δu = q - w

Definition

The equation δu = q - w represents the first law of thermodynamics, which states that the change in internal energy (δu) of a system is equal to the heat added to the system (q) minus the work done by the system (w). This fundamental relationship emphasizes the conservation of energy principle, illustrating how energy can neither be created nor destroyed, only transformed from one form to another. It connects heat transfer, work interaction, and internal energy, providing a framework for understanding energy exchanges in various processes.

5 Must Know Facts For Your Next Test

1. This equation indicates that if a system does work on its surroundings, it loses internal energy, which must be compensated by either adding heat or by doing less work.
2. In an isolated system, where no heat or work is exchanged, the internal energy remains constant, showcasing the conservation of energy principle.
3. The signs of q and w are important; q is positive when heat is added to the system and negative when heat is released, while w is positive when work is done by the system and negative when work is done on the system.
4. This equation forms the basis for analyzing thermal processes in chemical engineering, including reactions and phase changes.
5. Understanding this relationship helps in calculating efficiency in energy conversion processes and evaluating performance in thermal systems.

Review Questions

• How does the equation δu = q - w illustrate the principle of energy conservation in thermodynamic processes?
  • The equation δu = q - w illustrates energy conservation by showing that the change in internal energy of a system results from the balance between heat added and work done. If a system receives heat, it increases its internal energy. Conversely, if the system performs work on its surroundings, it loses internal energy. Thus, this relationship emphasizes that while energy can change forms through heat transfer and work interactions, the total energy within a closed system remains constant.
• Discuss how positive and negative values of q and w affect the internal energy (δu) of a thermodynamic system.
  • Positive values of q indicate that heat is added to the system, which increases internal energy (δu). Negative values of q show that heat is being lost from the system, resulting in decreased internal energy. For work (w), positive values mean that the system is doing work on its surroundings, thereby reducing internal energy. Conversely, negative work indicates that work is being done on the system, leading to an increase in internal energy. Understanding these sign conventions is crucial for analyzing thermodynamic processes accurately.
• Evaluate how δu = q - w can be applied to real-world chemical engineering problems involving heat engines or refrigeration cycles.
  • In real-world applications like heat engines or refrigeration cycles, δu = q - w helps engineers optimize energy efficiency. For example, in a heat engine, maximizing q (heat input) while minimizing w (work output) can enhance performance. Conversely, in refrigeration systems, engineers aim to manipulate these variables to increase cooling efficiency. By applying this equation, engineers can predict system behavior under different conditions and improve designs for better thermal management and energy use.

Related terms

Internal Energy: The total energy contained within a system due to the kinetic and potential energies of its molecules.

Heat Transfer: The movement of thermal energy from one object or substance to another due to a temperature difference.

Work: The energy transferred when a force is applied to an object causing it to move, which can occur in various forms such as mechanical or electrical.