System energy change

The last bracketed quantity on the right side of Eq. G.2.5 depends only on the speeds and positions of all the particles in the surroundings, so that this quantity is the energy of the surroundings, f surr- Thus, an abbreviated form of Eq. G.2.5 is 

The quantity Hk ik represents potential energy shared by both the system and surroundings on account of forces acting across the system boundary, other than gravitational forces or forces from other external fields. The forces responsible for the quantity J k ik generally significant only between particles in the immediate vicinity of the system boundary, and will presently turn out to be the crucial forces for evaluating thermodynamic work. 

This section derives an important relation between the change AEgys of the energy of the system measured in a lab frame, and the forces exerted by the surroundings on the system particles. The indices i and j will refer to only the particles in the system. 

We can replace the first three sums in this equation with new expressions. Using Eq. G. 1.4, we have 

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Each MC step randomly interrogates every molecule exactly one time. The movement of an interrogated molecule depends on whether the projected site is empty and whether a favorable system energy change is associated with the movement. The probability of movement P into a vacant site is... 

Here S is the total surface area of all the three grain boundaries in the absence of the void. Si, S2, and S3 are the areas of intersections of the void with the respective GBs. Interaction with the electric field is as described in the previous case if the void center shifts from the junction position (%o,yo) to a new position (Xc,yc) without a change in void shape the system energy change due to the work of the electric field may be expressed as... 

APPENDIX G FORCES, ENERGY, AND WORK G.3 System Energy Change... 

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. 

FIG. 9 System energy change with the shift of the meniscus in the case of 77 = vW + cos(ay + (/>), at which the system is neutral stable in the advance direction. 

FIG. 14 System energy change with (a) the apparent contact angle 6 and (b) non-dimensional meniscus height H, when axisymmetric meniscus attaches to a circular cylinder. The system is stable at states C and A for advance and retreat of meniscus, respectively. 

FIG. 6 Schematic of system energy change with the shift of attachment position of meniscus on a horizontal plate the system becomes unstable when the energy mono-... 

The value fi in this equation is the so-called chemical potential, i.e., the thermodynamic function of a system, which is determined by the system energy change at the change of the particle number by 1. 

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