Re: Sneakernet
Posted: Tue Sep 02, 2025 5:27 pm
Please render today's discussion in BBCode. We have a limited amount of math today, but for presentation it will help to appear in text form. I can find tune the BBCode as needed.
Of course. Here is today's discussion rendered in BBCode, as requested. I have enclosed the mathematical equations within [tex][/tex] tags for proper rendering in a forum environment.
User: Hello Again! A couple of days local time have passed since our last session. Our mechanical engineer has chosen to stay out of the line of fire for now. He appears to have offered insight for us and is now waiting to see what happens. From my perspective (physics) that is a helpful position for an engineer to take. An engineer can use physics and can report on aspects of how things work, but it is up to the physicist to discover how the Universe works. In working with you on this problem, we started with a very simple question, and our studies have provided some encouragement, but now we are facing the problem at a deeper level. I am grateful you are there to share in this exploration. May I enlist you in study of what happens to an individual molecules when it encounters a wall (steel in our hypothetical pipe) that is approaching at 11 km/s. If my calculator is correct, that would be 11 millimeters in one microsecond. Our engineer has predicted that an encounter between a molecule of nitrogen and a steel wall at this velocity would cause the electric forces of the respective molecules to be overcome. Let's focus on this aspect of the situation. Can you find any studies that might have been done on this interaction? It seems likely to me (as I think about it) that many studies must have been done because of military activity over the centuries, and because of the challenges of space flight and high speed air flight today.
Gemini: I can help you investigate the interaction of a nitrogen molecule with a steel wall at such high velocities. Your engineer is correct that at a relative velocity of 11 km/s, the kinetic energy of the incoming molecules is so high that it will overcome the typical electrical forces that hold a molecule together. This phenomenon has been extensively studied, particularly in the context of hypervelocity impacts, reentry physics, and plasma dynamics.
Physics of Hypervelocity Impacts
When a gas molecule like nitrogen (N
2
) hits a solid surface at 11 km/s (1.1×10
4
m/s), the collision is an inelastic process where the molecule's kinetic energy is converted into other forms of energy. Here's a breakdown of what happens:
Kinetic Energy Calculation: The kinetic energy (KE) of a single nitrogen molecule can be calculated using the formula KE=
2
1
mv
2
. The mass (m) of a nitrogen molecule is approximately 4.65×10
−26
kg.
[tex]KE = \frac{1}{2}(4.65 \times 10^{-26} \text{ kg})(1.1 \times 10^4 \text{ m/s})^2 \approx 2.82 \times 10^{-18} \text{ J}[/tex]
Bond Dissociation: To break the triple bond of a nitrogen molecule, the energy required is about 9.8 eV or 1.57×10
−18
J. Our calculated kinetic energy (2.82×10
−18
J) is more than enough to dissociate the nitrogen molecule into two separate nitrogen atoms.
Ionization: Ionizing a nitrogen atom (stripping an electron) requires 14.5 eV or 2.32×10
−18
J. Our calculated kinetic energy is also sufficient to cause ionization, creating a charged particle and a free electron (N
+
+ e
−
). This is the plasma state your engineer mentioned.
Heating the Wall: The remaining energy from the collision will be transferred as heat to the wall. This energy transfer will cause a sharp, localized increase in the wall's temperature. Over time, as more molecules collide with the wall, this heating will propagate and increase the overall temperature of the pipe.
The Phenomenon of Sputtering
At these extreme velocities, a phenomenon called sputtering occurs. Sputtering is the process where atoms are ejected from a solid material due to the bombardment of the material by energetic particles. In our scenario, the hypervelocity nitrogen molecules hitting the steel pipe will not only heat it, but will also have enough energy to knock iron and other atoms off the pipe's surface. This would be a form of material loss and would generate additional friction and heat.
Relevant Studies
While specific military documents are not publicly available, the physics of these interactions has been extensively studied in publicly accessible research.
NASA Hypervelocity Impact Studies: NASA has done a lot of research on micrometeoroid and orbital debris impacts on spacecraft, which are essentially hypervelocity impacts. These studies focus on the resulting damage and the physics of plasma formation.
Aerospace Engineering Research: High-speed atmospheric reentry and hypersonic flight require a deep understanding of how air molecules interact with vehicle surfaces. A major focus of this research is predicting the heat flux and drag, which are direct consequences of the kinetic to thermal energy conversion you're asking about. The shock layer in front of a hypersonic vehicle is a region of intensely hot, dissociated, and ionized gas (a plasma) due to these collisions.
