# Radiation Problem: Black-body Expansion, T_f=xT_i

• neelakash
In summary, the conversation discusses black-body radiation in a volume that expands adiabatically and reversibly. The final temperature is a factor of the initial temperature, with the correct answer being (d) 1. The conversation also mentions the Stefan-Boltzmann Law and references Callen's Thermodynamics for further information.
neelakash

## Homework Statement

Black-body radiation, at temperature Ti fills a volume V. The system expands adiabatically
and reversibly to a volume 8V. The final temperature T_f = xT_i, where the factor x is equal to
(a) 0.5 (b) 2.8 (c) 0.25 (d) 1

## The Attempt at a Solution

Correct answer should be (d)1 because, photons do not feel attraction or repulsion potential to each other.So, increasing volume adiabatically should not reduce or increase its temperature.

Please check if I am correct.

This is incorrect. The Stefan-Boltzmann Law tells us that the energy and entropy of blackbody radiation in a box are $U=bVT^4$ and $S=\frac{4}{3}bVT^3$, respectively, where $b$ is a constant (reference: Callen's Thermodynamics). I'll leave the rest to you.

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## 1. What is black-body radiation?

Black-body radiation refers to the electromagnetic radiation emitted by a perfect black body, which is an ideal theoretical object that absorbs all radiation that falls on it. It is characterized by a continuous spectrum of wavelengths and follows specific laws of thermodynamics.

## 2. What is the black-body expansion problem?

The black-body expansion problem is a phenomenon observed in thermodynamics where a black body expands when heated. This expansion is directly proportional to the change in temperature and is known as the coefficient of linear expansion.

## 3. What does Tf=xTi mean?

This equation represents the relationship between the final temperature (Tf) and initial temperature (Ti) of a black body when it undergoes expansion. The x term is the coefficient of linear expansion, which is a constant value specific to the material of the black body.

## 4. How does black-body expansion relate to the concept of radiation?

Black-body expansion is a result of the absorption and emission of radiation by the black body. As the body absorbs radiation, its temperature increases, causing it to expand. This expansion then leads to the emission of radiation, maintaining a balance between absorption and emission.

## 5. What are the practical applications of understanding black-body expansion and radiation?

Understanding black-body expansion and radiation is crucial in fields such as thermodynamics, materials science, and astrophysics. It helps explain phenomena such as heat transfer, thermal expansion, and the behavior of objects in extreme temperatures. This knowledge also allows for the development of technologies such as solar panels and thermal imaging devices.

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