If the work done on the system or by the system is zero, which one of the following statements for a gas kept at a certain temperature is correct?

The first law of thermodynamics establishes the relationship between heat transfer (Q), work done (W), and the change in internal energy (ΔU) of a system. Mathematically, this is expressed as ΔU = Q − W, where W is the work done by the system, or ΔU = Q + W, where W is the work done on the system. In a scenario where the work done on or by the system is zero (W = 0), the equation simplifies to ΔU = Q. This implies that any energy transferred into or out of the system as heat results in an equivalent change in the system's internal energy [1]. Therefore, the change in internal energy is exactly equal to the flow of heat in or out of the system, as no energy is being diverted to or from mechanical work.

Sources

1. [1] https://www.khanacademy.org/science/in-in-class11th-physics/in-in-11th-physics-thermodynamics/in-in-laws-of-thermodynamics/a/what-is-the-first-law-of-thermodynamics