δu = -w

Definition

The equation δu = -w expresses the principle of energy conservation in a closed system, indicating that the change in internal energy (δu) of a system is equal to the negative of the work done by the system (w). This highlights that when work is done by the system, it loses internal energy, reinforcing the idea that energy cannot be created or destroyed but only transformed from one form to another.

5 Must Know Facts For Your Next Test

1. In this equation, δu represents an infinitesimal change in internal energy, emphasizing that even small changes can significantly impact the system's energy balance.
2. The negative sign indicates that work done by the system results in a decrease in its internal energy, which is crucial for understanding energy exchanges.
3. This relationship is essential for processes like expansion or compression in gases, where work can lead to noticeable changes in temperature and pressure.
4. Understanding δu = -w helps clarify how systems respond to external forces and how they achieve thermal equilibrium through energy transfer.
5. It lays the groundwork for more complex thermodynamic analyses, including those involving heat transfer and changes in state variables.

Review Questions

• How does the equation δu = -w relate to the concept of internal energy in a thermodynamic system?
  • The equation δu = -w connects directly to internal energy by illustrating how the internal energy of a system changes when work is performed. When work is done by the system, it expends energy, leading to a decrease in its internal energy (δu). This relationship shows that internal energy is not static; it can change dynamically based on work interactions with the surroundings.
• Discuss the implications of δu = -w for understanding heat engines and their efficiency.
  • The equation δu = -w is vital for analyzing heat engines, as it helps explain how these systems convert heat into work. In an ideal engine cycle, the work done (w) comes from the difference in heat absorbed from a hot reservoir and heat expelled to a cold reservoir. Understanding this relationship allows engineers to assess efficiency by comparing work output to heat input, ultimately guiding improvements in engine design.
• Evaluate how δu = -w supports or contradicts traditional ideas about energy conservation in physical systems.
  • The equation δu = -w supports the traditional concept of energy conservation by showing that while a system may perform work and lose internal energy, the total energy within an isolated system remains constant. It illustrates that energy transformation occurs rather than loss, reinforcing the First Law of Thermodynamics. This framework helps debunk misconceptions about energy being created or destroyed during mechanical processes, emphasizing its role as a conserved quantity.

Related terms

Internal Energy:

The total energy contained within a system, associated with the random motion of its particles, including kinetic and potential energy.

Work:

A form of energy transfer that occurs when a force is applied over a distance, resulting in displacement in the direction of the force.

First Law of Thermodynamics:

A fundamental principle stating that energy cannot be created or destroyed, only transformed from one form to another, often summarized as ΔU = Q - W.