How is the 2nd law of thermodynamics obeyed in this system?

In summary, a radiation concentrator surrounded by layers of foil for insulation will have the same amount of thermal radiation flowing through the smaller opening in both directions. However, if a winstone cone is attached to one side, more radiation will be focused on the opening, causing a decrease in temperature inside the setup. This may seem to contradict the second law of thermodynamics, but the emissivity of the winstone cone and foil can be substituted for a box lined with metal. The "view factor" of the receiving surface plays a role in the exchange of energy between the two surfaces, guaranteeing equal exchange at thermal equilibrium despite differences in area.
  • #1
Christofer Br
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Imagine there is an radiation concentrator (winston cone) surrounded with extremely many layers of foil for radiation insulation, except at the smaller opening. Every part of the setup is initially in thermal equilibrium with the surroundings. The amount of thermal radiation flowing through the smaller opening in both directions through the hole would be the same in both directions, except since on one side we attached a winstone cone, there will be more radiation coming out into the surroundings from the inside of the setup since some of the radiation that otherwise would miss the opening is being focused on it by the winstone cone. We assume that the energy losses through the insulation are vastly smaller than the energy of radiation focused on the opening by the winston cone.

It seems now that since there is more radiation coming out of the setup than coming in [through the opening], the temperature inside would spontaneously lower until the lower temperature radiation coming out has the same energy flux as the radiation coming in.
This of course would be at odds with the second law of thermodynamics. How is the entropy decrease prevented in this case?
In case you start wondering about the emissivity of the winstone cone and the foil at its larger opening, note that the 'surroundings' can substitued for a box with an opening shared with the winstone cone, with sides lined with metal (the same material as winston cone), if we consider an isolated system
 
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  • #2
It is not only the area, but also the solid angle or view factor which is important.

Suppose that you have a small flat source radiating thermal energy. It does not send its energy in a sharp beam normal to the surface, but it sends it out over all ##2\pi## steradians. If a receiving surface only covers ##1\pi## steradian then the “view factor” is 0.5 and only half of the energy emitted by the first surface is received by the second surface.

Due to geometry you are guaranteed that any increase in area is associated with a decrease in view factor. So although you can make a large area exchange energy with a small area, only a small portion of the large area’s energy can exchange while a large portion of the small area’s energy will exchange. The product of the area and the view factor are the same on both sides.

The net result is that the exchange is geometrically guaranteed equal at thermal equilibrium.
 
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Related to How is the 2nd law of thermodynamics obeyed in this system?

1. How does the 2nd law of thermodynamics relate to this system?

The 2nd law of thermodynamics states that the total entropy of a closed system will always increase over time. This means that in any process, there will always be some energy that is lost or dissipated, resulting in a decrease in the overall organization and usable energy in the system. In other words, the 2nd law of thermodynamics governs the direction of energy flow in a system and sets limits on the efficiency of energy transformations.

2. What is the difference between the 1st and 2nd law of thermodynamics?

The 1st law of thermodynamics, also known as the Law of Conservation of Energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another. The 2nd law, on the other hand, focuses on the direction of energy flow and the concept of entropy, which is a measure of the disorder or randomness in a system. While the 1st law deals with the quantity of energy in a system, the 2nd law deals with the quality of energy and its tendency to become more dispersed and less useful over time.

3. How can we observe the 2nd law of thermodynamics in action in this system?

The 2nd law of thermodynamics can be observed in various ways in different systems. For example, in a car engine, the energy from burning fuel is converted into motion, but some of that energy is always lost as heat, sound, and friction, leading to a decrease in the total usable energy in the system. In a biological system, the 2nd law can be seen in the flow of energy from the sun through plants and animals, with some energy always lost as heat and waste products. Essentially, any process that involves energy transformation will follow the principles of the 2nd law of thermodynamics.

4. Can the 2nd law of thermodynamics be violated or reversed?

No, the 2nd law of thermodynamics is a fundamental law of nature and has been extensively tested and proven over many years. It has never been observed to be violated or reversed. While it is possible to increase the organization or decrease the entropy in a small part of a system, the overall entropy of a closed system will always increase over time, following the 2nd law.

5. Are there any exceptions to the 2nd law of thermodynamics?

There are some exceptions or apparent violations of the 2nd law of thermodynamics, but these can be explained by understanding the entire system and its surroundings. For example, living organisms can decrease their own entropy by consuming energy from their environment, but this ultimately increases the total entropy of the entire system. Additionally, on a quantum scale, there are some phenomena that appear to violate the 2nd law, but these are still being studied and understood. Overall, the 2nd law of thermodynamics is a fundamental principle that is observed in all macroscopic systems.

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