The System and Surroundings

The significance of Eq. G.l. 11 is that the total energy tot defined by Eq. G.l. 12 is conserved. This will be true provided the reference frame used for kinetic energy is inertial and the only forces acting on the particles are those responsible for the particle-particle potential functions. 

Now we are ready to assign the particles to two groups particles in the system and those in the surroundings. This section will use the following convention indices i and j refer to particles in the system indices k and I refer to particles in the surroundings. This division of particles is illustrated schematically in Fig. G.l(a). With this change in notation, Eq. G.l. 12 becomes 

A portion of the surroundings may create a time-independent conservative force field (an external field) for a particle in the system. In order for such a field to be present, its contribution to the force exerted on the particle and to the particle s potential energy must depend only on the particle s position in the lab frame. The usual gravitational and electrostatic fields are of this type. 

In order to clarify the properties of a conservative external field, the index k will be used for those particles in the surrovmdings that are not the source of an external field, and k for those that are, as indicated in Fig. G.l(b). Then the force exerted on system particle i due to the field is If this were the only force acting on particle i, 

For conservation of energy, the potential energy change in the time interval should have the same magnitude and the opposite sign  

---

Proved that in a reversible process net entropy change for the system and surroundings is zero. 

Already, you should be thinking to yourself But the particles in solids really don t move that mnch and you are certainly correct. They do move or translate in the liquid state of that same solid, however, and don t forget about rotation and vibration, which we will see in subsequent chapters can be very important in solids. But along this line of thinking, we can simplify the First Law of Thermodynamics, which in general terms can be written for a closed system (no transfer of matter between the system and surroundings) as... 

Work can be defined as the energy transferred between the system and surroundings. It is often expressed as a vector force acting through a vector displacement on the system boundaries ... 

The force exerted by the substance within the cylinder on the lower force of the piston under these conditions is the product of the pressure exerted by the substance on the surface of the piston and the area of the piston. Moreover, the product of the area and the differential displacement of the piston is equal to the differential change of volume. The integral J F dh is then equal to P dV. This relation is the only change that is made in Equation (2.15) or a similar equation for quasistatic processes. The frictional effects or the collisions result in a temperature increase either of the surroundings, or of both the system and surroundings as the case may be, or the effects may be interpreted in terms of heat, as discussed above. 

If the multi-criteria evaluation of energy system is introduced in this analysis, indicators which are reflecting all potential interaction of the system and surrounding must be also recognized. In this respect, the... 

Because it takes some practice to be able to use the recipes for calculating entropy changes in the system and surroundings, a few simple examples are presented here. 

We have adopted the standard procedure of not explicitly indicating that the temperature is reversible for a reversible process. Because heat is transferred reversibly, the system and surroundings are at thermal equilibrium and the temperature of the system must equal that of the external reservoir. 

Heat transfer between the system and surroundings is also possible in this case, but the problem is worked for the instant after the process has occurred and before appreciable heat transfer has had time to take place. Thus Q is assumed to be zero in Eq. (2.3), giving... 

However, the first law applies to the system and surroundings, and not to the system alone. In its most basic form, the first law may be written ... 

If heat is transferred reversibly while maintaining the system and surroundings at constant temperature, Eq. (5.8.27) may be simplified to read... 

One should note how the temperatures of the system and surroundings occur in the above expression. Eq. (1.12.6a) can then be trivially rearranged to solve for the heat transfer for any given infinitesimal process under irreversible conditions ... 

It is now expedient to introduce explicitly the difference in intensive variables between the system and surroundings, by rewriting the above in the form... 

---