# Time of Impact of Gas Molecules on the Inner Wall of a Pressure Vessel

• Zahid Iftikhar
In summary, the derivation of the relation for pressure of gas involves considering the time for which the wall of the vessel and the gas molecules interact, rather than the time between successive collisions. This can cause confusion as the time of impact between the wall and molecules is what causes the change in momentum and pressure. However, in a steady state situation, the average pressure is determined by the frequency and number of collisions. This can be seen in a problem involving machine gun bullets being fired at Superman's chest.
Zahid Iftikhar
In derivation of relation for pressure of Gas ,(see pic below) the time for rate of change of momentum of molecules should be the time for which the wall of the vessel and the molecules kept interacting with each other, not the time between successive collisions. As circumscribed below, my confusion is how the time between two such collisions can be equal to the time of impact between the wall and the molecules. The time of impact has actually caused the change of momentum, thereby causing the pressure. I further argue, that let us suppose there are 100 or so molecules colliding just once on the wall, bounce back, and then never return (just assume), during this one-time collision, pressure has been exerted on the wall of the vessel. In this case, there is no time between successive collisions involved. I would be obliged if learned people on this forum help me to understand. High regards
Zahid

Zahid Iftikhar said:
I further argue, that let us suppose there are 100 or so molecules colliding just once on the wall, bounce back, and then never return (just assume), during this one-time collision, pressure has been exerted on the wall of the vessel.

In that case you would get a force exerted on the wall, and of course you could divide that force by the wall's area and get a pressure. But it would be a pressure pulse, and would last for a very short time. In that case, your reasoning is correct.

But if you go back and carefully read the derivation of the expression for the pressure of a gas in a box, you should see it stated that we are interested in a steady state pressure. There is a huge number of molecules colliding with the wall, and we are interested in the average pressure exerted on the wall due to the collisions. In this case we are interested in how often they collide and the number of such collisions.

There's a chapter-end problem in some textbooks where machine gun bullets are fired at Superman's chest. It's the same situation as above. To get the average force exerted on Superman we look at the frequency of collisions and the number and nature of the collisions.

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## 1. What is the time of impact of gas molecules on the inner wall of a pressure vessel?

The time of impact of gas molecules on the inner wall of a pressure vessel refers to the amount of time it takes for gas molecules to collide with and exert pressure on the inner wall of a pressure vessel.

## 2. Why is the time of impact important in pressure vessel design?

The time of impact is important in pressure vessel design because it affects the amount of stress and strain that the vessel experiences. A longer time of impact means a longer duration of pressure, which can lead to higher levels of stress and potential failure of the vessel.

## 3. How is the time of impact calculated?

The time of impact can be calculated using the ideal gas law, which relates pressure, volume, and temperature of a gas. It can also be estimated using experimental data and simulations.

## 4. How does the time of impact vary with different gases?

The time of impact can vary with different gases due to differences in their molecular size, shape, and speed. For example, smaller and faster-moving gas molecules will have shorter times of impact compared to larger and slower-moving molecules.

## 5. Can the time of impact be controlled in pressure vessel design?

Yes, the time of impact can be controlled in pressure vessel design by adjusting factors such as gas pressure, temperature, and flow rate. Additionally, the design of the vessel itself, such as the shape and size of the inner wall, can also influence the time of impact.

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