Gases, free expansion

Hydroearbon dew point eontrol is aehieved by eooling the gas. There are three eooling alternatives free expansion or Joule-Thomson expansion, external refrigeration, and using a turboexpander. Joule-Thomson expansion does not always produee the needed refrigeration over the life of the plant and, henee, is not eonsidered as a viable... 

Because entropy is a state function, the change in entropy of a system is independent of the path between its initial and final states. This independence means that, if we want to calculate the entropy difference between a pair of states joined by an irreversible path, we can look for a reversible path between the same two states and then use Eq. 1 for that path. For example, suppose an ideal gas undergoes free (irreversible) expansion at constant temperature. To calculate the change in entropy, we allow the gas to undergo reversible, isothermal expansion between the same initial and final volumes, calculate the heat absorbed in this process, and use it in Eq.l. Because entropy is a state function, the change in entropy calculated for this reversible path is also the change in entropy for the free expansion between the same two states. 

Self-Test 7.16A Determine AS, ASsllrr, and AStot for (a) the reversible, isothermal expansion and (b) the isothermal free expansion of 1.00 mol of ideal gas molecules... 

Figure 4-9 A free expansion gas leak. The gas expands isentropically through the hole. The gas properties (P, T) and velocity change during the expansion.

If the gas is allowed to expand against zero external pressure (a free expansion Fig. 5.3), then from Equation (3.6) W equals zero. Although the temperature of the gas may change during the free expansion (indeed, the temperature is not a well-defined quantity during an irreversible change), the temperature of the gas will return to that of the surroundings with which it is in thermal contact when the system has reached a new equilibrium. Thus, the process can be described as isothermal, and for the gas,... 

Figure 5.3. Schematic representation of a free expansion. A small valve separating the two chambers in (a) is opened so that the gas can msh in from left to right. The initial volume of the gas is Vi, and the final volume is V2.

No compression equivalent to a free expansion exists. We shall consider that the free expansion is reversed by an irreversible compression at a constant external pressure P that is greater than the final pressure of the gas, as shown in Figure 5.4. 

Figure 5.4. The irreversible compression at pressure P used to return a gas to its initial state after a free expansion or an intermediate expansion. The area bounded by dashed lines represents the negative of the work performed.

So far we have not specified whether the adiabatic expansion under consideration is reversible. Equations (5.40), (5.42), and (5.44) for the calculation of the thermodynamic changes in this process apply to the reversible expansion, the free expansion, or the intermediate expansion, so long as we are dealing with an ideal gas. However, the niunerical values of W, AU, and AH will not be the same for each of the three types of adiabatic expansion because T2, the final temperature of the gas, will depend on the type of expansion, even though the initial temperature is identical in aU cases. 

For a scientist, the primary interest in thermodynamics is in predicting the spontaneous direction of natural processes, chemical or physical, in which by spontaneous we mean those changes that occur irreversibly in the absence of restraining forces—for example, the free expansion of a gas or the vaporization of a hquid above its boiling point. The first law of thermodynamics, which is useful in keeping account of heat and energy balances, makes no distinction between reversible and irreversible processes and makes no statement about the natural direction of a chemical or physical transformation. 

As we noticed in Table 5.1, AC/ = 0 both for the free expansion and for the reversible expansion of an ideal gas. We used an ideal gas as a convenient example because we could calculate easily the heat and work exchanged. Actually, for any gas, AC/has the same value for a free and a reversible expansion between the corresponding initial and final states. Furthermore, AC/ for a compression is equal in magnitude and opposite in sign to AC/ for an expansion no indication occurs from the first law of which process is the spontaneous one. 

As 5 is a thermodynamic property, ASsys is the same in an irreversible isothermal process from the same initial volume Vi to the same final volume V2. However, the change in entropy of the surroundings differs in the two types of processes. First let us consider an extreme case, a free expansion into a vacuum with no work being performed. As the process is isothermal, AU for the perfect gas must be zero consequently, the heat absorbed by the gas Q also is zero ... 

Initially, a sample of ideal gas at 323 K has a volume of 2.59 L and exerts a pressure of 3.67 atm. The gas is allowed to expand to a final volume of 8.89 L via two pathways (a) isothermal, reversible expansion and (b) isothermal, irreversible free expansion. Calculate AStot, AS, and ASsurr for both pathways. 

