Work, External

Claude process A process similar to the Linde process for the liquefaction of air, except that additional cooling is produced by allowing the expanding gas to do external work. 

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

After burning, the sensible heat in the products of combustion can then be converted into steam that can be used for external work or can be converted directly into energy to drive a shaft, eg, in a gas turbine. In fact, the combustion process actually represents a means of achieving the complete oxidation of... 

Inert, Ideal Gas-Filled Vessels The energy available for external work following the rapid disintegration of the vessel is calcuJated by assuming that the gas within the vessel expands adiabatically to atmospheric pressure. 

The theory is initially presented in the context of small deformations in Section 5.2. A set of internal state variables are introduced as primitive quantities, collectively represented by the symbol k. Qualitative concepts of inelastic deformation are rendered into precise mathematical statements regarding an elastic range bounded by an elastic limit surface, a stress-strain relation, and an evolution equation for the internal state variables. While these qualitative ideas lead in a natural way to the formulation of an elastic limit surface in strain space, an elastic limit surface in stress space arises as a consequence. An assumption that the external work done in small closed cycles of deformation should be nonnegative leads to the existence of an elastic potential and a normality condition. 

The following work assumption is now made. The external work done on any arbitrarily chosen region of a body undergoing a finite smooth closed cycle of homogeneous deformation %(ti, f ) is nonnegative... 

If the work assumption is made, i.e., if it is assumed that the external work done by surface and body forces on a finite region in the reference configuration of a body undergoing homogeneous closed cycles of deformation is nonnegative, then an inequality may be deduced paralleling (5.37) by arguments essentially the same as those of Section 5.2.4. 

Older proeesses used Joule-Thomson eooling entirely. The Joule-Thomson effeet is defined as the eooling that oeeurs when a highly eompressed gas is allowed to expand in sueh a way that no external work is done. This eooling is inversely proportional to the square of the absolute temperature. The system worked satisfaetorily, but it required mueh higher pressures to remove the same amount of energy. 

Comparing this with equation (2.84) and assuming that the external work is zero then it is apparent that... 

External work Energy used in overcoming external mechanical forces on the... 

Throttling The expansion of a fluid through a constricted passage (across which there is a pressure difference), during which no external work is done. The initial and final velocities of the fluid are equal, and there is no heat exchange with external sources. A change in entropy will, however, take place. 

Fig. 2.3 shows such a fully reversible steady flow through the control volume CV. The heat transferred [GrevIx. supplies a reversible heat engine, delivering external work [( c)rev]x and rejecting heat [(2o)rev1x to the environment. 

The area contained within the P-V diagram represents the total mechanical work performed by the piston. Some of this work is required to sustain the cycle and must be subtracted from the work calculated tiom the P-V diagram to determine the total external work available from ilie piston. 

The metabolic rate can be measured in several ways. When no external work is being performed, the metabolic rate equals the heat output of the body. This heat output can be measured by a process called direct calorimetry. In this process, the subject IS placed m an insulated chamber that is surrounded by a water jacket. Water flows through the jacket at constant input temperature. The heat from the subject s body warms the air of the chamber and is then removed by the water flowing through the jacketing. By measuring the difference between the inflow and outflow water temperatures and the volume of the water heated, it is possible to calculate the subject s heat output, and thus the metabolic rate, in calories. 

The gas turbine shown in Figure 3-7 is an open-cycle type. An open-cycle type gas turbine uses the same air that passes through the combustion process to operate the compressor. This is the type most often used for stationary power unit applications. A typical example of power requirements for an open-cycle type gas turbine would be for the unit to develop a total of 3,000 hp. However, about 2,000 hp of this would be needed to operate its compressor. This would leave 1,000 hp to operate the generator (or other systems connected to the ga.s turbine). Thus, such a gas turbine power unit would be rated as a 1,000-hp unit because this is the power that can be utilized to do external work. 

Heat can be made to go from a body at lower temperature to one at higher temperature only if external work is done. 

The change is adynamic, i.e., no external work is performed. Thus, we may imagine the system enclosed in a perfectly rigid envelope which, however, permits the free passage of heat. Then ... 

The heat absorbed in the change at constant pressure is this plus the external work ... 

If the circuit is made up of two or more loops, the total external work done is the algebraic sum of the areas of the loops. 

The area is positive if traced out clockwise. Since the heat absorbed in the cycle is equal to the work done, the areas of the Carnot s cycle on the (p, v) and (S, T) diagrams are equal. This may be generalised to apply to any reversible cycle where the only external work is done by expansion. 

The suffix x indicates that besides T, all the variables xu a, . . . during the change of which external work is done, are maintained constant (adynamic condition). Thus, if the only external force is a normal and uniform pressure p, then x — v, the volume of the system, and (11) is the condition of equilibrium at constant temperature and volume. 

In the investigation of the properties of the free energy no assumption has been made as to the nature of the external work At. Let us now assume that there is some function 12 of the variables defining the physical and chemical state of the system, such that ... 

It must be remembered that all these functions were introduced for the purpose of simplifying the mathematical operations, just as were the energy and entropy functions in the earlier stages of thermodynamics. It is only their changes which admit of physical measurement these changes can be represented as quantities of heat and external work. 

We shall now consider the properties of systems the state of which is determined by the values of the absolute temperature T, and n other independent variables x , 2, x3i. . . xn. If the latter are chosen in such a way that no external work is done when the temperature changes provided all the s are maintained constant, they, along with T, are called the normal variables, and the state so defined is said to be normally defined (Duhem Mecanique chimiqne, I., 83). 

Taking the simple case of a homogeneous fluid of unchanging composition we see that its state may be defined in terms of any pair of the three variables temperature T, specific volume v, and pressure p. If the state is to be normally defined, T must be taken as one variable, and v must be taken as the other, because there is the condition to be satisfied that no external work is done when the temperature changes whilst the variable remains constant. This condition is satisfied by v, but not by/>. 

We observe that the expression for the external work now involves the temperature, since the variables are no longer normal. 

This shows that a part of the heat absorbed depends on the change of temperature, and another on the change of volume. The latter is composed of the external work pdv and a part depending on the change of intrinsic energy with volume. 

The isothermal expansion of an ideal gas is an aschistic process.— If a mass of gas expands isothermally, the heat absorbed is equal to the external work done. 

If a volume of air (or other gas) is allowed to expand without doing external work the process is adynamic ... 

For the element of external work in an infinitesimal expansion we have generally ... 

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