Liquid solution in a centrifuge cell

This section derives equilibrium conditions of a dilute binary solution confined to a cell embedded in a spinning centrifuge rotor. 

The system is the solution. The rotor s angle of rotation with respect to a lab frame is not relevant to the state of the system, so we use a local reference frame fixed in the rotor as shown in Fig. 9.12(a). The values of heat, work, and energy changes measured in this rotating frame are different from those in a lab frame (Sec. G.9 in Appendix G). Nevertheless, the laws of thermodynamics and the relations derived from them are obeyed in the local frame when we measure the heat, work, and state functions in this frame (page 498). 

Note that an equilibrium state can only exist relative to the rotating local frame an observer fixed in this frame would see no change in the state of the isolated solution over time. While the rotor rotates, however, there is no equihbrium state relative to the lab frame, because the system s position in the frame constantly changes. 

We assume the centrifuge rotor rotates about the vertical z axis at a constant angular velocity (O. As shown in Fig. 9.12(a), the elevation of a point within the local frame is given by z and the radial distance from the axis of rotation is given by r. 

In the rotating local frame, a body of mass m has exerted on it a centrifugal force centr directed horizontally in the outward +r radial direction (Sec. G.9). The 

---

Hereafter in this book, thermodynamic work w will be called simply wort For all practical purposes you can assume the local frames for most of the processes to be described are stationary lab frames. The discussion above shows that the values of heat and work measured in these frames are usually the same, or practically the same, as if they were measured in a local frame moving with the system s center of mass. A notable exception is the local frame needed to treat the thermodynamic properties of a liquid solution in a centrifuge cell. In this case the local frame is fixed in the spinning rotor of the centrifuge and has rotational motion. This special case will be discussed in Sec. 9.8.2. 

---