Use of the Stefan Boltzmann Law in a Non Equilibrium system?

In summary, the question being discussed is whether the Stefan-Boltzmann law can be used to describe the emission of radiation from a block of metal in vacuum that is being heated by a laser. This is because the law assumes that the system is in equilibrium with its surroundings, which is not the case in this situation. However, as long as the total power of radiation incident on the block is equal to the power radiated by the block, the law can still be used.
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TL;DR Summary
Is it possible to be able to use the Stefan Boltzmann law for a system which is being constantly heated and is in contact with a perfect vacuum (T = 0K).
Hi everyone,

I am currently trying to work something out in regards to non-equilibrium thermodynamics. If I have a block of metal in vacuum that is being heated by a laser with a constant power P, is it even possible to be able to describe the emission of radiation by the block via the Stefan Boltzmann law (ie E ~ T^4).
The reason why I ask this is that the Stefan-Boltzmann law can be derived from Planck's Radiation law which implicitly assumes that the system is in equilibrium with its surrounding. Clearly that is not occurring in this problem. Any suggestions for what should be used?
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A body that radiates energy at the same rate that it absorbs energy will be in thermodynamic equilibrium. The body only needs to be in thermodynamic equilibrium in its surroundings. The surroundings do not have to be in an equilibrium state. The surroundings consist of everything external to the body i.e the universe, which is not in equilibrium. If the block is surrounded by a vacuum, it is not "in contact" with anything. All that matters is that the total power of the radiation incident on the block is equal to the power that is radiated by the block into space.

AM
 
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1. What is the Stefan Boltzmann Law and how is it used in a non-equilibrium system?

The Stefan Boltzmann Law is a physical law that describes the relationship between the temperature and the total amount of energy radiated by a blackbody. In a non-equilibrium system, this law is used to calculate the rate of energy transfer between objects with different temperatures.

2. How does the Stefan Boltzmann Law apply to real-world situations?

The Stefan Boltzmann Law is applicable in many real-world situations, such as calculating the amount of heat transferred between the Earth and the Sun, determining the efficiency of solar panels, and understanding the thermal radiation emitted by objects in space.

3. Can the Stefan Boltzmann Law be used to calculate the temperature of an object?

No, the Stefan Boltzmann Law cannot be used to directly calculate the temperature of an object. It only describes the relationship between temperature and energy radiated by a blackbody. Other factors, such as the object's emissivity, must also be taken into account.

4. How does the Stefan Boltzmann Law relate to the second law of thermodynamics?

The second law of thermodynamics states that energy always flows from hotter objects to colder objects. The Stefan Boltzmann Law is a mathematical representation of this principle, as it shows that the rate of energy transfer increases with a larger temperature difference between two objects.

5. Are there any limitations to using the Stefan Boltzmann Law in a non-equilibrium system?

Yes, the Stefan Boltzmann Law assumes that the objects involved are in thermal equilibrium and have a constant temperature. In real-world situations, this may not always be the case, and other factors such as convection and conduction may also play a role in energy transfer.

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