Final answer:
The volume of each container connected by closed stopcocks will remain constant, as gases are contained and cannot move between containers. When stopcocks are opened, the behavior of the gases will depend on their initial conditions and the new shared environment.
Step-by-step explanation:
The question pertains to the behavior of gases in containers connected by stopcocks, specifically whether the volume of each container will remain constant when the stopcocks are manipulated. As per gas law principles in physics, the volumes of the containers will indeed remain constant if the stopcocks are closed because the gases contained within each vessel cannot move into another container. However, once the stopcocks are opened, should the conditions allow, the gases may mix, and the distribution of volume would depend on the overall volume of the connected system and the conditions (like pressure and temperature) each container was initially at.
Figures and references from a textbook describe various scenarios illustrating principles of gas behavior. Figure 3.12 contrasts two vessels with ideal gases and differing piston conditions, reflecting on volume changes with temperature increase under a fixed or varying volume condition. Figure 14.9 explains how liquid levels equalize to balance pressure, reinforcing the concept of pressure equilibrium in connected vessels. The Van der Waals equation acknowledges that actual gas molecules occupy space, although this volume is usually minor compared to the container volume, which would support the case when the stopcocks are closed.