In which type of system can heat cross the boundary but nothing else?

A diathermic system is defined as one that allows heat transfer across its boundary while preventing the transfer of matter. This characteristic is critical in thermal dynamics, especially in thermodynamic processes where understanding heat exchange is important.

In a diathermic system, heat can flow into or out of the system without any mass flow. This is distinct from other types of systems. An adiabatic system, on the other hand, does not allow any heat transfer at all; it is insulated completely. An isolated system is one that prevents both heat and matter transfer, essentially being closed off from the surroundings. An isobaric system refers specifically to a constant pressure process, but it does not inherently define the conditions for heat and matter transfer.

Thus, the defining feature of a diathermic system makes it the correct answer as it specifies that only heat can cross the system's boundaries, allowing for the clear exchange of thermal energy with the environment while maintaining the same chemical and mass composition within the system.