System adiabatically enclosed

One may now consider how changes can be made in a system across an adiabatic wall. The first law of thermodynamics can now be stated as another generalization of experimental observation, but in an unfamiliar form the M/ork required to transform an adiabatic (thermally insulated) system, from a completely specified initial state to a completely specifiedfinal state is independent of the source of the work (mechanical, electrical, etc.) and independent of the nature of the adiabatic path. This is exactly what Joule observed the same amount of work, mechanical or electrical, was always required to bring an adiabatically enclosed volume of water from one temperature 0 to another 02. 

Consider two ideal-gas subsystems a and (3 coupled by a movable diatliemiic wall (piston) as shown in figure A2.1.5. The wall is held in place at a fixed position / by a stop (pin) that can be removed then the wall is free to move to a new position / . The total system (a -t P) is adiabatically enclosed, indeed isolated q = w = 0), so the total energy, volume and number of moles are fixed. 

When we apply these statements to the universe, the ultimate adiabatically enclosed system, the result is the Clausius statement... 

Description of a thermodynamic system requires specification of the way in which it interacts with the environment. An ideal system that exchanges no heat with its environment is said to be protected by an adiabatic wall. To change the state of such a system an amount of work equivalent to the difference in internal energy of the two states has to be performed on that system. This requirement means that work done in taking an adiabatically enclosed system between two given states is determined entirely by the states, independent of all external conditions. A wall that allows heat flow is called diathermal. 

The process described above is irreversible. Irreversibility means that, given two states A and B of an adiabatically enclosed system of constant composition, either of the processes A - B or B —> A may be driven mechanically or electromagnetically, but not both. By such a procedure the energy difference between two states AU — Ub - Da can always be measured. 

The practical applications of the theory just outlined divide themselves into two broad classes (1) Those which are based on the existence and properties of the functions U and S and some others related to them—all "thermodynamic identities being merely the integrability condition for the total differentials of these functions and (2) those which aie based on die Principle of Increase of Entropy the entropy of the actual state of an adiabatically enclosed system being greater than that of any neighboring virtual state. 

The beauty and power of phenomenological thermodynamics lies just in the generality and paucity of its basic laws which hold independently of any assumptions concerning the microscopic structure of the systems which they govern. Its quantitative content is limited to conditions of equilibrium. Its conceptual framework is too narrow to permit the description of the temporal behavior of systems, except to the extent that it makes it possible to decide which, of any pair of states of an adiabatically enclosed system, must have been die earlier state. 

Distinguish clearly between boundaries which enclose an adiabatic and those which enclose an isolated system. For this purpose, enumerate several changes in surroundings which can alter the properties of an adiabatically enclosed system. 

Now in the container there may be a gas adiabatically enclosed or a sophisticated gear mechanism connected to a spring that simulates this behavior. That is why the system is a black box. ... 

The most remarkable characteristic of entropy, however, is this While it is generated to some extent in every process, there is no known means of destroying it. The cumulative supply of entropy can increase, but can never decreasel If entropy has been generated in a process, one cannot consequently reverse this process as one would rewind a film. The process is irreversible as one says. This does not mean, however, that the body in question cannot attain its initial state again. This may be possible by way of detours, but only if the entropy which was generated can flow out of it. If there is no such disposal available or accessible, because the system is enclosed by entropy-insulating (= heat-insulating or adiabatic) walls, the initial state is indeed inaccessible. 

The first law may now be re-expressed as follows the work done on a body in cm adiabatic process not involving changes of the body s kinetic or potential ermgy is equal to the increase in a quantity t7, which is a function of the state of the body. It follows that if a body is completely isolated (i.e. it does no work, as well as being adiabatically enclosed) the function U remains constant. The internal energy is thus conserved in processes taking place in an isolated system. 

We isolate the system by enclosing it in a rigid, stationary adiabatic container. The constraints needed to isolate the system, then, are given by the relations... 

