# Calculating Total Power Emitted by a Black Body in a Spherical Chamber

• Krushnaraj Pandya
In summary, the problem involves a spherical body enclosed in a spherical chamber with a reflectance of 0.4 and negligible transmittance. The temperature of both the body and the surrounding environment is constant at T Kelvin. The total power emitted by the body per unit area is given by P=σεAT^4, where ε is the emissivity of the body. However, there is some confusion about whether the reflected radiation should be counted as part of the power coming out of the body. Both "radiating" and "emitting" are used interchangeably in this context. The correct solution is σT^4, as the reflected radiation should not be included in the power emitted by the body.
Krushnaraj Pandya
Gold Member

## Homework Statement

A spherical body is enclosed in a spherical chamber which acts like a perfectly black body. The reflectance of the body is 0.4 and transmittance is negligible, the temperature of the body and surrounding temperature is constant at T Kelvin. The total power that comes out of the body per unit area is?

P=σεAT^4

## The Attempt at a Solution

reflectance is 0.4 so emissivity is 0.6, power radiated by body per unit area is 0.6σT^4 but the correct answer is σT^4- where am I wrong? I think the reflected radiation shouldn't be counted as coming "out" from the body

Krushnaraj Pandya said:
I think the reflected radiation shouldn't be counted as coming "out" from the body
If that's the case, from where did the spherical chamber get the radiation it's emitting?

kuruman said:
If that's the case, from where did the spherical chamber get the radiation it's emitting?
I am confused between the terms "radiating" and "emitting". Are they considered the same?

Yes.

So this is what's going on- the chamber emits σT^4 (per unit area), the body emits 0.6 of it back and reflects 0.4 of it back, correct?

?

Krushnaraj Pandya said:
So this is what's going on- the chamber emits σT^4 (per unit area), the body emits 0.6 of it back and reflects 0.4 of it back, correct?
Yes.

haruspex said:
Yes.
Thank you very much :D

## 1. What is black body radiation?

Black body radiation refers to the electromagnetic radiation emitted by a perfect thermal emitter, known as a black body. A black body absorbs all radiation that falls on it and emits radiation at all wavelengths.

## 2. What is the significance of black body radiation?

Black body radiation plays a crucial role in understanding the behavior of electromagnetic radiation and is a fundamental concept in quantum physics. It also helps in understanding the temperature and energy distribution of objects in the universe.

## 3. How does the temperature of a black body affect its radiation?

The temperature of a black body is directly proportional to the amount of radiation it emits. As the temperature increases, the intensity of the radiation and the peak wavelength of the emitted radiation shift towards shorter wavelengths.

## 4. What is the Stefan-Boltzmann law in relation to black body radiation?

The Stefan-Boltzmann law states that the total energy radiated from a black body is proportional to the fourth power of its absolute temperature. This means that as the temperature of a black body increases, the amount of energy it emits also increases exponentially.

## 5. How is black body radiation related to the color of objects?

The color of an object is determined by the wavelengths of light it reflects. A black body absorbs all wavelengths of light, so it appears black. However, as the temperature of a black body increases, it begins to emit visible light, and its color shifts from red to orange to white as the temperature increases further.

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