Final answer:
For a closed system undergoing a cycle, the change in internal energy and total momentum are always zero, and for reversible processes, the total change in entropy is zero. These principles are fundamental to the first and zeroth laws of thermodynamics and conservation laws.
Step-by-step explanation:
For a closed system undergoing a cycle the quantities that are always zero include the change in internal energy, the total change in entropy for reversible processes, and, in the absence of external forces, the change in total momentum. In regards to internal energy, the first law of thermodynamics indicates that for a cyclical process, ΔU (change in internal energy) is zero since the system returns to its initial state at the conclusion of each cycle; mathematically, this is due to Δ0 = Q - W, where Q is the net heat transfer, and W is the net work done by the system. For reversible processes, the total change in entropy is also zero, demonstrating that the system has returned to its initial state without any increase or decrease in entropy.
The applicability of the zeroth law of thermodynamics ensures that a closed system in thermal equilibrium maintains uniform temperature throughout. And as per the conservation laws, in a closed system without external forces, there is no change in the total momentum, because the mass remains constant and the net external force is zero. The preservation of these quantities across a cycle is foundational to understanding concepts such as thermal efficiency and the limits imposed by the second law of thermodynamics.