What is the relationship between ΔU, q, and w in a closed system with no fields?

In thermodynamics, ΔU represents the change in internal energy of a system, q denotes the quantity of heat added to the system, and w represents the work done on the system. The first law of thermodynamics states 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 can be mathematically stated as:

ΔU = q - w.

However, in the context of the question, if we define work done on the system (as is often the convention in some fields), we can represent the equation as:

ΔU = q + w,

where positive q corresponds to heat entering the system, and positive w indicates work done on the system (as opposed to work done by the system).

Thus, the correct relationship given the context of the question is that the change in internal energy (ΔU) is equal to the heat added to the system (q) plus the work done on the system (w), which highlights how both heat and work contribute to the overall energy state of a closed system. This formulation provides a clear understanding of energy conservation within closed systems devoid of external fields.