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

1. Nov 8, 2011

AzzidReign

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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: Nov 8, 2011
2. Nov 8, 2011

therealnihl

Hmm, what is big M and W?

3. Nov 8, 2011

AzzidReign

MW is the mass of one mole of air.

4. Nov 8, 2011

Macch

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

5. Nov 8, 2011

Macch

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

6. Nov 8, 2011

AzzidReign

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?