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

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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. It establishes that the pressure (P) divided by the density (p) of air equals the gas constant (R) divided by the molar mass (MW) of air, multiplied by the temperature (T). Key transformations include substituting n with m/MW and recognizing that density is defined as p=m/V. The final equation is confirmed as valid through proper manipulation of the initial equations.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Knowledge of density and its relationship to mass and volume (P=m/V)
  • Familiarity with the concept of molar mass (MW)
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the derivation of the ideal gas law from kinetic molecular theory
  • Learn about the significance of the gas constant (R) in various gas equations
  • Explore the concept of molar mass and its calculation for different gases
  • Investigate applications of the ideal gas law in real-world scenarios, such as atmospheric science
USEFUL FOR

Students in physics or chemistry, educators teaching gas laws, and anyone interested in thermodynamics and the behavior of gases.

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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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