Physics - Thermodynamics - Pressure caused by Nitrogen atoms hitting a surface

[WolfeSieben]

Hi there,

I'm a first timer on this forum and am hoping to get some help.

Homework Statement

4.00×10^23 nitrogen molecules collide with a 18.0 cm^2 wall each second. Assume that the molecules all travel with a speed of 350 m/s and strike the wall head on.

Homework Equations

F = MA
Pressure (Pascals) = Newtons/M^2
Avagraddo's Number = 6.02 x 10^23 molecules per mole

The Attempt at a Solution

Alright, so I'm not sure what I did wrong here so I'm hoping someone here can help.

To start I figured out the weight of the nitrogen molecules:

(4.00 x 10^23 molecules of N2)/(6.02 x 10^23 molecules per mole)

= 0.664 moles

.664 moles x 28g/mol (as nitrogen is diatomic, 2x14g/mol) = 18.6 g = 0.0186kg


Then to get the force:
When the molecules hit the wall, I am assuming there is an instant acceleration in the opposite direction. thus;

F = ma

(0.0186kg)(350 m/s/s)

= 6.51 Newtons

Then, Pressure = F/A (Pascals)

(6.51N)/(0.0018m^2)

= 3616 Pascals.

This is the answer I obtained on my own, and with the help of a tutor and yet my assignment is saying it is wrong. Can you please shed some light on my mistake(s)?

Thank you!

 

[Dick]

You are given that the velocity is 350 m/s. Just because you incorrectly write it as 350 m/s/s doesn't magically turn it into an acceleration. Momentum is p=m*v. So the force is also equal to the rate of change of momentum with respect to time since dp/dt=m*dv/dt=m*a=F. Try taking that approach.

 

[WolfeSieben]

Alright, for this course my prof said we do not have to use derivatives, and I am actually quite unfamiliar with how to use them. so is there any other way to approach the problem?

Just so I can clear up the concept for my own knowledge;
In the question itself it says it is over a time of 1 second. so wouldn't that mean even though the momentum is (Mass x velocity) can I not just divide it by that 1 second interval mentioned in the initial question to make it into an acceleration of 350 m/s/s?

Thanks for your time and help.

 

[Dick]

Right. Now I see how you are doing it. I'm not sure what's going wrong. But are you supposed to assume the molecules bounce off of the wall or do they stick to it? That would alter your change in velocity.

 

[WolfeSieben]

From all of the other example problems from this chapter, they all say they bounce off the wall. So for this one I am assuming they would just bounce off. I also double checked and the question is asking for the value in Pascals so I know I obviously made a mistake, but i just don't see where.

 

[Dick]

From all of the other example problems from this chapter, they all say they bounce off the wall. So for this one I am assuming they would just bounce off. I also double checked and the question is asking for the value in Pascals so I know I obviously made a mistake, but i just don't see where.

If they bounce, then they come in at 350 m/s and then they go the other way at 350 m/s. What's the correct change in velocity? Yours is right if they stick.

 

[WolfeSieben]

so the change in velocity should be a total of 700 m/s?

This is one of those lightbulb moments in my mind haha.

 

[WolfeSieben]

So i just re-did the last couple steps and i came out with a answer of 7,233 Pa.
Could you please just verify if this correct, I only have 1 attempt left to answer the question and just want to be sure.

Thank you so much for your help, it is much appreciated!

 

[Dick]

So i just re-did the last couple steps and i came out with a answer of 7,233 Pa.
Could you please just verify if this correct, I only have 1 attempt left to answer the question and just want to be sure.

Thank you so much for your help, it is much appreciated!

Mmm. Tough call. I got 7235 Pa. But I was rounding Avogadro's number and using using an molecular weight of EXACTLY 28. You are pretty close I think. If the homework rejects it I hope you can appeal.

 

[WolfeSieben]

Perfect, So I punched in 7233 and it said the proper answer was 7230, but it gave me full credit for the answer.

Thanks again.

 

[Dick]

Very welcome. The important thing was the lightbulb.