A hot air balloon along with its cargo has a mass of 4.0 x 10⁵ kg, and it holds 7.0 x 10⁵ m³ of hot air. It is floating at a constant height in air with a density of 1.29 kg/m³. What is the density of the hot air in the balloon? A) 1.4 kg/m³ B) 0.72 kg/m³ C) 0.57 kg/m³ D) 0.86 kg/m³ E) 0.43 kg/m³

Question

Quizplus · Accepted Answer

The hot air balloon and its cargo are in equilibrium with the surrounding air, which means the weight of the balloon and its cargo is equal to the weight of the air displaced by the balloon. We can use the formula:

Weight of air displaced = density of air x volume of air displaced x g

where g is the acceleration due to gravity.

The weight of the balloon and its cargo is given as 4.0 x 10^15 kg.

The volume of air displaced can be found using the formula:

Volume of air displaced = mass of hot air in balloon / density of air

We are given the volume of hot air as 7.0 x 10^13 m^3, so we can find the mass of the hot air:

Mass of hot air in balloon = density of hot air x volume of hot air

We can rearrange this formula to find the density of hot air:

Density of hot air = mass of hot air in balloon / volume of hot air

Putting all of these values into the equation, we get:

4.0 x 10^15 kg = 1.29 kg/m^3 x volume of air displaced x g

volume of air displaced = 3.10 x 10^15 m^3

Mass of hot air in balloon = density of hot air x volume of hot air

Mass of hot air in balloon = density of hot air x 7.0 x 10^13

density of hot air = (4.0 x 10^15) / (1.29 x 3.10 x 10^15 / 7.0 x 10^13)

density of hot air = 0.72 kg/m^3

Therefore, the density of the hot air in the balloon is 0.72 kg/m^3, which corresponds to answer choice B.

A Hot Air Balloon Along with Its Cargo Has a Mass