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

• AzzidReign

## 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

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:

Hmm, what is big M and W?

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

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?