Exchanged entropy

Therefore, from equation (6) the entropy exchanged with the environment is... 

The term dJS/dt is the reversible entropy change in time as a result of an entropy flow between the system and its surroundings. On the other hand, djS/dt represents the rate of entropy production inside the system. Equation (3.48) shows that the entropy exchange with the surrounding must be negative at stationary state... 

So the stationary state is maintained through the decrease in entropy exchanged between the system and its surrounding. Entropy change inside an elementary volume by irreversible phenomena is the local value of the sum of entropy increments. By the second law of thermodynamics, the entropy production c/,5 is always positive for irreversible changes and zero for reversible changes. 

The change of total entropy is dS d,.S + d S. The term dJS is the entropy exchange through the boundary, which can be positive, zero, or negative, while the term dtS is the rate of entropy production, which is always positive for irreversible processes and zero for reversible ones. The rate of entropy production is djS/dt = %JkXk. A near equilibrium system is stable to fluctuations if the change of entropy production is negative A S < 0. For isolated systems,... 

This means that the rate of overall changes in the system entropy, dS/dt, is equal to the sum of the rate of emergence (production) of entropy inside the system (djS/dt) and of the rate of entropy exchange between the sys tern and the environment (dgS/dt). Further, we shall use, along with the rate of entropy production in the system a = djS/dt, the quantity P of the rate of dissipation (scattering) of energy in the form of heat. In the temperature isotropic system ... 

In the earth atmosphere, there are usually certain fluxes of heat, therefore both approaches that treat the gas column as a closed thermodynamic system are not correct. The adiabatic case is more suitable, if the respective process of movement of a gas to some height is fast in comparison to the rate of heat conduction, thus entropy exchange of the gas. It was pointed out by Schaefer that the isothermal assumption in the barometric formula is highly unrealistic, and the adiabatic equation should be used [13]. 

In summary, we have determined that the entropy content 5 of a body can basically increase in two ways through the entropy generated inside it 5g(enerated) (cp. Sect 3.4) and, as described in this section, by the entropy exchanged with the surroundings 5e(xchanged) (and that conductively by conduction in matter at rest, Sx, or convectively, carried by a flow of matter. Sc) ... 

Fig. 3.37 Entropy generation by entropy exchange through a resistor.

In an open system, entropy production d5 is made up of d S, entropy exchanged with the surroundings, and dj5, the internal production of entropy within the system itself. Thus,... 

Photosynthetic processes have the main responsibility of energy transfer in biological systems. This is possible because living systems are open systems, otherwise, the free energy F would not be available. In open systems, variations of entropy can be the consequence of different processes dgS, is the entropy exchanged with the environment, and dtS, is the entropy variation due to irreversible processes within the system. The second term is clearly positive, but the first term does not have a definite sign. So the inequality of Clausius-Carnot becomes ... 

The entropy exchange with the exterior, d S, is expressed in terms of the flow of heat and matter For isolated systems, since there is no exchange of energy or matter, we have... 

As in the case of thermal conduction, we can relate the entropy exchange to the inflow of A and outflow of B due to contact with the chemical reservoirs. Section... 

The term d S in (17) represents the flux of entropy exchanged by the environment only with the system under consideration. With (14) and (17), the balance equation (13) becomes ... 

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