What type of boundary allows energy to pass through as heat?

The correct answer identifies a diathermic boundary, which is specifically characterized by its ability to allow energy to transfer as heat. In thermodynamics, a diathermic boundary is one that is not insulating; it does not prevent the flow of thermal energy. This means that when there is a temperature difference across this boundary, heat can flow from the hotter region to the cooler one, thereby facilitating thermal exchange.

In contrast, an adiabatic boundary is designed to prevent the transfer of heat, maintaining thermal isolation between systems. An isolated boundary also prevents heat transfer, as well as particle transfer, effectively separating a system from its surroundings. Lastly, a permeable boundary typically refers to the ability to allow particle transfer (such as mass) but does not inherently imply the capability for heat transfer unless specified as thermally conductive. Therefore, the defining characteristic of the diathermic boundary is its role in allowing thermal energy to flow, making it the correct answer.