Process thermodynamics

Any change taking place which results in an increase in entropy has a positive entropy change (AS). Most spontaneous thermodynamic processes are accompanied by an increase in entropy. Entropy has units of Joules per degree K per mole. For representative values see table on p. 393. 

As pointed out in Section 2.4, shock waves are such rapid processes that there is no time for heat to flow into the system from the surroundings they are considered to be adiabatic. By the second law of thermodynamics, the quantity (S — Sg) must be positive for any thermodynamic process in an isolated system. According to (2.54), this quantity can only be positive if the P-V isentrope is concave upward. Thus, the thermodynamic stability condition for a shock wave is... 

The need for auxiliary heating is another factor that must be carefully evaluated. Due to the nature of the thermodynamic process, the gas discharging from an expander is at a much lower temperature than gas discharging from a regulator station operating within the same pressure bounds. If temperatures downstream of the expander are allowed to drop too low, potential problems may arise, such as hydrate formation and material compatibility. 

Consider the thermodynamic process in the fan (Fig. 9.33). As the fan is a stationary flow system, consideration is directed to the total enthalpy change. As the suction openings are often at the same, or almost the same level, the potential energy change can be neglected. 

Analytical Work. Analytical work performed on pressure vessel explosions can be divided into two main categories. The first attempts to describe shock, and the second is concerned with the thermodynamic process. 

The thermodynamic method has limitations. Since the method ignores the intermediate stages, it cannot be used to determine shock-wave parameters. Furthermore, a shock wave is an irreversible thermodynamic process this fact complicates matters if these energy losses are to be fully included in the analysis. Nevertheless, the thermodynamic approach is a very attractive way to obtain an estimate of explosion energy because it is very easy and can be applied to a wide range of explosions. Therefore, this method has been applied by practically every worker in the field. 

Cogeneration encompasses several distinct thermodynamic processes of simultaneous heat and power production. One utilizes air as a medium, another steam, a third employs heat rejected from a separate combustion process, such as an internal-combustion engine, and a fourth utilizes a thermochemical process such as found in a fuel cell. Although each process is distinct, they are often combined together to inaxiniize the energy production in a single thermodynamic system. 

The thermodynamic processes that may occur during a compression operation are ... 

An early concept of the cycle of thermodynamic processes as relating to steam engine heat-energy performance. 

A concept of the cycle of thermodynamic processes, introduced later than the Carnot cycle. Modifications of the Rankine cycle are of practical importance in boiler design, in relating the successive thermodynamic changes as water is converted to steam, expands and converted to mechanical energy in a turbine, then condenses and returns to the boiler. 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

Equation (1.30) can be integrated to calculate AZ, the change in Z for a thermodynamic process. Thus... 

As we have seen before, exact differentials correspond to the total differential of a state function, while inexact differentials are associated with quantities that are not state functions, but are path-dependent. Caratheodory proved a purely mathematical theorem, with no reference to physical systems, that establishes the condition for the existence of an integrating denominator for differential expressions of the form of equation (2.44). Called the Caratheodory theorem, it asserts that an integrating denominator exists for Pfaffian differentials, Sq, when there exist final states specified by ( V, ... x )j that are inaccessible from some initial state (.vj,.... v )in by a path for which Sq = 0. Such paths are called solution curves of the differential expression The connection from the purely mathematical realm to thermodynamic systems is established by recognizing that we can express the differential expressions for heat transfer during a reversible thermodynamic process, 6qrey as Pfaffian differentials of the form given by equation (2.44). Then, solution curves (for which Sqrev = 0) correspond to reversible adiabatic processes in which no heat is absorbed or released. 

A block diagram helps us to visualize the thermodynamic processes. The liquid refrigerant evaporates at constant temperature as it absorbs heat from the contents of the refrigerator, which are at a different constant temperature. 

The values of these functions change when thermodynamic processes take place. Processes in which the Gibbs energy decreases (i.e., for which AG<0), will take place spontaneously without specific external action. The Gibbs energy is minimal in the state of equilibrium, and the condition for equilibrium are given as... 

It has been seen thus far that the first law, when applied to thermodynamic processes, identifies the existence of a property called the internal energy. It may in other words be stated that analysis of the first law leads to the definition of a derived property known as internal energy. Similarly, the second law, when applied to such processes, leads to the definition of a new property, known as the entropy. Here again it may in other words be said that analysis of the second law leads to the definition of another derived property, the entropy. If the first law is said to be the law of internal energy, then the second law may be called the law of entropy. The three Es, namely energy, equilibrium and entropy, are centrally important in the study of thermodynamics. It is sometimes stated that classical thermodynamics is dominated by the second law. 

Thermodynamic processes play an important, or even dominant, role in all branches of science, from cosmology to biology and from the vastness of space to the microcosmos of living cells. Energy and entropy determine and direct all the processes which occur in the observable world. Thermodynamics only describes the properties of large populations of particles it cannot make any statements about the behaviour of single atoms or molecules. The most important properties of a system are determined by ... 

While the chemical substance involved dictates the magnitude of A U (i.e. the amount of it), its sign derives from the direction of the thermodynamic process. We can go further if the same mass of substance is converted from state A to state B, then the change in internal energy is equal and opposite to the same process occurring in the reverse direction, from B to A. This essential truth is depicted schematically in Figure 3.3. 

The value of AU when condensing exactly 1 mol of water is termed the molar change in internal energy. We will call it AUm (condensation), where the small m indicates that a mole is involved in the thermodynamic process. Similarly, the molar... 

A thermodynamic process is adiabatic if it occurs within a (conceptual) boundary across which no energy can flow. 

Reversibility can be a fairly difficult concept to grasp, but it is invaluable. In fact, the amount of work that can be performed during a thermodynamic process is maximized when performing it reversibly. 

The amount of work that can be performed during a thermodynamic process is maximized by performing it reversibly. 

A thermodynamic process is reversible if an infinitesimal change in an external variable (e.g. pressure) can change the direction in which the process occurs. 

Imagine we want to convert 1 mol of water starting at a room temperature of, say, 25 °C to steam. In fact we must consider two separate thermodynamic processes we first consider the heat needed to warm the water from 25 °C to its boiling temperature of 100 °C. The water remains liquid during this heating process. Next, we convert 1 mol of the liquid water at 100°C to gaseous water (i.e. we boil it), but without altering the temperature. 

The change in enthalpy A H during a thermodynamic process is defined in terms of internal energy and pressure-volume work by... 

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