In a period of 2s, 4.8E23 nitrogen molecules strike a wall area of 8.6 cm^2.
If the molecules move at 308 m/s and strike the wall head-on in a perfectly elastic collision, find the pressure exerted on the wall. The mass of one N2 molecule is 4.68E-26kg.
Answer in terms of kPa.
I found the mass of all the molecules by multiplying the total molecules by the mass given. I converted the area to .00086 m^2, and found P by dividing the Force (mass times g or 9.8) by the area. I got 255.985 Pa, and .255985 kPa. I don't think I did this right, can someone please check my work?
The pressure on the wall is the rate (per second) at which the momentum of colliding molecules is changed per unit area. For elastic head-on collisions, each molecular collision changes its momentum by
delta (mv) = m * 2 * 308 m/s
where m is the mass of the molecule.
At the wall, half of the molecules are heading towards the wall and half are going away
P = (1/2)*delta(mv)*(number density)
= (delta mv)*(number of molecules hitting wall per second per area)
In your case,
(number of molecules hitting wall per second per area) = (4.8*10^23)/[2s * 8.6*10^-4 m^2] = 2.79*10^26 s^-1 m^-2
Look up the mass of a nitrogen atom (in kg) and complete the calculation. The answer will be in pascals.
To find the pressure exerted on the wall by the nitrogen molecules, you need to use the formula:
Pressure = Force / Area
First, let's calculate the force exerted on the wall by the nitrogen molecules.
The force experienced by the wall when a molecule collides with it and bounces off elastically can be found using Newton's second law of motion. The change in momentum of the molecule during the collision is equal to two times the mass of the molecule multiplied by its velocity.
Change in momentum = 2 * mass * velocity
Now, let's calculate the total change in momentum caused by all the nitrogen molecules striking the wall.
Number of molecules = 4.8E23
Mass of one N2 molecule = 4.68E-26 kg
Velocity of the molecules = 308 m/s
Total change in momentum = Number of molecules * (2 * mass * velocity)
Next, we need to calculate the force applied to the wall.
Force = Total change in momentum / Time interval
The time interval is given as 2 seconds.
After calculating the force, we can determine the pressure by dividing the force by the area of the wall.
Area of the wall = 8.6 cm^2 = 8.6E-4 m^2
Pressure = Force / Area
Finally, we need to convert the pressure to kPa.
1 Pascal (Pa) = 1 N/m^2
1 kPa = 1000 Pa
Therefore, to convert the pressure from Pa to kPa, divide the pressure value in Pa by 1000.
Now, using the given values and formulas, you can re-calculate the pressure exerted on the wall and check your work.