Question

Helium atoms in a closed container at room temperature are constantly colliding with one another and with the walls of their container. Does this "perpetual motion" violate the law of conservation of energy? Explain.

Short answer

No, this motion does not violate energy conservation; it's a transfer of existing energy.

Step-by-step solution

Understanding the Problem

First, we need to understand what is meant by 'perpetual motion' in the context of gas particles. In thermodynamics, atoms and molecules of a gas are in constant, random motion, and they collide with each other and the walls of the container.

Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed but only transformed from one form to another. We need to consider whether this constant motion of helium atoms involves any energy changes that would violate this law.

Analyzing Molecular Motion

The kinetic energy of the helium atoms comes from thermal energy, which is maintained by the temperature of the gas. As long as the temperature remains constant, energy is transferred between atoms during collisions without any net energy loss or gain.

Closed System Consideration

A closed container means that no energy is being introduced from outside. The energy within this system is already accounted for; it is distributed among the particles as thermal energy.

Conclusion

Since no energy is being added or removed from the container, the perpetual motion of helium atoms does not create new energy; it's merely the constant transformation of kinetic energy among particles. Thus, this motion does not violate the law of conservation of energy.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, temperature, and energy. It explains how these elements interact in a system. In this context, thermodynamics helps us understand the behavior of helium atoms in a closed container. When these atoms collide with each other and the walls of the container, they demonstrate a key aspect of thermodynamic principles.
This perpetual motion within the container is a form of kinetic energy. The overall energy of the system is determined by the temperature, which corresponds to the average kinetic energy of the gas particles. Thermodynamic laws, such as the law of conservation of energy, govern these interactions and movements.

• Energy transformation, not creation, occurs during atomic collisions.
• The system’s temperature remains constant, supporting stable kinetic energy transfer.

Therefore, the study of thermodynamics is crucial in analyzing how energy conservation applies, even in systems that appear to be in constant motion, like our helium atoms.

Kinetic Energy

Kinetic energy is the energy associated with the motion of objects. For helium atoms in a closed container, kinetic energy is derived from their constant motion. Every time these atoms move and collide, they possess kinetic energy, which is a fundamental concept in physics.
The temperature of the gas is a direct measure of the average kinetic energy of its molecules. If the temperature stays constant, the kinetic energy of helium atoms remains unchanged during their collisions. Here's why this is important:

• Kinetic energy fluctuates between particles but doesn't disappear.
• Collisions redistribute, but do not eliminate, energy in the system.

Understanding kinetic energy helps clarify why such collisions and perpetual motion don't lead to energy loss or creation, aligning with the conservation of energy principles.

Molecular Motion

Molecular motion refers to the constant, random movement of atoms and molecules. In our helium atoms' scenario, this motion represents their constant movement and the frequent collisions they undergo within a closed container.
These collisions illustrate energy transfer between molecules, explained by their kinetic energy. Molecular motion is understood through:

• Random movement patterns due to thermal energy.
• Energy transfer during direct collisions, maintaining system stability.

Ultimately, molecular motion in a closed system appears frenetic but is quite stable. Energy consistently shifts among particles without any loss outside of the system, adhering to energy conservation laws.

Closed System

A closed system is one that does not exchange matter with its surroundings, though it can exchange energy to a certain extent. In the context of helium atoms in the container, this closed system means that no energy enters or exits the system from external sources.
This bounded environment ensures that all energy transformations happen within. The system's total energy, present as kinetic energy among atoms, remains constant.

• Maintains energy equilibrium within the container.
• No external factors alter internal energy distribution.

Therefore, the concept of a closed system supports the law of conservation of energy by containing energy transformations internally, without adding or losing energy to the outside environment.