Calculating the average force of a molecule in a vessel

In summary, the problem asks to calculate the average force exerted by an oxygen molecule bouncing back and forth between opposite sides of a cubical vessel with a side length of 0.1 m. The formula used is F=p/t, where t is found to be 0.2 m / 484 m/s = 4.13 * 10^-4 seconds. The factor of 2 is multiplied on the impulse because each impact on a given wall involves the molecule striking the wall with velocity v and bouncing back, resulting in a net change in velocity. This is why the distance traveled between impacts is doubled to 0.2 m.
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Homework Statement



Suppose an oxygen molecule traveling at the speed of 484 m/s bounces back and forth between opposite sides of a cubical vessel 0.1 m on a side. What is the average force the molecule exerts on one of the walls of the container?

Homework Equations


F=p/t

The Attempt at a Solution


t=0.2 m / 484 m/s = 4.13 *10^-4 seconds

In a collision v changes direction so delta p = 2*mv

(mv was calculated in a previous question so it is known)

The average force can then be calculated as:

F = 2mv / t

My question here is, how come when calculation the time, they use 0.2 m and not 0.1 as given in the assignment? Is this because the molecule moves back and forth 0.1 m during the collision?

Second question: why do they multiply a factor 2 on the impulse? Where does this come from?
 
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  • #2
They are considering impacts on a given wall. How far does the molecule travel between successive impacts there?
Each impact, the molecule strikes the wall with velocity v, head on, and bounces back. What is the net change in velocity?
 

1. How do you calculate the average force of a molecule in a vessel?

The average force of a molecule in a vessel can be calculated by dividing the total force exerted on the vessel by the total number of molecules present. This can also be expressed as the pressure of the vessel, which is equal to the force divided by the surface area of the vessel.

2. What factors affect the average force of a molecule in a vessel?

The average force of a molecule in a vessel is affected by several factors, including the temperature and volume of the vessel, the number of molecules present, and the type of molecules present. Additionally, the type of vessel and its shape can also impact the average force.

3. How does temperature affect the average force of a molecule in a vessel?

As the temperature of a vessel increases, the average force of a molecule in the vessel also increases. This is because higher temperatures result in faster molecular movement, leading to more collisions and a higher average force on the vessel walls.

4. What is the relationship between pressure and average force of a molecule in a vessel?

Pressure and average force are directly related, as an increase in pressure will result in a higher average force of molecules on the vessel walls. This relationship can be described by the ideal gas law, which states that pressure is directly proportional to the number of molecules and the temperature, and inversely proportional to the volume of the vessel.

5. Can the average force of a molecule in a vessel be negative?

No, the average force of a molecule in a vessel cannot be negative. While individual molecules can exert a negative force on a vessel wall, the overall average force will always be positive since it takes into account the net force of all the molecules present in the vessel.

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