Question

If a steel cylinder of helium gas is heated from \(50^{\circ} \mathrm{C}\) to \(100{ }^{\circ} \mathrm{C}\), does the motion of helium atoms increase or decrease?

Short answer

The motion of helium atoms increases.

Step-by-step solution

Understanding Temperature and Kinetic Energy

The kinetic energy of a gas is directly related to its temperature. When the temperature of a gas increases, the molecules gain more kinetic energy, meaning they move faster. Conversely, when the temperature decreases, the kinetic energy of the molecules decreases, resulting in slower movement. This relationship is described by the kinetic molecular theory of gases.

Analyze Initial and Final Temperatures

In the problem, the initial temperature of the helium gas is given as \(50^{\circ} \mathrm{C}\) and the final temperature is \(100^{\circ} \mathrm{C}\). This indicates a temperature increase.

Relate Temperature Change to Motion of Atoms

As established in Step 1, an increase in temperature results in an increase in the kinetic energy of gas molecules. Therefore, when the helium gas is heated from \(50^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\), the motion of helium atoms increases.

Key concepts

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. In the context of gases like helium, the kinetic energy of the gas molecules is directly proportional to their speed. When we talk about a gas's temperature, we are actually discussing the average kinetic energy of its particles.
Each gas molecule moves at a different speed, but collectively, they contribute to the overall kinetic energy of the gas. The faster the molecules move, the greater their kinetic energy. As a result, any increase in temperature will typically result in an increase in kinetic energy, causing the gas molecules to move more vigorously.

Gas Temperature

The temperature of a gas is a measure of the average kinetic energy of its molecules. The higher the temperature, the faster the gas molecules move on average. This principle is a cornerstone of the kinetic molecular theory.

• When considering a gas, such as helium, if we heat it from a lower temperature to a higher one, the average speed and energy of the helium atoms increase.
• This concept helps to explain why gases expand when heated—since their molecules move more quickly and collide more frequently, they require more space.

This correlation between temperature and kinetic energy ensures that temperature increases lead to faster molecular movement, as seen when the helium gas in the exercise is heated.

Helium Atoms

Helium atoms are unique because they belong to the noble gases, meaning they are relatively inert and do not easily react with other elements. Despite being simple atoms, they follow the same physical laws as other gas molecules when it comes to kinetic energy and temperature.

• When heated, helium atoms accelerate because the added heat energy translates to higher kinetic energy.
• Despite their non-reactive nature, helium atoms still adhere to the fundamental principles of the kinetic molecular theory.

By understanding how helium atoms behave at varying temperatures, we can better predict and explain phenomena such as the increase in motion when they are heated from 50°C to 100°C, as seen in the problem exercise.