Question

A \(\mathrm{CO}_{2}\) fire extinguisher is located on the outside of a building in Massachusetts. During the winter months, one can hear a sloshing sound when the extinguisher is gently shaken. In the summertime there is often no sound when it is shaken. Explain. Assume that the extinguisher has no leaks and that it has not been used.

Short answer

In winter, the low temperature keeps more \( \mathrm{CO}_{2} \) in liquid form, creating a sloshing sound when shaken. In summer, warmer temperatures convert more \( \mathrm{CO}_{2} \) to gas, reducing the sloshing sound.

Step-by-step solution

Understanding the Problem

The problem involves a carbon dioxide \( (\mathrm{CO}_{2}) \) fire extinguisher, which behaves differently in winter and summer regarding the sound it makes when shaken. We need to understand why there is a difference in the sound heard during these two seasons.

Review Concepts of States of Matter

\( \mathrm{CO}_{2} \) in a fire extinguisher exists as both liquid and gas. The state changes with temperature due to CO2's properties. At lower temperatures (winter), more \( \mathrm{CO}_{2} \) is likely in the liquid state, while at higher temperatures (summer), more may become gas.

Winter Analysis

During winter, the low temperatures in Massachusetts can cause \( \mathrm{CO}_{2} \) inside the extinguisher to remain largely in a liquid state. Liquid inside a container allows for a sloshing sound because of the movement of the liquid when the extinguisher is gently shaken.

Summer Analysis

In the summertime, higher temperatures can cause more of the \( \mathrm{CO}_{2} \) to convert to gas, since gases occupy more space and the pressure increases. With less liquid present, there may be little to no sloshing sound when the extinguisher is shaken.

Conclusion

In summary, the presence of a sloshing sound in winter and its absence in summer is due to the temperature-dependent state of \( \mathrm{CO}_{2} \) within the extinguisher. Cold temperatures keep more \( \mathrm{CO}_{2} \) in liquid form, while warm temperatures cause it to become more gaseous.

Key concepts

States of Matter

Every substance can exist in different forms or states, namely solid, liquid, and gas. These states depend largely on temperature and pressure. Carbon dioxide (\(\mathrm{CO}_{2}\)) in a fire extinguisher can exist as a gas and as a liquid. The state that the \(\mathrm{CO}_{2}\) is in depends on the temperature and pressure inside the extinguisher.
During winter, the cold temperatures cause \(\mathrm{CO}_{2}\) to remain in liquid form, as gases lose energy and become liquids. In warmer conditions, like in the summer, \(\mathrm{CO}_{2}\) takes on a gas state because the molecules have more energy and can move freely. Recognizing how temperature changes affect the state of matter is essential for understanding how fire extinguishers work.

Temperature Effects on Gases

Temperature plays a key role in how gases behave. As the temperature increases, the molecules of a gas gain energy and move faster.
When the temperature decreases, these molecules slow down and can come closer together, sometimes forming a liquid if the conditions are right. This behavior is central to how \(\mathrm{CO}_{2}\) fire extinguishers operate. At higher temperatures in summer, the \(\mathrm{CO}_{2}\) molecules move rapidly, and more of the \(\mathrm{CO}_{2}\) turns into gas, which fills the available space in the extinguisher.

• In winter, temperature decrease results in reduced energy of \(\mathrm{CO}_{2}\) molecules.
• The slowed down molecules are closer, increasing the chance of staying in a liquid state.
• The change in the state of \(\mathrm{CO}_{2}\) is what causes the sloshing sound in winter.

Liquid to Gas Conversion

The process of converting a liquid to a gas is called vaporization. In the case of \(\mathrm{CO}_{2}\) fire extinguishers, this conversion is crucial. During the summer, the heat outside causes liquid \(\mathrm{CO}_{2}\) inside a fire extinguisher to vaporize.
This increases the pressure within the extinguisher.
When all or most of the \(\mathrm{CO}_{2}\) has converted to gas, there's no liquid left to create a sloshing sound when the extinguisher is shaken. Similarly, in winter, the cooler environment prevents this vaporization, meaning liquid \(\mathrm{CO}_{2}\) remains inside. Thus, when you shake the extinguisher, the liquid moves around, creating a sound. Understanding this conversion helps explain the absence of sound in summer compared to winter.

Seasonal Temperature Variation

Seasons have a profound impact on temperature variation and, subsequently, on how substances like \(\mathrm{CO}_{2}\) behave. In places like Massachusetts, winters can be extremely cold, leading to temperatures that keep \(\mathrm{CO}_{2}\) close to its liquid state. Conversely, summer can be quite warm, causing \(\mathrm{CO}_{2}\) to remain primarily in gaseous form.
The seasonal temperature changes create different environmental conditions that affect the behavior of \(\mathrm{CO}_{2}\) in fire extinguishers.

• Winter keeps \(\mathrm{CO}_{2}\) in a liquid state, provoking a sloshing sound.
• Summer raises temperatures, increasing gaseous conversion, leading to little or no sloshing sound.

Thus, understanding these temperature variations across seasons helps explain the observations made with the \(\mathrm{CO}_{2}\) fire extinguisher.