Isothermic processes entropy

Figure 4.1 Schematic diagram showing the thermodynamics of the demagnetization process. By changing the magnetic field from the initial value Hl to the final one Hf, with Hf < Hj a gain in magnetic entropy, ASm, occurs during the isothermal process from...

As 5 is a thermodynamic property, ASsys is the same in an irreversible isothermal process from the same initial volume Vi to the same final volume V2. However, the change in entropy of the surroundings differs in the two types of processes. First let us consider an extreme case, a free expansion into a vacuum with no work being performed. As the process is isothermal, AU for the perfect gas must be zero consequently, the heat absorbed by the gas Q also is zero ... 

Then from the entropy change in a reversible, isothermal process [Equation (6.72)]... 

The parameter V is the volume per mole, or m/n. Thus, in an isothermal process, when a mole of solid sublimates to make a perfect gas, the entropy changes with the volume according to... 

Shown that entropy change in a binary mixture for isothermal process is maximum when Xj=X2... 

It is used internally and rarely enters directly into ealens, but rather in the form of its increments or changes. Entropy is arrived at in thermodynamics in the form of the conception of a change in the entropy of the system, which is equal to the heat taken up during each infinitesimal change of a reversible or isothermal process, divided by the temperature at which it is absorbed. For the entire change in the system, the change in entropy is equal to the summation of the infinitesimal terms as denoted by the equation ... 

The integral molar entropy of adsorption is obtained from a well-known thermodynamic relation for a reversible, isothermal process the heat is equal to the change in entropy multiplied by the temperature. This directly leads to... 

The choice of magnetic field variation as the process that distinguishes the two curves in Figs, la and lb is of practical, but not of theoretical, significance. If we could find any reversible isothermal process whose entropy change remained finite as 0 K was approached, it would be described by a diagram similar to Fig. la and theoretically permit the attainment of 0 K in a finite number of steps. The third law therefore requires the following ... 

The entropy change of any reversible isothermal process must approach zero as T approaches 0 K. 

From the general entropy balance equation dS= dJS+ dxS, we conclude that for an incompressible and isothermal process, we have deS d,S. This relation shows the equality between the dissipated heat flow and internal entropy production and hence the loss of power is q = Eloss. Therefore, Eq. (b) becomes... 

For an isothermal process the simplest evolution equations for J and Pv that are compatible with the positive chracter of the entropy production are... 

For an isothermal process we have seen that the change in entropy is defined by the relationship... 

It was shown in Chapter V. that the isothermal transformation of unit mass of a substance from one phase to another is reversible when the two phases are in equilibrium with one another. The change in entropy during this isothermal process... 

This equation may be interpreted as follows If the concentration of any substance taking part in an equilibrium is altered while temperature and pressure, or temperature and volume, are kept constant, chemical action must proceed until the concentrations of all the components have assumed such values that equation (1) is again satisfied. To prove this we shall make use of the theorem that the change in entropy produced by an isothermal process in a system at equilibrium is ... 

For a reversible isothermal process the entropy change of the phase transition follows from q, via to AS = q/T. By way of illustration, values for q and AS thus... 

It is easy to calculate entropy changes for isothermal processes, because T is constant and comes outside the integral to give AS = q ev/T. A specific example is the isothermal compression or expansion of an ideal gas, for which AS = nR InlVf/V ). A second example is any phase transition at constant pressure for which q, y = The entropy change is then AS ang =... 

The last equality is true because AH = 0 when the pressure of an ideal gas is changed at constant temperature. The entropy change for an ideal gas in an isothermal process was calculated in Section 13.5 ... 

The analysis for ecological function is similar to power output, and also leads to similar results. The shape of function u = u(Zl, Is, e) is the same as in Equation (87), but the form of Z =Z (e, Is, A) changes. Because heating and cooling in both isochoric and isobaric processes are considered constant, and taking into account Equations (75) and (78), the change of entropy can be taken only for isothermal processes. Then, the change of entropy for the non-endoreversible cycle considered is... 

Real compression processes operate between adiabatic and isothermal compression. Actual compression processes are polytropic processes. This is because the gas being compressed is not at constant entropy as in the adiabatic process, or at constant temperature as in the isothermal processes. Generally, compressors have performance characteristics that are analogous to those of pumps. Their performance curves relate flow capacity to head. The head developed by a fluid between states 1 and 2 can be derived from the general thermodynamic equation. 

The descriptive approach to entropy adopted here is adequate for the isothermal processes chosen as examples. It is not easy, for example, to visualize the change of entropy which occurs when two bodies at differing temperatures come into thermal... 

So far, we have considered only isothermal processes. How do we calculate the entropy change for a gas which is heated Now 6S=AqrJT, and... 

Secondly, we should note from equation 6.3 that whatever the sign and magnitude of AS may be, it will have increasing importance at high temperatures. Thus for an isothermal process carried out at low temperature, the AH term is dominant. At absolute zero, both AS and T are zero, and so AG=AH. On the other hand, many stellar processes are dominated by entropy considerations alone. We on earth, however, are neither in the freezer nor in the fire, but somewhere between the two. As a result, we must learn to cope with both factors. 

The entropy change in a closed system in thermal equilibrium with its surroundings (isothermal process) is described by... 

Historically, the third law of thermodynamics emerges from the heat theorem, by Nernst which states A chemical reaction between pure crystalline phases that occurs at absolute zero produces no entropy change. This means that adiabatic and isothermal processes approach each other at very low temperatures. The importance of Nernst s theorem is that it gives a solid base for the calculation of thermodynamic equilibria. 

---