To determine how much H2 gas is required to lift a 65 kg object vertically via combustion, we need to consider the principles of buoyancy and the properties of hydrogen gas. We also need to assume ideal conditions and neglect factors like air resistance. Let's proceed with the calculations:
- Buoyant Force: The buoyant force acting on an object is equal to the weight of the fluid displaced by the object. In this case, the fluid is air, and we want the buoyant force to equal the weight of the object for it to be lifted.
Buoyant Force = Weight of the Object
- Weight of the Object: Weight = mass * acceleration due to gravity
Given: Mass of the object = 65 kg Acceleration due to gravity = 9.8 m/s^2
Weight of the Object = 65 kg * 9.8 m/s^2 = 637 N
- Buoyant Force = Weight of the Object: Buoyant Force = Volume of H2 gas * Density of air * gravitational acceleration
Hydrogen gas (H2) is lighter than air, so the buoyant force can be achieved by displacing an equivalent volume of air with H2 gas.
Density of air at standard conditions = 1.225 kg/m^3
Buoyant Force = Volume of H2 gas * 1.225 kg/m^3 * 9.8 m/s^2
- Volume of H2 gas: The molar mass of H2 gas is approximately 2 g/mol. Therefore, the density of H2 gas is 0.0899 kg/m^3 (at standard conditions).
To find the volume of H2 gas required, we divide the mass of the object (65 kg) by the density of H2 gas.
Volume of H2 gas = Mass of the object / Density of H2 gas
Volume of H2 gas = 65 kg / 0.0899 kg/m^3 = 723.03 m^3
- Speed of Ascent: To determine the speed at which the object would move when lifted by the H2 gas, additional information is needed, such as the force generated by the combustion of H2 gas and the design of the lifting mechanism. Without those details, it is not possible to calculate the exact speed of ascent.
It's important to note that working with hydrogen gas can be hazardous, and proper safety precautions should be followed when handling and using it.
Please keep in mind that the calculations provided are based on idealized conditions and simplifications, and real-world scenarios may involve additional complexities and considerations.