A low water cut-off device on an automatically fired hot water heating boiler rated at 450,000 Btuh is:

A low water cut-off device is a critical safety feature designed to prevent overheating or damage to a boiler when the water level drops below a safe operating threshold. For automatically fired hot water heating boilers, such as one rated at 450,000 Btuh, the presence of a low water cut-off is always mandated as it ensures that the boiler operates only under safe conditions.

The requirement for a low water cut-off device stems from the need to provide safety and protection to both the system and its operators. This device interrupts the combustion process when the water level falls to a predetermined level, thereby preventing the boiler from running dry, which could lead to equipment failure or dangerous conditions such as exploding due to excessive heat.

In contrast, other scenarios mentioned in the options do not negate the need for such a safety device. For instance, a limit control may manage the temperature and pressure within the boiler but does not address low water levels. Similarly, whether in commercial or industrial applications, the risk associated with low water levels remains significant. Thus, regardless of the application type, the requirement for a low water cut-off device remains consistent and is designed to ensure safety across all operating environments.