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The temperature of the sun can be measured by: (a) Planck's law (b) Kirchoff's law (c) Stefan-Boltzmann law (d) Wien's displacement law

Short Answer

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(d) Wien's displacement law

Step by step solution

01

Understanding the Options

We need to understand what each law is related to. Planck's law describes the electromagnetic radiation emitted by a black body in thermal equilibrium. Kirchoff's law deals with the conservation of charge and energy in electrical circuits. The Stefan-Boltzmann law relates the temperature of a black body to its total emitted radiation. Wien's displacement law relates the peak emission wavelength to the temperature of the black body.
02

Identifying Temperature Measurement

The question asks for a law that measures temperature. Planck's law can be used for this purpose, but it is quite complex and involves the spectrum. Kirchoff’s law does not directly involve temperature measurement. The Stefan-Boltzmann law can be used to find temperature from the total energy radiated by a black body. Wien's displacement law provides a direct method to find temperature using the peak emission wavelength.
03

Choosing the Best Option

Given the focus on temperature measurement, Wien's displacement law is the best option because it specifically relates temperature directly to the peak wavelength of radiation, making it a more straightforward tool for determining temperature than the other laws in the context of this problem.

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Key Concepts

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

Black body radiation
Black body radiation refers to the theoretical concept of an ideal object, known as a black body, that absorbs all incoming radiation, regardless of frequency or angle of incidence. A black body emits radiation called black body radiation, purely due to its temperature, without reflecting any external light. This concept is crucial in understanding how objects at a certain temperature emit radiation.

The characteristics of black body radiation depend only on the body's temperature, giving off a spectrum of electromagnetic energy. As temperature increases, the intensity and nature of radiation change. A higher temperature leads to higher intensity and the shift of peak frequency towards the ultraviolet end of the electromagnetic spectrum.

Understanding black body radiation is fundamental for many areas of physics. It provides insight into energy emission based purely on thermal states and serves as a model for real-world objects. While no perfect black body exists, stars, including the Sun, approximate black body emitters, making this concept key for astronomical studies.
Stefan-Boltzmann law
The Stefan-Boltzmann law quantifies the amount of heat energy radiated from a black body in terms of its temperature. It asserts that the power emitted per unit area by a black body is directly proportional to the fourth power of the body's absolute temperature.

Mathematically, this is given by the formula \[ E = \sigma T^4 \]where \( E \) is the energy radiated per unit area, \( T \) is the absolute temperature of the black body, and \( \sigma \) is the Stefan-Boltzmann constant.

This concept is instrumental in determining the temperature of stars, including our Sun, from the total radiation they emit. By measuring the energy radiated, we can back-calculate the temperature thanks to this profound law. The Stefan-Boltzmann law underpins critical concepts in thermodynamics and helps scientists infer temperatures of astronomical objects from afar.
Electromagnetic spectrum
The electromagnetic spectrum encompasses all types of electromagnetic radiation, spanning from gamma rays with the shortest wavelengths to radio waves with the longest wavelengths. In between, it includes X-rays, ultraviolet, visible light, infrared, and microwaves.

Every type of radiation carries energy, and its properties change with frequency and wavelength. Visible light, a small part of this spectrum that human eyes can see, varies in color from violet to red, each corresponding to different wavelengths.

The understanding of the electromagnetic spectrum is vital in physics because it affects how energy and information travels through space. For example, in astrophysics, different wavelengths probe different layers and processes in celestial bodies like stars.
  • Gamma rays - Reveal energetic processes like supernovae
  • X-rays - Highlight high-temperature regions like the Sun's corona
  • Infrared - Penetrates cosmic dust to observe star formation
A comprehensive grasp of this spectrum assists in leveraging different radiation forms for various technologies, from medical imaging to communications and beyond, proving the electromagnetic spectrum's vast importance.

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Most popular questions from this chapter

A solid sphere and a hollow sphere of same material and size are heated to same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is \(T\), then (a) the hollow sphere will cool at a faster rate for all values of \(T\) (b) the solid sphere will cool at a faster rate for all values of \(T\) (c) both spheres will cool at the same rate for all values of \(T\) (d) both spheres will cool at the same rate only for small values of \(T\)

A heated piece of green glass seen in darkness will (a) appear white (b) appear red (c) appear green (d) not be visible

Liquid oxygen at \(50 \mathrm{~K}\) is heated to \(300 \mathrm{~K}\) at constant pressure of 1 atm. The rate of heating is constant. Which of the following graphs represents the variation of temperature with time? (a) (b) (c) (d)

A ball of thermal capacity \(10 \mathrm{cal} /{ }^{\circ} \mathrm{C}\) is heated to the temperature of furnace. It is then transferred into a vessel containing water. The water equivalent of vessel and the contents is \(200 \mathrm{gm}\). The temperature of the vessel and its contents rises from \(10^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\). What is the temperature of furnace? (a) \(640^{\circ} \mathrm{C}\) (b) \(64^{\circ} \mathrm{C}\) (c) \(600^{\circ} \mathrm{C}\) (d) \(100^{\circ} \mathrm{C}\)

\(10 \mathrm{gm}\) of ice cubes at \(0^{\circ} \mathrm{C}\) are released in a tumbler containing water (water equivalent \(55 \mathrm{gm}\) ) at \(40^{\circ} \mathrm{C}\). Assuming that negligible heat is taken from the surrounding the temperature of water in the tumbler becomes nearly \((L=80 \mathrm{cal} / \mathrm{gm})\) (a) \(31^{\circ} \mathrm{C}\) (b) \(22^{\circ} \mathrm{C}\) (c) \(19^{\circ} \mathrm{C}\) (d) \(15^{\circ} \mathrm{C}\)

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