Fusion Research: The science of nuclear fusion involves colliding particles at immense speeds to overcome repulsive forces. While the scale is different, the underlying physics of kinetic energy conversion and plasma formation is directly relevant.
Conclusion
The short answer is yes, extensive studies have been done. Your engineer is correct that the kinetic energy of an incoming nitrogen molecule at 11 km/s is sufficient to cause it to dissociate and even ionize. The collision would create a localized plasma and transfer energy to the pipe's wall, increasing its temperature. Our simulation needs to account for this energy transfer, and the energy required to both dissociate and ionize the gas, in order to get a more realistic result.
User: I would like to offer a slight correction to your analysis. In our scenario, the nitrogen molecule is at rest, and it is rudely interrupted by the oncoming steel plate at the bottom of the pipe. I wonder if this change of perspective makes any difference? The kinetic energy is in the steel wall as it approaches the nitrogen molecule. I am thinking of offering our discussion for study, and we will want to have the wording correct to avoid confusion.
Gemini: You're right. Thank you for that correction. It's a critical distinction to make for clarity and proper framing of the physics.
From a physics perspective, the numbers don't change. This is due to the principle of relativity in classical mechanics. Whether the nitrogen molecule is at rest and the pipe wall is approaching it at 11 km/s or the pipe wall is at rest and the nitrogen molecule is approaching it at 11 km/s, the relative velocity between them is identical. This means the kinetic energy of the collision is the same in both frames of reference.
The kinetic energy of the nitrogen molecule in the pipe's frame of reference is what we calculated before:
[tex]KE = \frac{1}{2} m_{N_2} v_{relative}^2[/tex]
However, for a study, it's more intuitive and accurate to describe the kinetic energy as being associated with the pipe, since it's the large, moving object. This energy is transferred from the pipe to the air molecules. The physics of what happens to the molecule upon impact—dissociation, ionization, and energy transfer—remains the same.
Your proposed wording is much more precise and will be valuable for avoiding confusion in your forum. It accurately reflects the reality of the situation: the pipe is doing the work on the air, converting its macroscopic kinetic energy into the microscopic thermal energy of the gas.
Of course. Here is today's discussion rendered in BBCode, as requested. I have enclosed the mathematical equations within [tex][/tex] tags for proper rendering in a forum environment.
User: Hello Again! A couple of days local time have passed since our last session. Our mechanical engineer has chosen to stay out of the line of fire for now. He appears to have offered insight for us and is now waiting to see what happens. From my perspective (physics) that is a helpful position for an engineer to take. An engineer can use physics and can report on aspects of how things work, but it is up to the physicist to discover how the Universe works. In working with you on this problem, we started with a very simple question, and our studies have provided some encouragement, but now we are facing the problem at a deeper level. I am grateful you are there to share in this exploration. May I enlist you in study of what happens to an individual molecules when it encounters a wall (steel in our hypothetical pipe) that is approaching at 11 km/s. If my calculator is correct, that would be 11 millimeters in one microsecond. Our engineer has predicted that an encounter between a molecule of nitrogen and a steel wall at this velocity would cause the electric forces of the respective molecules to be overcome. Let's focus on this aspect of the situation. Can you find any studies that might have been done on this interaction? It seems likely to me (as I think about it) that many studies must have been done because of military activity over the centuries, and because of the challenges of space flight and high speed air flight today.
Gemini: I can help you investigate the interaction of a nitrogen molecule with a steel wall at such high velocities. Your engineer is correct that at a relative velocity of 11 km/s, the kinetic energy of the incoming molecules is so high that it will overcome the typical electrical forces that hold a molecule together. This phenomenon has been extensively studied, particularly in the context of hypervelocity impacts, reentry physics, and plasma dynamics.
Physics of Hypervelocity Impacts
When a gas molecule like nitrogen (N
2
) hits a solid surface at 11 km/s (1.1×10
4
m/s), the collision is an inelastic process where the molecule's kinetic energy is converted into other forms of energy. Here's a breakdown of what happens:
Kinetic Energy Calculation: The kinetic energy (KE) of a single nitrogen molecule can be calculated using the formula KE=
2
1
mv
2
. The mass (m) of a nitrogen molecule is approximately 4.65×10
−26
kg.
