During WW1 U Class Zeppelins had hydrogen cells that contained 55,795 cubic meters of gas.
According to Peter Kämpf's excellent, detailed explanation of Zeppelin mechanics they began missions with their hydrogen cells filled with roughly 33% hydrogen. The rest of the volume contained air. Because hydrogen expands as air pressure falls starting at 33% allowed Zeppelins to reach high altitudes without rupturing their gas cells.
However given the constants below I'm not sure how 33% hydrogen produced enough lift to get a Zeppelin off the ground.
Sea Level, 0 Meters:
Temp Celsius: 15°
Temp Kelvin: 288.15°
Pressure Pascals: 101,325
Gas Moles per cubic meter: 42.29
Air mass per cubic meter: 1.221 Kg
Hydrogen mass per cubic meter: .085 Kg
55,795 cubic meters of gas cells * 33% full = 18,412 cubic meters hydrogen
18,412 cubic meters of displaced air mass = 22,481 Kg
18,412 cubic meters of hydrogen = 1,566 Kg
Useful lift = 22,481 kg - 1,566 kg = 20,915 Kg
The empty weight of a U class Zeppelin was 25,750 Kg. That's without fuel, ballast or bombs. If useful lift was less than empty weight how did it take off?
At 5,000 meters altitude useful lift stays the same because although the hydrogen cells expand and displace more air the atmosphere is less dense and has less mass per cubic meter. Lift at 0 meters altitude is the same as lift at 5,000 meters altitude.
Another detail I found interesting is that according to Wiki the U Class Zeppelin produced 64,750 Kg of useful lift.
When I plug in numbers at sea level that suggests that the gas cells were filled to the top with 100% hydrogen.
55,795 cubic meters of gas cells
55,795 cubic meters of displaced air mass = 68,126 Kg
55,795 cubic meters of hydrogen = 4,743 Kg
Useful lift = 68,126 Kg - 4,743 Kg = 63,383 Kg
However if the hydrogen cells were filled to 100% it couldn't climb without bleeding hydrogen all the way up. It should be noted that at 5,000 meters the air is thin and useful lift drops by almost half.
Altitude, 5,000 Meters:
Temp Celsius: -17.5°
Temp Kelvin: 255.65°
Pressure Pascals: 49,586
Gas Moles per cubic meter: 23.33
Air mass per cubic meter: .674 Kg
Hydrogen mass per cubic meter: .047 Kg
55,795 cubic meters of gas cells at 100% full
55,795 cubic meters of displaced air mass = 37,605 Kg
55,795 cubic meters of hydrogen = 2,622 Kg
Useful lift = 37,605 Kg - 2,622 Kg = 34,983 Kg
34,983 Kg of lift is maybe barely enough to stay afloat with fuel, ballast and bombs.
But even if they did it this way when the Zeppelin descended the Hydrogen cells would be mostly empty and would fill with air causing the ship to gain weight and crash.
At 0 meters
55,795 cubic meters of gas cells filled with 66% air = 36,825 cubic meters
36,825 cubic meters of air mass = 44,963 Kg!