Center-of-mass Local Frame

If we use a center-of-mass frame (cm frame) for the local frame, the internal energy change during a process is related in a particularly simple way to the system energy change measured in a lab frame. A cm frame has its origin at the center of mass of the system and its Cartesian axes parallel to the Cartesian axes of a lab frame. This is a special case of the nonrotating local frame discussed in Sec. G.7. Since the center of mass may accelerate in the lab frame, a cm frame is not necessarily inertial. 

The indices i and j in this section refer only to the particles in the system. 

Thermodynamics and Chemistry, second edV.ion. neision 3 2a by Howard DeVoe. Latest version www.chem.umd.edu/themobook 

The center of mass of the system is a point whose position in the lab frame is defined 

We can use Eqs. G.8.1 and G.8.2 to derive several relations that will be needed presently. Because the Cartesian axes of the lab frame and cm frame are parallel to one another (that is, the cm frame does not rotate), we ean add vectors or form scalar products using the vector components measured in either frame. The time derivative of Eq. G.8.2 is dr,- / dt = d/fcm/ dt + dr,7 dt, or 

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APPENDIX G FORCES, ENERGY, AND WORK G.8 Center-of-mass Local Frame... 

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