[tex]KE = \frac{1}{2}(4.65 \times 10^{-26} \text{ kg})(1.1 \times 10^4 \text{ m/s})^2 \approx 2.82 \times 10^{-18} \text{ J}[/tex]
Bond Dissociation: To break the triple bond of a nitrogen molecule, the energy required is about 9.8 eV or 1.57×10
−18
J. Our calculated kinetic energy (2.82×10
−18
J) is more than enough to dissociate the nitrogen molecule into two separate nitrogen atoms.
Ionization: Ionizing a nitrogen atom (stripping an electron) requires 14.5 eV or 2.32×10
−18
J. Our calculated kinetic energy is also sufficient to cause ionization, creating a charged particle and a free electron (N
+
+ e
−
). This is the plasma state your engineer mentioned.
Heating the Wall: The remaining energy from the collision will be transferred as heat to the wall. This energy transfer will cause a sharp, localized increase in the wall's temperature. Over time, as more molecules collide with the wall, this heating will propagate and increase the overall temperature of the pipe.
The Phenomenon of Sputtering
At these extreme velocities, a phenomenon called sputtering occurs. Sputtering is the process where atoms are ejected from a solid material due to the bombardment of the material by energetic particles. In our scenario, the hypervelocity nitrogen molecules hitting the steel pipe will not only heat it, but will also have enough energy to knock iron and other atoms off the pipe's surface. This would be a form of material loss and would generate additional friction and heat.
Relevant Studies
While specific military documents are not publicly available, the physics of these interactions has been extensively studied in publicly accessible research.
NASA Hypervelocity Impact Studies: NASA has done a lot of research on micrometeoroid and orbital debris impacts on spacecraft, which are essentially hypervelocity impacts. These studies focus on the resulting damage and the physics of plasma formation.
Aerospace Engineering Research: High-speed atmospheric reentry and hypersonic flight require a deep understanding of how air molecules interact with vehicle surfaces. A major focus of this research is predicting the heat flux and drag, which are direct consequences of the kinetic to thermal energy conversion you're asking about. The shock layer in front of a hypersonic vehicle is a region of intensely hot, dissociated, and ionized gas (a plasma) due to these collisions.
Fusion Research: The science of nuclear fusion involves colliding particles at immense speeds to overcome repulsive forces. While the scale is different, the underlying physics of kinetic energy conversion and plasma formation is directly relevant.
Conclusion
The short answer is yes, extensive studies have been done. Your engineer is correct that the kinetic energy of an incoming nitrogen molecule at 11 km/s is sufficient to cause it to dissociate and even ionize. The collision would create a localized plasma and transfer energy to the pipe's wall, increasing its temperature. Our simulation needs to account for this energy transfer, and the energy required to both dissociate and ionize the gas, in order to get a more realistic result.
User: I would like to offer a slight correction to your analysis. In our scenario, the nitrogen molecule is at rest, and it is rudely interrupted by the oncoming steel plate at the bottom of the pipe. I wonder if this change of perspective makes any difference? The kinetic energy is in the steel wall as it approaches the nitrogen molecule. I am thinking of offering our discussion for study, and we will want to have the wording correct to avoid confusion.
Gemini: You're right. Thank you for that correction. It's a critical distinction to make for clarity and proper framing of the physics.
From a physics perspective, the numbers don't change. This is due to the principle of relativity in classical mechanics. Whether the nitrogen molecule is at rest and the pipe wall is approaching it at 11 km/s or the pipe wall is at rest and the nitrogen molecule is approaching it at 11 km/s, the relative velocity between them is identical. This means the kinetic energy of the collision is the same in both frames of reference.
The kinetic energy of the nitrogen molecule in the pipe's frame of reference is what we calculated before:
[tex]KE = \frac{1}{2} m_{N_2} v_{relative}^2[/tex]
However, for a study, it's more intuitive and accurate to describe the kinetic energy as being associated with the pipe, since it's the large, moving object. This energy is transferred from the pipe to the air molecules. The physics of what happens to the molecule upon impact—dissociation, ionization, and energy transfer—remains the same.
Your proposed wording is much more precise and will be valuable for avoiding confusion in your forum. It accurately reflects the reality of the situation: the pipe is doing the work on the air, converting its macroscopic kinetic energy into the microscopic thermal energy of the gas.