δu = q - w

Definition

The equation $$\delta u = q - w$$ expresses the change in internal energy ($$\delta u$$) of a system in relation to heat added to the system ($$q$$) and work done by the system ($$w$$). This relationship highlights the first law of thermodynamics, which states that energy cannot be created or destroyed but can only change forms. By understanding this equation, you can analyze how energy is transferred and transformed within a system, affecting both internal energy and enthalpy, as well as various applications of the first law in real-world scenarios.

5 Must Know Facts For Your Next Test

1. The term $$\delta u$$ represents the change in internal energy, which is dependent on the amount of heat exchanged and work done.
2. $$q$$ can be positive or negative; it is positive when heat is absorbed by the system and negative when heat is released.
3. $$w$$ is defined as positive when work is done by the system on its surroundings and negative when work is done on the system by its surroundings.
4. In a closed system where no mass is exchanged with the surroundings, all energy changes are accounted for through heat and work.
5. This equation emphasizes that any increase in internal energy must come from added heat or work done on the system, reinforcing the concept of energy conservation.

Review Questions

• How does the equation $$\delta u = q - w$$ relate to the conservation of energy within a closed system?
  • The equation $$\delta u = q - w$$ illustrates how energy conservation is maintained in a closed system by showing that any change in internal energy ($$\delta u$$) results from heat exchange ($$q$$) and work interactions ($$w$$). It indicates that if a system absorbs heat, its internal energy increases unless it does an equivalent amount of work on its surroundings. This relationship reinforces the idea that while energy may change forms, it is neither created nor destroyed.
• Discuss how changes in internal energy ($$\delta u$$) can affect enthalpy in thermodynamic processes.
  • Changes in internal energy ($$\delta u$$) can directly influence enthalpy, particularly when considering processes at constant pressure. Enthalpy ($$H$$) is defined as $$H = u + PV$$, where $$P$$ is pressure and $$V$$ is volume. An increase in internal energy due to heat absorption ($$q > 0$$) at constant pressure results in an increase in enthalpy as well. Understanding this relationship helps to analyze heat transfer during various thermodynamic processes, such as phase changes or chemical reactions.
• Evaluate how the application of $$\delta u = q - w$$ can be observed in real-life scenarios, such as engines or refrigerators.
  • In real-life applications like engines or refrigerators, the equation $$\delta u = q - w$$ serves as a fundamental principle for understanding their operation. In an engine, fuel combustion adds heat ($$q > 0$$), increasing internal energy, while work ($$w > 0$$) is done by moving parts to produce mechanical output. Conversely, a refrigerator extracts heat from its interior ($$q < 0$$) to maintain cool temperatures while doing work on the refrigerant to transfer heat outside. Analyzing these systems through this equation provides insights into efficiency and performance based on energy transformations.

Related terms

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

Enthalpy: A thermodynamic quantity equal to the internal energy of a system plus the product of its pressure and volume, often used in the context of heat transfer during processes at constant pressure.

First Law of Thermodynamics: A principle stating that energy cannot be created or destroyed, only transformed from one form to another, emphasizing the conservation of energy within thermodynamic systems.