The number of mols in a balloon volume may be readily computed by dividing the air density, expressed in molar volume, at a given altitude into the balloon volume. The lift of the gas filling the balloon at any altitude is then equal to the number of mols multiplied by the buoyancy per mol. For example: To find the lift of the gas in a completely inflated (hydrogen filled) balloon of 20-foot diameter, at an altitude where the pound molar volume is 1000 ft.³ (This is equivalent to about 30,000 ft.):
Volume of a 20-foot diameter sphere = 4190 ft³.
Number of mols in sphere at this altitude = $\frac{4190}{1000} = 4.19$ mols
Buoyancy = 4.19 mols × 26.65 #buoyancy/mol = 111.7 # lift given by the gas at 30,000 feet.
In one step, this becomes:
$$
\text{Gross Lift/Balloon} = \frac{(\text{Balloon Volume}) \times (\text{Difference in molecular weights of air and lifting gas})}{\text{Molar Volume at a given altitude}}
$$
Conversely, the maximum altitude to which a given size balloon will carry itself and a specified load can be determined, as a molar volume, which may be evaluated from a graph of altitude versus molar volume. Such graphs, computed as in Part A of this Section, are given in Figures 19 and 20, at the left hand edge.
Hydrogen and helium lifts were computed for various molar volumes for spheres of lifting gas with diameters from 7.5 to 75 feet. Figures 19 and 20 were plotted using the values computed. To use these figures to determine the maximum altitude of a balloon with a specified pay load, enter the table with required buoyancy (balloon weight plus payload). Go vertically to the diagonal line representing the balloon's size, and then read horizontally on the left hand edge, either the molar volume or the equivalent altitude over
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