Final answer:
The process requiring the most work to reduce an ideal gas volume to one-half is adiabetic compression, because no heat is transferred and all the work increases the gas's internal energy.
Step-by-step explanation:
The process that requires the largest amount of work to be done on a system containing an ideal gas, when the volume of the system is reduced to one-half of its initial value, is adiabatic compression. In adiabatic processes, there is no heat exchange between the system and the surroundings, meaning all the work done on the gas will go into increasing the internal energy and therefore increasing the temperature of the gas. In contrast, during isothermal compression, the temperature remains constant and the system is in thermal contact with a reservoir, so it requires less work as some energy can be transferred as heat. Isobaric compression occurs at constant pressure and will also require less work than adiabatic compression because some energy can be transferred as heat. Lastly, isochoric compression does not apply here since it involves no change in volume and hence no work is done.