δu = q - w

Definition

The equation $$\delta u = q - w$$ represents the first law of thermodynamics, indicating that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This relationship highlights how energy transfers occur within a closed system, linking concepts like heat transfer, work, and internal energy. Understanding this equation is crucial as it lays the groundwork for various thermodynamic analyses and helps in understanding energy conservation principles in both physical and chemical processes.

5 Must Know Facts For Your Next Test

1. In an isolated system where no heat or work is exchanged, the internal energy remains constant (\(\delta u = 0\)).
2. If heat is added to the system (q > 0), it results in an increase in internal energy unless work is done by the system (w > 0).
3. When a gas expands against an external pressure, it does work on the surroundings, leading to a decrease in its internal energy if no heat is added.
4. For a closed system undergoing a process, all changes in energy must account for the forms of energy transfer present: heat and work.
5. This equation also applies to chemical reactions, where heat generated or absorbed (q) and work done (w) can be critical for understanding reaction energetics.

Review Questions

• How does the equation δu = q - w help in understanding internal energy changes in a system?
  • The equation $$\delta u = q - w$$ shows that any change in internal energy of a system is directly influenced by the amount of heat added or removed and the work done by or on the system. When heat is absorbed by the system, it increases internal energy, while work done by the system decreases it. This relationship allows for predicting how various processes affect a system’s internal energy, essential for understanding thermodynamic cycles and reactions.
• Discuss how δu = q - w relates to conservation of energy principles in thermodynamics.
  • The equation $$\delta u = q - w$$ embodies the conservation of energy principle by illustrating that energy within a closed system is conserved. Any change in internal energy (δu) must come from either heat transfer (q) or work (w). Thus, this law ensures that all forms of energy are accounted for during transformations and interactions, reinforcing that energy cannot be created or destroyed but can only change forms.
• Evaluate the implications of δu = q - w in analyzing a chemical reaction within a closed container.
  • When analyzing a chemical reaction in a closed container using $$\delta u = q - w$$, one must consider both heat exchange with the surroundings and any work done due to volume changes. For example, if a reaction absorbs heat from its surroundings (endothermic), it contributes positively to δu. Conversely, if there is gas expansion against atmospheric pressure, this results in work being done by the system, reducing δu. Understanding these interactions helps predict reaction behavior and energy shifts during chemical processes.

Related terms

Internal Energy: The total energy contained within a system due to its temperature, pressure, and volume, which is associated with the random motion of molecules.

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

Work: The energy transfer that occurs when a force is applied to an object, causing it to move over a distance.