Question

How much weight can be lifted by a Hydrogen (& also separately for Helium) filled balloon of 10 cubic Meter, at sea level & at a temp. of 20 Degree Centigrade. Pl. describe the inputs used.

Answer 1

Question#18865

How much weight can be lifted by a Hydrogen (̄) also separately for Helium) filled balloon of 10 cubic Meter, at sea level ̄ at a temp. of 20 Degree Centigrade. Pl. describe the inputs used.

Solution:

Let:

$$V = 10 \, \mathrm{m}^3$$ $$T = 20{}^\circ \mathrm{C}$$

m–?

$F = mg$, $m = \frac{F}{g}$ were: F – buoyant force

According to the Archimedes’ principle:

$$F = (\rho_{air} - \rho_{hydrogen}) V g$$

Were: $\rho_{air}$ – density of air, $\rho_{hydrogen}$ – density of hydrogen, $g = 9,8 \, \mathrm{m/s}^2$

$$\rho_{air} = 1.29 \, \mathrm{kg/m}^3, \quad \rho_{hydrogen} = 0.09 \, \mathrm{kg/m}^3$$ $$m = \frac{(\rho_{air} - \rho_{hydrogen}) V g}{g} = (\rho_{air} - \rho_{hydrogen}) V = (1.29 - 0.09) \times 10 = 12 \, \mathrm{kg}$$

Answer: 12 kg.

For Helium: $\rho = 0.178 \, \mathrm{kg/m}^3$, $m = (1.29 - 0.178) \times 10 = 11.12 \, \mathrm{kg}$