In Figure 8.7, the curves determine the restriction downstream pressure at which hydrate blockages will form for a given upstream pressure and temperature. Gas A expands from 2000 psia and 110°F until it strikes the hydrate formation curve at 700 psia (and 54°F), so 700 psia represents the limit to hydrate-free expansion. Gas B expands from 1800 psia (120°F) to intersect the hydrate formation curve at a limiting pressure of 270 psia (39°F). In expansion processes while the upstream temperature and pressure are known, the discharge temperature is almost never known, but the discharge pressure is normally set by a downstream vessel or pressure drop. 

Joule s experiments on the free expansion of an ideal gas showed that the internal energy of such a system is a function of temperature alone. For a real gas, this is only approximately true. For condensed phases, which are effectively incompressible, the volume dependence on the change in internal energy is negligible. As a result, the internal energies of liquids and solids are also considered a function of temperature alone. For this reason, the internal energy of a system may loosely be referred to as the thermal energy . 

Two ultrafast electron diffraction studies on the Fe(CO)5 system have been published [69, 70], In these experiments fs pump pulses excite Fe(CO)5 in the gas phase in a free expansion jet. Two photon excitation was used in these experiments... 

Another instructive exercise consists in examining the free expansion of a gas, depicted in Fig. 1.8.2. The gas is initially confined to a space of volume VA, volume VB being totally evacuated. A hole of macroscopic dimensions is now opened in the diaphragm separating the two volumes the gas ultimately occupies the total volume VA + VB. What is the work involved in this process The answer is not absolutely straightforward If the system is taken with boundaries encompassing only the volume VA, complications arise because... 

FIGURE 1.8.2 Schematic diagram pertaining to the free expansion of a gas. The gas is initially confined in compartment A of the system and is allowed to expand into compartment B through a hole opened in the diaphragm separating the two regions. 

When the process goes from state 1 (Pu Vj) to state 2 (Pi/4, 4Vi) with no mass on the pan, no heat flows into or out of the gas because T is constant and no work is done (no mass is lifted). Thus work = wo - 0. This is called a free expansion. 

Solvent shifts in van der Waals complexes of perylene have been studied in supersonic jet free expansion with rare gas and organic solvent molecules 9. -i complexes give results... 

Fig. 1.7.2. Schematic diagram illustrating the free expansion of a gas initially confined to compartment A. On opening the partition the gas then expands into compartment B.

Here, <55 s 0 is the entropy change arising from irreversible processes occurring within a completely closed system. As Eq. (1.12.9a) shows, S can then only increase. As soon as these processes have ceased, 50 = 55 = 0, so that 5 has assumed an extremal value which is a maximum under the present constraints. For example, the entropy change in the free expansion of a gas can be determined by finding AS under quasistatic conditions, as specified later in Section 2.3. Since 5 is a function of state the same entropy change takes place in a free expansion under the same conditions. All this, of course, merely repeats what has been well established in earlier sections. 

Fig. 2 Schematic diagram of the pulsed supersonic nozzle used to generate carbon cluster beams. The integrating cup can be removed at the indicated line. The vaporization laser beam (30-40 mJ at 532 nm in a 5-ns pulse) is focused through the nozzle, striking a graphite disk which is rotated slowly to produce a smooth vaporization surface. The pulsed nozzle passes high-density helium over this vaporization zone. This helium carrier gas provides the thermalizing collisions necessary to cool, react and cluster the species in the vaporized graphite plasma, and the wind necessary to carry the cluster products through the remainder of the nozzle. Free expansion of this cluster-laden gas at the end of the nozzle forms a supersonic beam which is probed 1.3 m downstream with a time-of-flight mass spectrometer.

Consider the free, isothermal (constant T) expansion of an ideal gas. Free means that the external force is zero, perhaps because a stopcock has been opened and the gas is allowed to expand into a vacuum. Calculate AU for this irreversible process. Show that q = 0,so that the expansion is also adiabatic [q = 0) for an ideal gas. This is analogous to a classic experiment first performed by Joule. 

FIGURE 13.2 The free expansion of a gas into a vacuum, (a) The stopcock is ciosed with aii gas in the ieft buib. (b) With the stopcock open, haif the gas is in each buib. 

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