Planck's Function in Physics

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Questions and Answers

What does Planck's function represent?

The range of absolute temperatures in Kelvin

The amount of radiant heat energy emitted per unit area

The upper bound of radiance for given temperature and wavelength (correct)

The constant of proportionality for peak wavelength emission

What is the value of Boltzmann's constant?

1.381 x 10^-23 J·K^-1 (correct)

2.897771955 x 10^-3 m·K

2.998 x 10^8 m·s^-1

6.626 x 10^-34 J·s

Wien's displacement law indicates that peak emission is inversely proportional to what?

Planck's constant

Speed of light

Absolute temperature (correct)

Radiance intensity

What does the Stefan-Boltzmann law state about radiant heat energy?

It is directly proportional to the fourth power of the absolute temperature Signup and view all the answers

What is the approximate value of Wien's displacement constant?

2.897 x 10^-3 m·K Signup and view all the answers

How is the power emitted by a unit area (E) described in the Stefan-Boltzmann law?

E is proportional to the fourth power of temperature Signup and view all the answers

What does the speed of light (c) equal?

2.998 x 10^8 m·s^-1 Signup and view all the answers

What type of objects emit radiation at longer wavelengths according to Wien's displacement law?

Cold objects Signup and view all the answers

What defines emissivity in the context of thermal radiation?

The amount of radiation emitted by a surface compared to a blackbody. Signup and view all the answers

Which of the following describes a blackbody?

It emits the maximum radiation at each wavelength at a given temperature. Signup and view all the answers

Which statement correctly describes blackbody radiation?

It is uniquely determined by the temperature of the emitter. Signup and view all the answers

What is Planck's Radiation Law primarily concerned with?

The spectral density of radiation emitted by blackbodies. Signup and view all the answers

What characteristic does NOT apply to blackbody radiation?

It can vary with environmental conditions. Signup and view all the answers

In which case does the concept of monochromatic emissivity apply?

To the emissivity at a single specific wavelength. Signup and view all the answers

At absolute zero (0 K), what happens to a material in terms of emission?

It does not emit any radiation. Signup and view all the answers

Which phenomenon describes our bodies losing heat energy?

Emission. Signup and view all the answers

Study Notes

Planck’s Function

Planck's function defines the relationship between temperature (T) and wavelength (λ) for radiance (Bλ) measured in Wm²Sr⁻¹μm⁻¹.
Boltzmann’s constant (kB) is 1.381 x 10⁻²³ JK⁻¹, used in the calculation of thermal energy.
The speed of light (c) is 2.998 x 10⁸ m/s, essential for understanding electromagnetic radiation.
Planck’s constant (h) equals 6.626 x 10⁻³⁴ Js, fundamental in quantum mechanics.
Absolute temperature (T) is measured in Kelvin (K), the standard unit for thermodynamic temperature.
Wavelength (λ) is expressed in micrometers (μm).

Wien’s Displacement Law

T represents absolute temperature, indicating that peak wavelength emission is inversely proportional to temperature.
Wien's displacement constant (b) is approximately 2.897771955 x 10⁻³ m⋅K, used to find peak emission wavelengths.
Cooler objects, like Earth, emit longer wavelengths compared to hotter objects, like the Sun, which emit at shorter wavelengths.

Stefan-Boltzmann Law

The radiant energy (E) emitted per unit area in one second is given by E = σT⁴, with σ as the Stefan-Boltzmann constant.
The emission per unit area of a black body is directly proportional to the fourth power of absolute temperature (T).

Emission

Emission is the process of converting internal energy into radiant energy, occurring at all temperatures above absolute zero (0 K).
Human bodies lose heat energy via radiation but rarely notice due to heat balance with surroundings.
Examples of emission include heat felt from a burning stove and visible radiation from glowing embers.

Emissivity

Emissivity measures the emitted radiation of a surface compared to that of a black body.
Monochromatic emissivity refers to emission at a single wavelength, while graybody emissivity pertains to emission across a spectrum of wavelengths.

Blackbody Characteristics

A blackbody is an ideal emitter with maximum radiation at all wavelengths, fully absorbing all incident radiation.
Blackbody radiation is determined solely by the emitter's temperature, showcasing maximum possible radiant energy at given temperatures.
The radiation emitted by a blackbody is isotropic, meaning it is uniform in all directions.

Planck’s Radiation Law

Describes the spectral density of radiation emitted by a black body in thermal equilibrium at temperature T.
A black body emits radiation across all wavelengths, but there exists a maximum amount for any specific wavelength at a defined temperature.

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Description

Explore the details of Planck's function, which describes the upper bound of radiance based on temperature and wavelength. This quiz covers fundamental constants such as Boltzmann's constant, speed of light, and Planck's constant, as well as their relationships in the context of black body radiation.