Reversible process temperature changes

Entropy is the ratio of a body s energy to its temperature according to the Clausius equality (as defined in the next section). For a reversible process, the change in entropy is defined by... 

Consider any number of systems that may do work on each other and also transfer heat from one to another by reversible processes. The changes of state may be of any nature, and any type of work may be involved. This collection of systems is isolated from the surroundings by a rigid, adiabatic envelope. We assume first that the temperatures of all the systems between which heat is transferred are the same, because of the requirements for the reversible transfer of heat. For any infinitesimal change that takes place within the isolated system, the change in the value of the entropy function for the ith system is dQJT, where Qt is the heat absorbed by the ith system. The total entropy change is the sum of such quantities over all of the subsystems in the isolated system, so... 

In accordance with the second law, the exergy loss is positive in an irreversible process and vanishes in a reversible process. The change in exergy of a system can be positive, negative, or zero. When the temperature of a process where heat transfer occurs is less than the temperature of the environment, the transfer of heat and exergy flows in opposite directions. Work and the accompanying exergy transfer can be in the same or opposite directions. 

In the case of a perfect gas undeigoing a reversible process or change from an initial state (r) in which the temperature is T0 and the volume V0, to a second state (2) in which the temperature is T and the volume V, the total heat effect, as we have already seen, is given by the expres-sion—... 

The spectral changes are completely reversible with temperature changes, and thus represent an equilibrium dissociation—recombination process, the first reported dissociation of a neutral hexacoordinate silicon complex [5], The Si chemical shifts of the equilibrium mixtures at various temperatures are listed in Table 1. 

Clausius proved that changes in S could be related to heat transfer, provided heat was transferred in a "reversible" way. As discussed in Chapter 7 (page 262), a reversible process involves changing the system variables by infinitesimal amounts. For example, to raise the temperature of a system from Tj to Tf in a reversible way means that the temperature is increased by infinitesimal amounts dT, as suggested below, until finally the temperature is reached. 

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

Low temperatures strongly favor the formation of nitrogen dioxide. Below 150°C equiUbrium is almost totally in favor of NO2 formation. This is a slow reaction, but the rate constant for NO2 formation rapidly increases with reductions in temperature. Process temperatures are typically low enough to neglect the reverse reaction and determine changes in NO partial pressure by the rate expression (40—42) (eq. 13). The rate of reaction, and therefore the... 

The coordinates of thermodynamics do not include time, ie, thermodynamics does not predict rates at which processes take place. It is concerned with equihbrium states and with the effects of temperature, pressure, and composition changes on such states. For example, the equiUbrium yield of a chemical reaction can be calculated for given T and P, but not the time required to approach the equihbrium state. It is however tme that the rate at which a system approaches equihbrium depends directly on its displacement from equihbrium. One can therefore imagine a limiting kind of process that occurs at an infinitesimal rate by virtue of never being displaced more than differentially from its equihbrium state. Such a process may be reversed in direction at any time by an infinitesimal change in external conditions, and is therefore said to be reversible. A system undergoing a reversible process traverses equihbrium states characterized by the thermodynamic coordinates. 

The second law of thermodynamics also consists of two parts. The first part is used to define a new thermodynamic variable called entropy, denoted by S. Entropy is the measure of a system s energy that is unavailable for work.The first part of the second law says that if a reversible process i f takes place in a system, then the entropy change of the system can be found by adding up the heat added to the system divided by the absolute temperature of the system when each small amount of heat is added ... 

This leads to what is called the Clausius form of the second law of thermodynamics. No processes are possible whose only result is the removal of energy from one reservoir and its absorption by another reservoir at a higher temperature. On the other hand, if energy flows from the hot reservoir to the cold reservoir with no other changes in the universe, then the same arguments can be used to show that the entropy increases, nr remains constant for reversible processes. Therefore, such energy flows, which arc vciy familiar, are in agreement with the laws of thermodynamics. 

The heat necessary to change the state of a substance from solid to liquid or from liquid to gas, or the heat given up during the reverse process. There is no change in temperature during these processes. For example, continuing to boil a kettle of water previously raised to I00°C to steam requires the addition of latent heat, but there is no change in temperature if the pressure remains constant. 

