Final answer:
In an isothermal process, the work done by the gas is the least amount compared to other processes.
Step-by-step explanation:
When an ideal monatomic gas undergoes a reversible expansion, the amount of work depends on the process involved. In this case, we are asked to determine the process that results in the least amount of work.
If the pressure increases in proportion to the volume (option A), the work done by the gas will be the largest because the area under the pressure-volume curve will be the greatest. This means that the gas is exerting more force over a larger distance.
On the other hand, if the pressure decreases in proportion to the volume (option B) or if the process occurs at constant pressure (option C), the work done by the gas will be less compared to option A. This is because the force exerted by the gas is smaller over a smaller distance in these processes.
The correct answer is option E, at constant temperature. In an isothermal process, the temperature remains constant. This means that the gas always has the same average kinetic energy, resulting in a constant pressure and volume relationship. As a result, the work done by the gas in an isothermal process is the least among the given options.