Isodynamic Process

In an isodynamic process, the energy remains constant, i.e., dt/ = 0. The motion of a friction-free pendulum is an isodynamic process. A friction-free pendulum is a pure mechanical system, and the system does not have any entropy. So the entropy cannot change at all and the process is a reversible one. 

In addition, the Gay - Lussac process is an isodynamic process. We will deal with the Gay - Lussac process in detail in Sect. 5.7.1. 

Equation (5.25) is the condition of the Gay - Lussac experiment. The isodynamic lines must be at the same time isotherms. Conversely, an isothermal process of an ideal gas is an isodynamic process. Such a process is taking place in the Carnot cycle. This means that the amount of energy is taken up from a thermal reservoir as thermal energy is released as expansion energy and vice versa. The situation is different in the Gay - Lussac experiment. Here the gas itself converts internally. When we write the energy as 

---

For both 104 and 105, values of AG (RI) 17 kcal/mol and AG (BS) 18 kcal/mol have been determined from NMR measurements (180). Analogous processes have been studied extensively in cyclooctatetraenes bearing other substituents (181). By way of comparison, ethoxycyclooctatetraene has AG (RI) = 12.5 kcal/mol and AGf(BS) = 16.0 kcal/mol (182). Values for other monosubstituted derivatives (118) differ by +2 kcal/mol and more heavily substituted compounds have substantially higher barriers for both processes, due to steric buttressing effects in the planar intermediate (181). Thus, while the transition metal substituent in 104 or 105 does increase the barriers for RI and BS relative to smaller substituents, this effect is not large enough to prevent observation of both these processes on the NMR time scale (180). Prior to our work, the effect of polyfluorination on the energetics of these isodynamic processes had not been evaluated. 

In an isodynamic process we have dU = 0. If only heat is exchanged in two subsystems, we have for this special system... 

Actually, the first law of thermodynamics states that for a completely isolated system the energy is constant. So we are confident that the laboratory world has some similarity with the real world in the thermodynamic sense. We will address thermodynamic processes where the energy of the system under consideration remains constant as isodynamic processes. 

We discuss now a few elementary thermodynamic processes. Traditionally, the thermodynamic processes are classified according to the variable of function that remains constant in the course of the process. Thus, an isothermal process occurs at constant temperature, an isochoric process occurs at constant volume, an isodynamic process occurs at constant energy, etc. 

There is a striking difference between an equilibrium process and a process that runs at constant energy. Both for an isodynamic process and for an equilibrium process in an isolated system dt/=0. If the energy is a function of a set of variable Xi, X2,U= U X, X2,...). then these variables may change in some way that the energy remains constant U = C, then the condition dC/ = 0 is certainly fulfilled. This is tme for an isodynamic process and for an equilibrium process. We emphasize that an isodynamic process is not necessarily an equilibrium process. 

We are dealing here with an isodynamic process, but not with an equilibrium process. Further, since we do not allow the exchange of matter, the mol numbers and thus the corresponding chemical potentials are not relevant in the present consideration. 

Because the 19F NMR spectra of all rjx-heptafluorocyclooctatetraenyl complexes exhibit seven resonances, with no line broadening or magnetization transfer observed at 80°C, a rapid BS process for these complexes on the NMR time scale is clearly ruled out. These observations provide no information about the isodynamical RI process. 

---