Final answer:
The random motion of gas particles is best demonstrated by recording how colored gas spreads from one jar to another, which visually shows the diffusion representing random motion. The change in pressure when heating an inflated tire or the response of a balloon in cold temperatures also correlates with particle motion.
Step-by-step explanation:
The postulate that gas particles are in constant random motion can be best demonstrated by observing an activity that visually or measurably shows the behavior of gas particles. Of the activities listed, recording the speed of colored gas spreading from one jar to an empty jar (Option B) would effectively show the constant and random motion of gas particles. In this activity, the diffusion of gas molecules from a region of higher concentration to a region of lower concentration until an equilibrium is reached can be observed, illustrating the random motion.
Another demonstration could include observing the change in pressure when heating an inflated tire (Option C) because as gas particles gain kinetic energy from the heat, they move more vigorously and collide with the walls of the tire more frequently, increasing the pressure. Additionally, placing an inflated balloon in cold liquefied nitrogen (Option D) would show a decrease in volume and internal pressure, suggesting particles move less as they lose kinetic energy in colder temperatures. However, the ease of pushing the plunger of a blocked nozzle syringe (Option A) does not directly show the random motion of particles.