Free expansion

Two convenient forms of bath are shown ui Fig. 11,10, 2, a and 6. The former consists of a long-necked, round-bottomed flask (a longnecked Kjeldahl flask of 100 ml. capacity is quite satisfactory) supported by means of a clamp near the upper part of the neck. The thermometer is fltted through a cork, a section of the cork being cut away (see inset) so that the thermometer scale is visible and also to allow free expansion of the air in the apparatus. The bulb is about three-quarters filled with... 

Fig. 9. Expansion of piping (a) free expansion, and (b) constrained expansion. See text.

These derivatives are also of interest for free expansions or isentropic changes. 

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... 

Removable tube bundle permits easy internal cleaning. Design allows free expansion of tubes in high-temperature service. Needs no expansion joint if shell is used. 

This constitutes a safety device, since it prevents diffusion of the oxides of nitrogen, but in case the reaction becomes violent it permits a free expansion of a sudden wave of gases. 

Exercise 1.—If =/is the free expansion effect, referring to adiabatic... 

We have seen that hydrogen becomes slightly warmed in this process, so that its liquefaction by free expansion would be impossible under ordinary conditions. Dewar in 1900 showed, however, that if the hydrogen was previously cooled, it suffered a further cooling on free expansion, and in this way he obtained liquid hydrogen. Olszewski (1902) found that the inversion point of hydrogen is situated at — 80 6° C. This effect of temperature is general, and implies that the ratio of the potential to the kinetic... 

If the external pressure is zero (a vacuum), it follows from Eq. 3 that w = 0 that is, a system does no expansion work when it expands into a vacuum, because there is no opposing force. You do no work by pushing if there is nothing to push against. Expansion against zero pressure is called free expansion. 

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. 

Because A.Ssllll = —AS, AStor = 0. This value is in accord with the statement that the process is reversible, (b) For the irreversible process, AS is the same, at +7.6 J K 1. No work is done in free expansion (Section 6.3), and so w = 0. Because AU = 0, it follows that q = 0. Therefore, no heat is transferred into the surroundings, and their entropy is unchanged ASslirr = 0. The total change in entropy is therefore ASt()t = +7.6 J-K. The positive value is consistent with an irreversible expansion. 

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... 

Frasch process A process for mining sulfur that uses superheated water to melt the sulfur and compressed air to force it to the surface, free energy See Gibbs free energy. free expansion Expansion against zero opposing pressure. 

Source models for throttling releases require detailed information on the physical structure of the leak they are not considered here. Free expansion release source models require only the diameter of the leak. 

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.

Thermal Displacements. A piping system will undergo dimensional changes with any change in temperature. If it is constrained from free expansion or contraction by connected equipment and restraints such as guides and anchors, it will be displaced from its unrestrained position. 

Supports, hangers, and anchors should be so installed as not to interfere with the free expansion and contraction of the piping between anchors. 

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. 

If we consider the free expansion, it is apparent from Equation (5.43) that, because no work is performed, no change in temperature occurs that is, 72 = Tj. Thus, AU and AH also must be zero for this process. A comparison with the results for a free expansion in Table 5.1 shows that an adiabatic free expansion and an isothermal free expansion are two different names for the same process. 

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. 

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