In the case of bottles or vessels of constant cross-section, the cross-sectional area
The analogy of the fluid model and the defintion of temperature show that in the energy storing process entropy assisted by thermal capacity plays the role of the storage size. This may be surprising at first because the molar thermal capacity* is often seen in this role. However, thermal capacity as the first derivative of entropy recieves all properties from its parent function. Numerous experimental findings confirm this interpretation of the entropy (see below 2. Refinement and see 5.2.). The three rules of the shelf model already indicated that the entropy is a thermal property that describes the size of the thermal energy storage system. The above image visualizes calculations based on one of the relations: In the following, we show that through different stages of the refinement of this model, the quite complex thermodynamic properties of real substances can be visualized very differentiated and made intelligible. *(Depending on the experimental context, the thermocapacity and entropy of an examined material portion are alternatively referred to the mass instead of the amount of substance, so that the respective specific values of entropy and thermocapacity are then used.)
Entropy and thermal capacity contribute both to the storage size for thermal energy of material systems, but in a different way. The difference, however, can be very well integrated into the fluid model: Entropy and thermal capacity together describe the size of a thermal energy store, ie, the energy that can be stored at the quantized energy levels of a substance system at a particular temperature. The entropy contains the statement about the total energy, which is stored from the absolute zero point to the current temperature of the experimental context, while the thermal capacity indicates the change of the entropy in the course of the temperature scale or in the range of the current current temperature. The following animation shows that the fluid model is transferring the quantum theoretical results to this model. During the temperature increase shown, the stored thermal energy triples, but the entropy increases only to 1.5 times. The radius of the model cylinder is only around 1.2 times: Animation: Thermal Work in Shelf and Fluid Model
When looking at the previous animation, the color change of the fluid medium is noticed, and it requires an explanation as to which phenomenon is referred to by this. We examine the above graph, which shows the entropy and thermal capacity values of silver [8.2/12]. With increasing temperature the quotient in the last column becomes smaller and we realize, that: For normal liquids, we assume that the density is not dependent on the fill level. The situation is different for the gases, which as well are fluid: We have developed the fluid model from the thermodynamic behavior of silver. It is to be shown now that this is not a special case of the silver, but that it is a general, thermal phenomenon. The diagram shows a whole range of solids: a polar molecular compound (H
The cylinder of our model storage system has two inflow options. We need these to reproduce the two fundamentally different types of temperature changes: The abovementioned temperature increase without entropy increase can also be represented by the fluid model. If the entropy remains constant despite the supply of energy, this means that the cross-sectional area remains the same. Although the hydrostatic pressure still rises with the filling height, the walls do not recede in this case. They become more rigid and thus more stable. This is symbolized by the increasing intensity of the wall color from light gray to dark gray. Please also look at the visualization of this issue in the fluid model: The animation shows that all levels are shifted horizontally parallel, so that all occupation numbers remain the same and only the level intervals increase. As a result of these higher level distances, the blue half-value energy line becomes longer, i.e. the temperature becomes higher. If no particle changes the energy level, this indicates that
This refinement leads us to a level appropriate to the universities. According to classical interpretation, In the case of the If the gas forms diatomic molecules, the number of degrees of freedom, ie the number of eigenvalue systems for the storage of thermal energy, is retained (see the following table). However, the dependence of the energy level distances on the particle mass, the interatomic forces and the size of molar volume changes. In the classical concept, diatomic molecules can * The implementation of a fourth storage, namely the storage of thermal energy in the electron states, is dispensed with here since it does not contribute to the entropy and therefore to the thermal behavior of the most substances. Thus, we have got to know three different types of thermal energy storage, and we now turn to the interaction of these storages in different cases, that is, we are now concentrating on the behavior of the molecular gases first in thermal work and afterwards in volume work. As an example of a molecular gas we take gaseous bromine and heat it with thermal radiation (from a torch or from an electrically heated wire) from the standard temperature to 500K. The following two figures show the three storage systems in the fluid model, left at standard temperature and right at 500K. The base line connects the three reservoirs so that they behave physically as well as classical vessels.
It is easy to see that the level, ie the temperature, as well as the amount of fluid medium, ie thermal energy, has become larger in all three storages. It is more difficult to see that the entropy, that is, the cross-sectional areas, have also increased. At best it is to recognize this from the vibration storage, since here the area is very small and thus the percental increase turns out to be quite large, about 75%. (Translation + 5.4%, rotation + 5.9%) The display was calculated by the Thermulation-II program and you have to take into account that due to the resolution of the screen, the percentage change may remain below one pixel, so the screen can not display it.
Here, as well, you can see that temperature and thermal energy have increased in all three storages. It would actually be expected that the volume work only affects the translation store, because only these eigenvalues depend on the volume. Then, however, the temperature in the translation storage should be different from that in the two other storages. Since this is difficult to imagine, we have to look for a mechanism by which the thermal energy is transferred from the translation storage to the other two. |