A black body covered by another black body.

From this, we can use the Stefan-Boltzmann law to find the temperature at which the two bodies are in thermal equilibrium. This temperature will be lower than the initial temperature T, as some heat will be lost to free space. In summary, to find the temperature at which the system is in thermal equilibrium, we can use the concept of heat loss and gain for both the inner and outer black bodies, and apply the Stefan-Boltzmann law.
  • #1
Sunny Kumar
7
0
Question:

A spherical black body is kept at constant temperature thermal equilibrium T and by supplying heat from some source. It is covered by another spherical surface which is also a black body (a very thin surface of radius almost equal to the previous one). Find the temperature at which the system is now in thermal equilibrium. Assume that heat radiated goes into free space.

Can we use the concept that heat lost by the inner black body is equal to heat gained by it? If not, then how to attempt the problem?
 
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  • #2
Moderator's note: thread moved to Advanced Physics

Sunny Kumar said:
Question:

A spherical black body is kept at constant temperature thermal equilibrium T and by supplying heat from some source. It is covered by another spherical surface which is also a black body (a very thin surface of radius almost equal to the previous one). Find the temperature at which the system is now in thermal equilibrium. Assume that heat radiated goes into free space.

Can we use the concept that heat lost by the inner black body is equal to heat gained by it? If not, then how to attempt the problem?
Yes, but more importantly the same is true for the outer blackbody as well.
 

Related to A black body covered by another black body.

1. What is a black body?

A black body is an idealized object that absorbs all incoming electromagnetic radiation, regardless of wavelength or angle of incidence. It also emits radiation at all wavelengths, making it a perfect emitter of thermal radiation.

2. What happens when a black body is covered by another black body?

When a black body is covered by another black body, the outer body will absorb all incoming radiation, including the radiation emitted by the inner body. This will cause the outer body to increase in temperature due to the absorption of thermal radiation from the inner body.

3. Why is a black body covered by another black body an important concept in physics?

This concept is important in physics because it helps us understand the behavior of thermal radiation in enclosed spaces. For example, the Earth's atmosphere can be thought of as a black body covering the Earth's surface, which affects the amount of incoming and outgoing radiation and plays a crucial role in maintaining the Earth's temperature.

4. Can a black body covered by another black body ever reach thermal equilibrium?

Yes, a black body covered by another black body can reach thermal equilibrium, where the amount of incoming and outgoing radiation is balanced and the temperature remains constant. This is known as a black body cavity, where the inner and outer bodies are in thermal equilibrium and the temperature of the cavity is the same at all points.

5. How does the temperature of a black body covered by another black body affect the amount of radiation emitted?

The temperature of a black body covered by another black body affects the amount of radiation emitted by the outer body. As the temperature of the outer body increases, it will emit more thermal radiation, leading to a higher rate of heat transfer between the two bodies. This can result in the inner body also increasing in temperature, creating a feedback loop.

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