Final answer:
The primary factor that affects the behavior of an ideal gas in a cylinder with a movable piston is the temperature, because it directly influences the kinetic energy of gas molecules, which can lead to changes in pressure and volume.
Step-by-step explanation:
The primary factor that affects the behavior of an ideal gas in a cylinder with a movable piston is the temperature of the gas. According to the kinetic-molecular theory, the particles of a gas move randomly and collide with the walls of the container. These collisions define the gas pressure. When you increase the temperature, the average kinetic energy of the gas molecules increases as well, leading to more frequent and forceful collisions with the container's walls, which can increase the pressure if the volume is held constant. However, if the piston is allowed to move, the volume can increase, allowing the inside pressure to equalize with the external pressure. In this case, an increase in temperature generally leads to an increase in volume if the pressure is kept constant.