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

AI Thread Summary
The discussion focuses on deriving the equation P/p = (R/MW)T from the ideal gas law PV = nRT using the relationship P = m/V. Participants clarify that n can be expressed as m/MW, leading to the substitution of variables to connect the equations. The conversion of volume and density is emphasized, with p defined as m/V. The final equation is confirmed by rearranging the terms appropriately, demonstrating the relationship between pressure, density, and temperature. The discussion successfully clarifies the derivation process and the significance of each variable involved.
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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:
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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?
 

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