Final answer:
The quality of water at the beginning of the heat rejection process in a Carnot-cycle engine with water as the working fluid is 1 (or 100% vapor). At the end of the heat rejection process, just before the isothermal compression at the low-temperature reservoir, the quality is 0 (or 100% liquid).
Step-by-step explanation:
To determine the quality of water at the beginning and end of the heat rejection process in a Carnot-cycle engine, we need to understand how the Carnot cycle operates with water as the working fluid. The quality of a substance in the context of a thermodynamic cycle refers to the proportion of the substance that is in the vapor phase at a particular point in the cycle.
Before the heat rejection process, the working fluid is often at the end of the isothermal expansion process at the high-temperature reservoir, which means it is typically in a state of saturated vapor. At the onset of the heat rejection process, which occurs isentropically, the quality is 1 (100% vapor). As heat is rejected and the fluid moves toward the low-temperature reservoir, it condenses, and the quality begins to decrease.
At the end of the heat rejection process, just before the isothermal compression begins at the low-temperature reservoir, the water is often in a saturated liquid state, indicating that the quality is 0 (0% vapor, 100% liquid). The quality at this point can be described by the x-value, where x represents the mass fraction of vapor in the mixture, and it would be close to zero.