Re: How much does air weigh?

Dan,

You can use the Ideal Gas Law to determine the weight (mass) of the air in 
your balloon.  The law is

pV = nRT

The variables in this equation, with SI units are:

p - pressure (Pa)
V - volume (m^3)
n - moles (mol)
R - universal gas constant - 8.314 Joules / mole Kelvin
T - temperature (K)

If you solve for the number of moles, n, you can then use the following 
relationship to calculate the mass:

m = nM

where

m - mass (g)
M - molecular weight (g / mol)

This mass is what a force must react against when accelerating the object 
and is sometimes described as the inertial mass (per Newton's Second Law).

Now, if your ballon is filled with room temperature air (not hot), it may 
not "feel" like it weighs the amount calculated by the above equations.  
This is because it is surrounded by air and has neutral buoyancy.  Also, 
as you move it through the air, you will feel more resistance than would 
be expected by its mass.  This is because of the drag on the balloon by 
the surrounding air.

Once you heat the air in the ballon, it will have buoyancy becuase it will 
be less dense than the surrounding air.  If you repeat the calculation 
above, using the higher temperature, you will find there is less mass of 
air in the same volume of balloon.  Density is just the ratio of mass to 
volume.

In the atmosphere, density decreases with altitude, so you hot air balloon 
will rise until its average density equals the average density of the 
surrounding air, thus achieving neutral buoyancy.

These concepts are explained in greater detail in any college level 
physics textbook.

Christopher M. Seaman
Alcoa Technical Center