# Homework Help: Deriving an equation for the density of air

1. Jan 20, 2004

### sickboy

First of all, I'm new to this forum, so please excuse any newbie etiquette errors I have made =)

My problem is this: I'm doing a lab report on an experiment where we attempted at measuring the density of air. I won't go to the details, but basically we just measured air on different pressures.

The task is to, given the following equations, derive an equation for the density of dry air as a function of the density of moist air, relative humidity, pressure of saturated 'steam' (can't figure a better translation..Oh yeah, I'm a Finn :) ) and the total pressure.

The first equation:
$$\frac{M_i^'}{M_i}=\frac{\rho_i^'}{\rho_i}=1-\frac{M_i-M_v}{M_i}*\frac{e}{p}\approx 1-0,378\frac{e}{p}$$

...and the second:
$$f=\frac{F}{F_m}*100\%=\frac{e}{e_m}*100\%$$

Notations:
$$M_i$$ = molemass for completely dry air
$$M_i^'$$ = molemass for moist air (air with some water vapour in it)
rhos are densities of dry & moist air, respectively
$$M_v$$ = molemass for water
e = partitial pressure of water vapour
p = total pressure
f = relative humidity
$$e_m$$ = the pressure required for the condensation of water ( again, not so sure of the translation)
F = absolute humidity (measured in, for example, g/m^3)

I hope I didn't forget anything. I have been trying to solve this with my mates for days and days now, and I'd really appreciate any help...

Oh yeah, and I'm sorry, but I can't provide you with any of my sketches, as all I have are red-rimmed eyes and a heap of trash paper =)