δu = q - w

Definition

The equation δu = q - w expresses the first law of thermodynamics, which states that the change in internal energy (δu) of a closed system is equal to the heat added to the system (q) minus the work done by the system (w). This fundamental relationship highlights how energy is conserved in thermodynamic processes, emphasizing that energy can neither be created nor destroyed, only transformed from one form to another. Understanding this equation is essential for analyzing various thermodynamic cycles and processes.

5 Must Know Facts For Your Next Test

1. This equation is a direct expression of the conservation of energy principle, which states that energy cannot be created or destroyed, only transformed.
2. The terms 'q' and 'w' can be positive or negative depending on whether heat is added to or removed from the system, and whether work is done by or on the system.
3. In an isothermal process, where temperature remains constant, the internal energy change (δu) is zero; thus, q = w.
4. For a closed system undergoing a cyclic process, the net change in internal energy over one complete cycle is zero, leading to the relation that q = w.
5. This equation forms the foundation for understanding more complex thermodynamic processes such as adiabatic processes, where no heat transfer occurs.

Review Questions

• How does the equation δu = q - w relate to the concept of energy conservation in thermodynamics?
  • The equation δu = q - w illustrates the principle of energy conservation in thermodynamics by showing how the internal energy of a system changes due to heat transfer and work done. It emphasizes that any increase in internal energy must result from heat added to the system or work done on it. Conversely, if work is done by the system or heat is lost, the internal energy decreases, reinforcing that energy within a closed system remains constant.
• Discuss how varying conditions (such as isothermal or adiabatic processes) affect the application of δu = q - w.
  • In an isothermal process, the temperature remains constant, leading to no change in internal energy (δu = 0). Thus, according to δu = q - w, any heat added (q) must equal the work done (w), meaning that all heat input goes into performing work. In contrast, during an adiabatic process, there is no heat exchange with the surroundings (q = 0), so all changes in internal energy are due to work done on or by the system. These conditions demonstrate how different thermodynamic scenarios can alter the balance between heat and work as described by this equation.
• Evaluate how δu = q - w can be used to analyze real-world thermodynamic systems like engines or refrigerators.
  • The equation δu = q - w is crucial in analyzing real-world thermodynamic systems like engines and refrigerators by providing insight into their efficiency and operational principles. For example, in an engine cycle, understanding how much heat (q) enters and how much work (w) is produced helps assess its efficiency. Similarly, for refrigerators, where work is done on the system to transfer heat from a cooler area to a warmer one, this equation helps understand how effectively they operate in terms of energy usage and performance. By applying this relationship, engineers can optimize designs for better energy conversion and usage.

Related terms

Internal Energy: The total energy contained within a system, including kinetic and potential energies at the molecular level.

Heat Transfer: The process by which thermal energy moves from one body or system to another due to a temperature difference.

Work: In thermodynamics, work refers to the energy transfer that occurs when a force acts through a distance, which can affect the internal energy of a system.