The equation $$\delta e = q - w$$ represents the change in internal energy of a system, where $$\delta e$$ is the change in energy, $$q$$ is the heat added to the system, and $$w$$ is the work done by the system. This relationship illustrates how energy is conserved in thermodynamic processes, emphasizing that the energy of a closed system is constant unless affected by heat transfer or work interactions. Understanding this equation is fundamental to grasping how energy moves and transforms within systems.
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The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed, which is encapsulated in the equation $$\delta e = q - w$$.
If heat is absorbed by the system, $$q$$ is positive; if heat is released, $$q$$ is negative.
When work is done by the system (like expanding against a piston), $$w$$ is positive; when work is done on the system (like compressing a gas), $$w$$ is negative.
This equation allows for the calculation of internal energy changes in various processes such as heating, cooling, and phase changes.
It highlights that any increase in internal energy comes from heat absorbed or work done on the system and vice versa.
Review Questions
How does the equation $$\delta e = q - w$$ illustrate the principle of energy conservation in thermodynamic systems?
The equation $$\delta e = q - w$$ directly illustrates the principle of energy conservation by showing that any change in internal energy of a system (represented by $$\delta e$$) results from the balance between heat added to the system ($$q$$) and work done by the system ($$w$$). This means that if a system gains heat, its internal energy increases unless it does work on its surroundings, which would decrease its internal energy. Conversely, if the system loses heat or does work on its surroundings, its internal energy decreases. Thus, this equation encapsulates how energy transitions occur within thermodynamic systems while adhering to the conservation principle.
Discuss how changes in heat transfer and work done can affect the internal energy of a closed system as expressed in $$\delta e = q - w$$.
Changes in heat transfer and work done significantly impact a closed system's internal energy as expressed in $$\delta e = q - w$$. When heat is added to the system ($$q > 0$$), it can increase the internal energy unless offset by work done by the system ($$w > 0$$). For example, if a gas expands doing work on its surroundings, it might lose some internal energy despite gaining heat. Conversely, when work is done on the system ($$w < 0$$), it can lead to an increase in internal energy even if no heat is added. This relationship underscores how both heat and work contribute to determining a system's overall energetic state.
Evaluate a scenario where a gas is heated while simultaneously doing work on its surroundings. How does this scenario illustrate the application of $$\delta e = q - w$$?
In a scenario where a gas is heated while simultaneously doing work on its surroundings, we can analyze how this illustrates $$\delta e = q - w$$. As heat ($$q > 0$$) flows into the gas, we expect an increase in internal energy. However, if during this process, the gas expands and performs work ($$w > 0$$) on its surroundings, some of that gained internal energy will be used to do that work. Consequently, while heating increases its internal energy, the work done reduces it. The final change in internal energy ($$\delta e$$) will be determined by subtracting the work from the added heat, demonstrating how both factors influence each other and are essential for understanding real-world thermodynamic processes.