Proof Question Help (Deals with speed of sound in air)

Click For Summary

Homework Help Overview

The discussion revolves around deriving a relationship between pressure, density, and temperature in the context of the ideal gas law, specifically focusing on the equation PV=nRT and its transformation into P/p=(R/MW)T.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between the variables in the equations, questioning how to properly match terms from the initial equations to derive the final form. There is also a discussion about the meaning of the variables, particularly MW, and how to manipulate the equations to reach the desired form.

Discussion Status

Participants are actively engaging with the equations and attempting to clarify the relationships between the variables. Some have provided steps toward the transformation, while others are questioning specific terms and their meanings. There is no explicit consensus yet, but the discussion is progressing with various interpretations being explored.

Contextual Notes

There is a focus on ensuring that the definitions of the variables are clear, particularly the mass of one mole of air (MW). Participants are also considering the implications of rearranging the equations and how that affects the overall understanding of the problem.

AzzidReign
Messages
5
Reaction score
0

Homework Statement



Using the equation P=m/V show that the equation PV=nRT can become P/p=(R/MW)T

P=pressure
p=density of air
n=number of moles of gas
R=gas constant
T=temperature
m=mass
V=volume
MW=mass of one mole of air

Homework Equations



P=m/V
PV=nRT
P/p=(R/MW)T

The Attempt at a Solution



I was reading that n=m/MW, is that right?
And where I'm stuck at is properly matching each letter from the first equation with the second one and how that can translate to the final equation.
 
Last edited:
Physics news on Phys.org
Hmm, what is big M and W?
 
therealnihl said:
Hmm, what is big M and W?

MW is the mass of one mole of air.
 
PV = nRT
PV = (m/MW)RT
PV/m = RT/MW

as V is the volume of air with mass m:

p = m/V

P/p = RT/MW
 
PV = nRT
PV = (m/MW)RT
PV/m = RT/MW

as V is the volume of air with mass m:

p = m/V

P/p = RT/MW
 
Macch said:
PV = nRT
PV = (m/MW)RT
PV/m = RT/MW

as V is the volume of air with mass m:

p = m/V

P/p = RT/MW
So you said it's safe to basically put it as 1/p=V/m?
Which would allow you to plug it into the final equation?
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
946
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
8
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
4
Views
3K