per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the temperature of the black body. The SI units of measure are joules per second per square meter (J·s^-1·m^-2), or, equivalently, watts per second. The emissivity of the surface emitting the radiation is generally between zero and one. An emissivity of one corresponds to a black body.
The Stefan-Boltzmann law can be applied to all matter, provided that the matter is in a state of local thermodynamic equilibrium (LTE) so that its temperature is well-defined. This law holds for all convex black bodies, as long as the surface has the same temperature throughout. The law also extends to radiation from non-convex bodies by using the fact that the convex hull of a black body radiates as though it were itself a black body.
The Stefan-Boltzmann law is one of the three laws of radiation that help us understand how different surfaces can interact with radiation. Plank's Law is another law of radiation that states that every object emits radiation over the entire electromagnetic spectrum.
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Lambert's Cosine Law: Radiant intensity from a flat surface varies with the cosine of the angle to the surface normal
Radiation is a complex phenomenon that follows a set of laws governing the interactions between temperature, energy, and wavelength. One of these laws, known as Lambert's Cosine Law, specifically addresses the behaviour of radiant intensity from flat surfaces.
Lambert's Cosine Law, named after Johann Heinrich Lambert, states that the radiant intensity from a flat surface is directly proportional to the cosine of the angle to the surface normal. In simpler terms, it explains how the intensity of light reflected or emitted from a flat surface changes as the angle between the observer's line of sight and the surface normal varies. This law is expressed mathematically as I = I0 cos θ, where I is the radiant intensity, I0 is the intensity when θ (the angle between the observer's line of sight and the surface normal) is zero, and θ is the angle itself.
The significance of Lambert's Cosine Law lies in its ability to describe the uniform brightness of a flat surface from different viewing angles. When an observer looks at a flat surface, the law dictates that the surface's radiance remains constant regardless of the observer's position. This is because the decrease in emitted power from a given area due to the cosine of the emission angle is counterbalanced by an increase in the projected surface area viewed by the observer, again due to the cosine relationship.
Lambert's Cosine Law has important applications in the field of optics and the measurement of light. For example, it helps explain why the sun, a spherical body, often appears as a flat disk. Additionally, the law is relevant in the design of light sources, such as arcs, which appear as uniform flat disks due to the cosine law. Furthermore, it is applied in the orientation of flat sources like low-power quartz tungsten halogen filaments to achieve maximum irradiance.
Beyond its practical applications, Lambert's Cosine Law also contributes to our fundamental understanding of radiation. It highlights the relationship between the direction of incident light and the normal to a surface, providing insights into the behaviour of light as it interacts with different materials. By studying this law, scientists and researchers can better comprehend the complex nature of radiation and its applications in various fields, including meteorology and physics.
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Wein's Law: The sun's peak emission occurs in the visible light portion of the spectrum
Radiation laws are mathematical ways to define the relationships between temperature, energy, and wavelength. They help us understand how different surfaces interact with radiation and how variations in the atmosphere can alter the amount of energy available at the surface.
Wein's Law, also known as Wein's Displacement Law, states that the wavelength of peak emission is inversely proportional to the temperature of the emitting object. In other words, as the temperature of an object increases, the wavelength of its peak emission decreases, and vice versa. This law is derived from Planck's Law, which states that every object emits radiation at all times and over the entire electromagnetic spectrum.
The Sun's radiating temperature is approximately 6000 degrees Celsius, and its peak emission occurs near 0.5 microns, towards the short-wave end of the visible light spectrum. This is in contrast to the Earth's peak emission, which is located in the infrared portion of the electromagnetic spectrum due to its much lower temperature of 15 degrees Celsius. The Sun's peak emission in the visible range is unusual among stars, most of which peak in the invisible portion of the spectrum.
Using Wein's Law, we can determine that the Sun's peak emission per nanometer (of wavelength) is at a wavelength of about 500 nm, in the green portion of the spectrum near the peak sensitivity of the human eye. This is why we perceive the Sun as having a yellow hue. However, in terms of power per unit optical frequency, the Sun's peak emission is at 343 THz or a wavelength of 883 nm in the near-infrared range.
The importance of Wein's Law extends beyond just understanding the Sun's emissions. It helps us apply this knowledge to other emission sources that affect the Earth's atmosphere, such as those outlined in Planck's Law, which states that all matter emits radiation at all wavelengths all the time, but not equally across all wavelengths.
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