Finding RMS Speed of Gas Atoms: Ideal Gas

Click For Summary
SUMMARY

The discussion focuses on calculating the root mean square (RMS) speed of gas atoms in an ideal gas scenario with a density of 2.4 kg/m³, pressure of 2.0 × 105 Pa, and temperature of 300 K. The relevant equation used is p = (1/3) * (N/V) * v2, where N is the total number of atoms. Participants clarify that the density can be expressed as mN/V, linking it to the RMS speed calculation without needing to specify the number of atoms explicitly, as the problem is framed for one atom.

PREREQUISITES
  • Understanding of ideal gas laws
  • Familiarity with the concept of root mean square speed
  • Knowledge of density and its relation to mass and volume
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the RMS speed formula for ideal gases
  • Learn about the relationship between pressure, density, and temperature in gas laws
  • Explore the concept of Avogadro's number and its application in gas calculations
  • Investigate the differences between moles and individual atoms in gas calculations
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone involved in gas law applications or calculations related to ideal gases.

AllenHe
Messages
74
Reaction score
0

Homework Statement


The ideal gas has a density of 2.4 kgm–3 at a pressure of 2.0 × 105 Pa and a
temperature of 300 K.Find the root mean square speed of the gas atoms.


Homework Equations



p=(1/3)*(Nm/V)*v(squared)


The Attempt at a Solution


I tried to make v(squared) the subject, but N(the number of atoms) is not given, and when I looked at the answer, it made v(squared) the subject, and omitted N. I don's understand why do they have to omit N, is it because we are suppose to find the speed for one atom?
Sorry for my bad English.
 
Physics news on Phys.org
AllenHe said:

Homework Statement


The ideal gas has a density of 2.4 kgm–3 at a pressure of 2.0 × 105 Pa and a
temperature of 300 K.Find the root mean square speed of the gas atoms.


Homework Equations



p=(1/3)*(Nm/V)*v(squared)


The Attempt at a Solution


I tried to make v(squared) the subject, but N(the number of atoms) is not given, and when I looked at the answer, it made v(squared) the subject, and omitted N. I don's understand why do they have to omit N, is it because we are suppose to find the speed for one atom?
Sorry for my bad English.

Well, N/V is the number of particles per unit of volume. If you multiply this by m, the mass per particle, you get the mass per unit volume. What's another name for that?
 
Thanks

cepheid said:
Well, N/V is the number of particles per unit of volume. If you multiply this by m, the mass per particle, you get the mass per unit volume. What's another name for that?

Oh, I get it, so you mean the density is mN/v, right?
 
AllenHe said:
Oh, I get it, so you mean the density is mN/v, right?

Yes, he means that in,

P= mnvrms2/3V

Density is mn/V

m=molar mass
n=number of moles

But you have written N=avogadro's number
m=mass of one molecule ?

Are you giving this formula for 1 mole of gas ?
 
AllenHe said:
Oh, I get it, so you mean the density is mN/v, right?

Yes, that is exactly what I meant :)
 
sankalpmittal said:
Yes, he means that in,

P= mnvrms2/3V

Density is mn/V

m=molar mass
n=number of moles

But you have written N=avogadro's number
m=mass of one molecule ?

Are you giving this formula for 1 mole of gas ?

The OP explicitly stated that N was the total number of atoms. So this problem isn't doing anything with moles.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
5K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 13 ·
Replies
13
Views
1K
Replies
10
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 9 ·
Replies
9
Views
914