The zeppelin Hindenburg exploded on May 6, 1937, in Lakehurst, New Jersey. The accident was due to this type of dirigible using hydrogen (density of H2, M = 2g/mol) as a gas. It carried up to 70 passengers and crew. Estimate how many passengers and crew the Hindenburg could have carried had they used helium gas (density He, M = 4 g/mol) instead.

Compute the weight difference between a hydrogen fill and a helium fill. You will need to know the volume of the derigibile and (for the number of fewer paeengers with helium), the average weight per passenger, including luggage and extra seats. According to

http://www.unmuseum.org/hindenburg.htm ,
the volume was 7.06 million cubic feet

I would assume an average weight per passenger of 120 kilograms

They are only asking for an estimate, so making some reasonable assumptions is necessary and acceptable.

wow I still don't understand how to do this problem. Are there any equations i need to use?

To estimate the number of passengers and crew the Hindenburg could have carried if it used helium gas instead of hydrogen, we need to consider the difference in density between the two gases.

The density of hydrogen gas (H2) is approximately 2 g/mol, while the density of helium gas (He) is approximately 4 g/mol. As helium is less dense than hydrogen, it would require a smaller volume to provide lift.

First, we need to calculate the difference in density between hydrogen and helium:

Density difference = Density of hydrogen - Density of helium
Density difference = 2 g/mol - 4 g/mol
Density difference = -2 g/mol

Next, we need to determine the lifting capacity of the Hindenburg.

Assuming that each passenger and crew member weighs 75 kg, we can estimate the weight (W) supported by 1 mole of gas in the Hindenburg using the ideal gas law:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Since the volume (V) and temperature (T) remain constant, we can rewrite the equation as:

P = (nRT)/V

The weight is equal to the mass (m) times the acceleration due to gravity (g):

W = m * g

Assuming the pressure (P) remains constant, we have:

W = (nRT)/V * g

To account for the density difference, we can rewrite this equation using the difference in density (Δρ) between hydrogen and helium:

W = (nRT)/V * g * Δρ

Now, let's calculate the difference in lifting capacity between hydrogen and helium:

Weight difference = (nRT)/V * g * Δρ

Since we are comparing the weight difference, we can set it equal to the weight capacity (W_H2) of the Hindenburg using hydrogen:

W_H2 = (n_H2 * R * T)/V * g * Δρ

To calculate the weight capacity (W_He) if helium was used, we can rearrange the equation:

W_He = (n_He * R * T)/V * g * Δρ

By comparing the weight capacities, we can determine the number of passengers and crew the Hindenburg could have carried with helium:

(Weight of passengers and crew) / (Weight capacity per person with helium) = Total number of passengers and crew

Assuming a weight of 75 kg per passenger and crew member, we can use this equation to estimate the maximum number of passengers and crew:

Total number of passengers and crew = (W_H2/W_He) * (Weight of passengers and crew with helium)

Please note that this is a simplified estimation, and other factors like safety regulations, structural limitations, and other operational requirements should also be taken into consideration.