It must be emphasised that the heat q which appears in the definition of entropy (equation 20.137) is always that absorbed (or evolved) when the process is conducted reversibly. If the process is conducted irreversibly and the heat absorbed is q, then q will be less than q, and q/T will be less than AS the entropy change (equation 20.137). It follows that if an irreversible process takes place between the temperatures Tj and 7 , and has the same heat intake q at the higher temperature 7 2 as the corresponding reversible process, the efficiency of the former must be less than that of the latter, i.e. 

Our problem is to determine how the changes of total and free energy, AU and A P, or, what are the same, the heat absorption at constant configuration and the maximum work, Qx and At, of an isothermal and reversible process, alter with the temperature of execution of the process. 

Let the change of configuration be annulled at the infinitesimally higher temperature T + ST by an isothermal reversible process so that all the normal configuration variables recover the initial values (a). This is a second isothermal process. 

A liquid solution may be separated into its constituents by crystallising out either pure solvent or pure solute, the latter process occurring only with saturated solutions. (At one special temperature, called the cryohydric temperature, both solvent and solute crystallise out side by side in unchanging proportions.) We now consider what happens when a small quantity of solute is separated from or taken up by the saturated solution by reversible processes. Let the saturated solution, with excess of solute, be placed in a cylinder closed below by a semipermeable septum, and the w7hole immersed in pure solvent. The system is in equilibrium if a pressure P, equal to the osmotic pressure of the saturated solution when the free surface of the pure solvent is under atmospheric pressure, is applied to the solution. Dissolution or precipitation of solute can now be brought about by an infinitesimal decrease or increase of the external pressure, and the processes are therefore reversible. If the infinitesimal pressure difference is maintained, and the process conducted so slowly that all changes are isothermal, the heat absorbed when a mol of solute passes into a solution kept always infinitely... 

Thus, in a reversible process that is both isothermal and isobaric, dG equals the work other than pressure-volume work that occurs in the process." Equation (3.96) is important in chemistry, since chemical processes such as chemical reactions or phase changes, occur at constant temperature and constant pressure. Equation (3.96) enables one to calculate work, other than pressure-volume work, for these processes. Conversely, it provides a method for incorporating the variables used to calculate these forms of work into the thermodynamic equations. 

FIGURE 6.23 The enthalpy change for a reverse process has the same value but the opposite sign of the enthalpy change for the forward process at the same temperature. 

Therefore, the detailed analysis of concentration of defects in surface-adjacent layer and in the volume of adsorbent as well as assessment of the values of diffusion coefficients of defects and particles of various gases in material of adsorbent are very important for understanding the processes of both reversible and irreversible change in electrophysical characteristics of semiconductor during low temperature (if compared to the temperature of creation of defects) interaction with gaseous phase. 

The simplest process involving a change in entropy is a reversible process occurring at a constant temperature, T. For such a process, the change in entropy, AS, can be expressed as... 

At a constant pressure, the entropy of any pure substance can be calculated for any temperature through the use of the procedure that is herein being described. The entropy change taking place during an isothermal reversible process, it may be recalled, is equal to the heat change involved divided by the absolute temperature ... 

Physical adsorption is a readily reversible process, and alternate adsorption and desorption stages can be carried out repeatedly without changing the character of the surface or the adsorbate. Chemisorption may or may not be reversible. Often one species may be adsorbed and a second desorbed. Oxygen adsorbed on charcoal at room temperature is held very strongly, and high temperatures are necessary to accomplish the desorption. CO and/or C02 are the species that are removed from the surface. Chemical changes like these are prima facie evidence that chemisorption has occurred. 

Incidentally, ICD in DPPC liposomes is observed in the temperature range below Tm but not above. Consequently, the non-linear depression of ICD will be relevant to disordering of DPPC molecular arrangement. The change in ICD is a reversible process. Reverse photoisomerization to the trans isomer restores the initial ICD. 

Thermoplastic polymers can be heated and cooled reversibly with no change to their chemical structure. Thermosets are processed or cured by a chemical reaction which is irreversible they can be softened by heating but do not return to their uncured state. The polymer type will dictate whether the compound is completely amorphous or partly crystalline at the operating temperature, and its intrinsic resistance to chemicals, mechanical stress and electrical stress. Degradation of the basic polymer, and, in particular, rupture of the main polymer chain or backbone, is the principal cause of reduction of tensile strength. 

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