Final answer:
The adiabatic process is path-dependent and shows a change in temperature without heat transfer. In a pV diagram, an isobaric process is represented by a horizontal line, an isochoric process by a vertical line, and the final isothermal or adiabatic process by a curve returning to the start. Isothermal processes generally produce more work per cycle compared to adiabatic processes.
Step-by-step explanation:
The process described in the question which is dependent on the path by which the change occurs is the adiabatic process. Unlike isobaric, isochoric, and isothermal processes, an adiabatic process pertains to a scenario in which no heat is transferred to or from the system, and it involves a change in temperature. A key characteristic of an adiabatic process is that it is path-dependent, meaning that the specific sequence of states through which the system goes determines the outcome.
In drawing a pV diagram, the isobaric process with increasing volume would be represented as a horizontal line moving to the right (since pressure is constant while volume increases). The isochoric process with decreasing pressure follows, shown by a vertical line moving downwards (since volume is constant while pressure decreases). Completing the cycle with an isothermal process would result in a smooth curve returning to the starting point while maintaining constant temperature. An adiabatic return path would instead be a steeper curve, reflecting the temperature change with no heat added or removed.
Regarding which process yields greater net work per cycle, the isothermal process typically results in more work compared to the adiabatic option because during the isothermal expansion, stored internal energy is transformed into work with no loss of heat, while in an adiabatic expansion, some of the internal energy is used to do work and the rest manifests as a change in temperature.