If a system at eqnilibrinm is enclosed by an adiabatic wall, tlie only way the system can be disturbed is by movmg part of the wall i.e. the only conpling between the system and its snrronndings is by work, nomially mechanical. (The adiabatic wall is an idealized concept no real wall can prevent any condnction of heat over a long time. Flowever, heat transfer mnst be negligible over the time period of an experiment.)... 

The change is adiabatic, i.e., the transfer of heat to or from the system from outside is prevented, say by enclosing the system in a perfectly non-conducting envelope. Then ... 

A closed system cannot perforin an isentropic process without performing work. Example (Fig. 3) A quantity of gas enclosed by an ideal, tfictionless, adiabatic piston in an adiabatic cylinder is maintained at a pressure p by a suitable ideal mechanism, so that Gl = pA (A being the area of piston). When the weight G is increased (or decreased) by an infinitesimal amount dG, the gas will undergo an isentropic compression (or expansion). In this case,... 

We next carry out an adiabatic reversible expansion from B to C in which the additional quantity of work, W2, represented by the area BCV3V2 is done on the system (a negative value). During this expansion the cylinder is enclosed by an adiabatic envelope. No heat is transferred to the fluid, and its temperature decreases to 0X. 

As a general case, let us consider a set of n processes enclosed in an adiabatic enclosure shown in Fig. 13 (a). Such a system is called a process system. In this paper, the boundary of process systems is represented by broken lines, as shown in Fig. 13. 

In practice, adiabatic walls around any system (container) are achieved by pulling a very good vacuum between two metal surfaces (a) the inner surface enclosing the system and (b) the outer surface facing ambient conditions. The mass connecting the inner and outer surfaces, needed for mechanical stability,... 

We now assume that the system (a gas) is enclosed in a vessel of variable volume this volume may be defined, say, by the position coordinate a of a piston. Thus the energy values are functions of a. If changes in a are made extremely slowly, no quantum jumps are excited by these changes the numbers % for the quantum states are therefore not changed. Such processes are called adiabatic (a better word would be quasistatic ). The work done in a small change is... 

For each of the experimental systems now to be described, the student should ask himself. What exactly is the system which is regarded as being enclosed by adiabatic and moving walls This is perhaps least obvious in experiment (6). f PhU. Mag. 31 (1847), 173 35 (1849), 533. 

If we enclose a rare gas in a box that is closed, adiabatic and of constant volume (i.e., an isolated system of a rare gas) and keep the steady state at a given temperature, the internal energy does not change, therefore the entropy never increases. This system has no autonomous internal mechanism to increase the entropy. 

Suppose 100.00 mol of liquid H2O is placed in a container maintained at a constant pressure of 1 bar, and is carefully heated to a temperature 5.00 °C above the standard boiling point, resulting in an unstable phase of superheated water. If the container is enclosed with an adiabatic boundary and the system subsequently changes spontaneously to an equiUbrium state, what amount of water will vaporize (Hint The temperature will drop to the standard boiling point, and the enthalpy change will be zero.)... 

T0 compute the maximum work, we need tw o other idealizations. A reversible work source can change volume or perform work of any other kind quasi-statically, and is enclosed in an impermeable adiabatic waU, so 6g = TdS = 0 and dU = S w. A reversible heat source can exchange heat quasi-statically, and is enclosed in a rigid wall that is impermeable to matter but not to heat flow, so = pdV = 0 and dU = 6q = TdS. A reversible process is different from a reversible heat or work source. A reversible heat source need not have AS = 0. A reversible process refers to changes in a whole system, in w-hich a collection of reversible heat plus work sources has AS = 0. The frictionless weights on pulleys and inclined planes of Newtonian mechanics are reversible w ork sources, for example. The maximum possible work is achieved w hen reversible processes are performed with reversible heat and work sources. 

Consider an energetically isolated (adiabatic) system composed of a fixed number of particles N (closed) and enclosed in a motionless container of fixed volume V. The energy of the system, given by the classical Hamiltonian lies in an eneigy shell of width l E, i.e., E < H p, q ) macroscopic state of this system is called a microcanonical ensemble. 

If a system can exchange thermal energy with its surroundings, it is considered to be in thermal contact with them and the wail enclosing it, as diathermal. If not, as adiabatic. 

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