Question

Suppose a flexible container is filled with a gas at an elevation of \(9000 \mathrm{ft}\). What will happen to this gas if the container is transported to sea level?

Short answer

The gas in the flexible container will get compressed when brought from elevation of 9000 ft to sea level due to increase in atmospheric pressure.

Step-by-step solution

Understand the Correlation between Altitude and Atmospheric Pressure

At a higher altitude, the air pressure is lower because there's less air above to apply pressure downwards. This is why at 9000 ft, the gas within the container was subject to lower atmospheric pressure.

Analyze the Transition to Sea Level

When the gas-filled container is transported to sea level, the atmospheric pressure is substantially higher than that at 9000 ft. As the container is flexible, this atmospheric pressure will exert force on the container.

Realize the Impact on the Gas

The increased pressure from the atmosphere forces the flexible container to compress. This increased pressure externally reduces the volume of the gas in the container and thus the gas gets compressed.

Key concepts

Altitude and Atmospheric Pressure

When we talk about altitude, we are referring to the height above sea level. One of the essential factors that change with altitude is atmospheric pressure. The higher you go up in elevation, the less atmospheric pressure there is. This happens because there is less air above to exert a downward force. Essentially, the higher you climb, the fewer air molecules are pressing down on you and everything around.
This phenomenon is vital for understanding how gases behave in different environments. At 9000 feet, for example, the pressure is significantly lower compared to at sea level because the column of air above is shorter. Recognizing this difference in pressure helps us understand why gases expand or contract in different altitudes.

Volume and Pressure Relationship

For gases, there is a fascinating relationship between volume and pressure, described by Boyle's Law. This law tells us that the pressure of a gas is inversely proportional to its volume, provided the temperature remains constant. In simpler terms, if you increase the pressure on a gas, its volume decreases and vice versa.
Mathematically, Boyle's Law is expressed as: \[ P_1 V_1 = P_2 V_2 \] Where:

• \( P_1 \) and \( V_1 \) are the initial pressure and volume
• \( P_2 \) and \( V_2 \) are the final pressure and volume

Understanding this relationship is crucial when dealing with gases in situations where pressure changes, like moving from high altitude to sea level.

Flexible Container

A flexible container is specially designed to adjust its shape and volume according to the pressure exerted on it. Imagine a balloon filled with air; as the atmospheric pressure increases, the balloon's walls are pushed inward, compressing the gas inside. This is similar to what happens to our gas-filled container when it is relocated from high altitude to sea level.
The flexibility of the container allows it to accommodate the changes in pressure without rupturing or cracking. As the gas inside the flexible container is subjected to higher atmospheric pressure at sea level, the pressure causes the container to compress, decreasing the volume of the gas within it. This mechanism ensures that the container can safely adapt to various atmospheric conditions while keeping the gas securely contained.