What does the equation ∆U = q + w represent?

The equation ∆U = q + w represents the first law of thermodynamics, which describes how the internal energy (∆U) of a system changes in response to heat (q) added to or removed from the system and work (w) done on or by the system. This equation emphasizes that internal energy is a state function and can be altered by energy transfer through heat and work.

In this context, "q" represents heat transfer, which can be either absorbed (positive q) or released (negative q), while "w" represents work done on the system (positive w) or by the system (negative w). Thus, the equation effectively captures the essence of energy conservation in thermodynamic processes: the change in internal energy of a system is equal to the heat added to it and the work done on it. This foundational principle allows understanding the energy exchanges taking place in physical and chemical processes.

The other choices relate to different concepts in thermodynamics, but they do not accurately define the relationship captured by this specific equation. For example, heat capacity pertains to a material's ability to absorb heat and is not directly derived from this equation, while the conservation of mass is a separate principle not covered by the internal energy equation. Similarly,