A balloon is launched at sea level, where the air pressure is 100 kPa. The density in the hot-ai

step 1 We know that the pressure is directly proportional to the volume, sorry, to the density of the a

A balloon is launched at sea level, where the air pressure...

A balloon is launched at sea level, where the air pressure is $100 \mathrm{kPa}$. The density in the hot-air chamber is $1.0 \mathrm{~kg} / \mathrm{m}^{3}$. What is the density of the air when the balloon has risen to a height where the atmospheric pressure is $33 \mathrm{kPa} ?$ A. $3.0 \mathrm{~kg} / \mathrm{m}^{3}$ B. $1.0 \mathrm{~kg} / \mathrm{m}^{3}$ C. $0.66 \mathrm{~kg} / \mathrm{m}^{3}$ D. $0.33 \mathrm{~kg} / \mathrm{m}^{3}$

A balloon is launched at sea level, where the air pressure is $100 \mathrm{kPa}$. The density in the hot-air chamber is $1.0 \mathrm{~kg} / \mathrm{m}^{3}$. What is the density of the air when the balloon has risen to a height where the atmospheric pressure is $33 \mathrm{kPa} ?$
A. $3.0 \mathrm{~kg} / \mathrm{m}^{3}$
B. $1.0 \mathrm{~kg} / \mathrm{m}^{3}$
C. $0.66 \mathrm{~kg} / \mathrm{m}^{3}$
D. $0.33 \mathrm{~kg} / \mathrm{m}^{3}$

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Key Concepts

Ideal Gas Law

The ideal gas law establishes a relationship between pressure, volume, temperature, and density. When temperature is held constant, the law implies that density is directly proportional to pressure. This relationship allows for the determination of a gas's density at different pressures, assuming the gas behaves ideally.

Pressure-Density Proportionality

Under conditions of constant temperature, the density of a gas changes proportionally with its pressure. This means that if the pressure is reduced by a certain factor, the density is reduced by the same factor, making it straightforward to calculate the new density when pressure changes.

Atmospheric Pressure Variation

Atmospheric pressure decreases as altitude increases. This variation affects the density of the surrounding air, and understanding this concept is essential for problems involving changes in atmospheric conditions, such as calculating the density of air at higher altitudes based on given pressure values.

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