Which of the following scenarios would most likely require the use of a pressure relief valve?

The scenario that involves preventing overpressure conditions in a boiler system most likely requires the use of a pressure relief valve. A pressure relief valve is a safety device designed to automatically release pressure when it exceeds a predetermined level, thereby protecting the system from damage due to excessive pressure buildup. In a boiler system, various factors such as temperature changes, equipment malfunction, or operational errors can lead to increased pressure. The pressure relief valve ensures that if the pressure exceeds safe limits, it can safely vent steam or water, thus mitigating the risk of explosion or catastrophic failure.

In contrast, maintaining constant temperature in a reactor focuses on temperature control mechanisms, which may not necessarily involve pressure considerations. Preventing water from leaking in a pipe relates more to sealing and joint integrity rather than pressure management. Controlling the speed of a motor pertains to electrical or mechanical controls, which also does not involve the context of pressure management as is critical in boiler systems. Therefore, the use of a pressure relief valve is fundamentally linked to the need to manage and prevent dangerous overpressure scenarios, making this the correct choice.