Which process occurs without gain or loss of heat?

The process that occurs without any gain or loss of heat is the adiabatic process. In an adiabatic process, the system does not exchange heat with its surroundings. This can happen when a system is perfectly insulated or when changes occur too rapidly for heat exchange to occur. As a result, all the energy transfer in an adiabatic process is in the form of work, leading to changes in internal energy without any heat flow.

In contrast, an isothermal process involves constant temperature, during which heat is exchanged to maintain that temperature as work is done on or by the system. An isobaric process maintains constant pressure and may require heat transfer to achieve that; while an isochoric process keeps the volume constant, which often necessitates heat transfer as well to change the internal energy of the system. Therefore, the defining characteristic of an adiabatic process is the absence of heat transfer, making it the correct choice.