Expansion work

If a system alters its volume against an opposing pressure, a work effect is produced in the surroundings. This expansion work appears in most practical situations. The system is a quantity of a gas contained in a cylinder fitted with a piston D (Fig. 7.2a). The piston is assumed to have no mass and to move without friction. The cylinder is immersed in a thermostat so that the temperature of the system is constant throughout the change in state. Unless a specific statement to the contrary is made, in all of these experiments with cylinders it is understood that the space above the piston is evacuated so that no air pressure is pushing down on the piston. 

In the initial state the piston D is held against a set of stops S by the pressure of the gas. A second set of stops S is provided to arrest the piston after the first set is pulled out. The initial state of the system is described by T, Fi. We place a small mass M on the piston this mass must be small enough so that when the stops S are pulled out, the piston 

The work of expansion accompanying the temperature increase is negligibly small and has been ignored to avoid obscuring the argument. 

If the area of the piston is A, then the downward pressure acting on the piston is Mg/A = Pop, the pressure which opposes the motion of the piston. Thus Mg = Pop A. Using this value in Eq. (7.1), we obtain 

However, the product Ah is simply the additional volume enclosed by the boundary in the change of state. Thus, Ah = V2 — = AV, and we have  

Consider the combustion of urea illustrated in Fig. 1.4 as an example of a reaction in which expansion work is done in the process of making room for the gaseous products, carbon dioxide and nitrogen in this case. We show in the following Justification that when a system expands through a volume A Vagainst a constant external pressure pex. the work done is 

To calculate the work done when a system expands from an initial volume Vj to afinal volume Vf, a change Ay= Vj- Vj, we consider a piston of area A moving out through a distance h (Fig. 1.9). There need not be an actual piston we can think of the piston as representing the boundary between the expanding gas and the surrounding atmosphere. However, there may be an actual piston, such as when the expansion takes place inside an internal combustion engine. 

The force opposing the expansion is the constant external pressure pe multiplied by the area of the piston (because force is pressure times area Fundamentals F.2). The work done is therefore 

The last equality follows from the fact that hA is the volume of the cyflnder swept out by the piston as the gas expands, so we can write hA = AV. That is, for expansion work, 

Now consider the sign. A system does work and thereby loses energy (that is, w is negative) when it expands (when AV is positive). Therefore, we need a negative sign in the equation to ensure that w is negative when A V is positive, so we obtain eqn 1.3. 

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Path III (a) Do electrical work on the system, holding the pressure constant at 1.000 atm, until the volume /has increased to 34.33 I under these circumstances, the system also does expansion work against the external pressure. 

Dearation can be either vacuum or over pressure dearation. Most systems use vacuum dearation because all the feedwater heating can be done in the feedwater tank and there is no need for additional heat exchangers. The heating steam in the vacuum dearation process is a lower quality steam thus leaving the steam in the steam cycle for expansion work through the steam turbine. This increases the output of the steam turbine and therefore the efficiency of the combined cycle. In the case of the overpressure dearation, the gases can be exhausted directly to the atmosphere independently of the condenser evacuation system. 

For the a/s example quoted earlier, with this form of two stage cooling (with a = 2.79, Ah = 1.22, i//h = 0.1, i/ l = 0.05), the thermal efficiency is reduced from 0.4442 (uncooled) to 0.4257, i.e. by 0.0185, still not a significant reduction. If the second step of cooling uses compressor delivery air rather than air taken at the appropriate pressure along the compressor, then the analysis proceeds as before, except that the expansion work for the processes 7, 11 in Fig. 4.7a is replaced by that corresponding to 7, 11 in Fig. 4.7b. It may be shown [5] that the efficiency may then be written as... 

Manfrida [4] argues that the heat demand and the substantial power loss associated with presssure-swing physical absorption makes it less attractive than chemical absorption, even for high pressure sequestration. The expansion work in the fonner is difficult to recover as. several expanders are needed. 

Figure 6.30. Expansion work per unit mass of ethane, propane, and isobutane.

To calculate expansion energy, multiply the specific expansion work by the mass of fluid released or else, if energy per unit volume is used, multiply by the volume... 

The speciflc work done by the fluid in expansion can be read from Figures 6.30 or 6.31 if its temperature is unknown. Saturated propane at a pressure of 1.9 MPa (19 bar) has a temperature of 328 K, almost the superheat-limit temperature. Note that it is assumed that temperature is uniform, which is not necessarily the case. From Figure 6.30, the expansion work per unit mass for saturated liquid propane is... 

The volume of the vapor is 0.10 x 22.7 = 2.27 m. The explosion energy of the vapor can be calculated by multiplying the expansion work per unit volume by the vapor volume ... 

Explosion energy can be calculated by employing a slight variation on Eq. (6.3.26), by multiplying expansion work per unit volume by fluid volume, instead of multiplying expansion work per unit mass by fluid mass. Both propane and butane must be considered. This gives, for example, for vapor energy for the 50% fill-ratio case ... 

Work (w) Any form of energy except heat exchanged between system and surroundings includes expansion work and electrical work, 214... 

A system can do two kinds of work. The first type is expansion work, the work needed to change the volume of a system. A gas expanding in a cylinder fitted with a piston pushes out against the atmosphere and thus does expansion work. The second type of work is nonexpansion work, work that does not involve a change in volume. A chemical reaction can do nonexpansion work by causing an electrical... 

First, we consider the expansion work done by a system consisting of a gas in a cylinder. The external pressure acting on the outer face of the piston provides the force opposing expansion. We shall suppose that the external pressure is constant, as when the piston is pressed on by the atmosphere (Fig. 6.5). We need to find how the work done when the system expands through a volume AV is related to the external pressure Pcx. 

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. 

In a constant-volume system in which neither expansion work nor nonexpansion work is done, we can set w = 0 in Eq. 7 (At/ = tv + q) and obtain... 

Next, suppose that the system can do no work other than expansion work. In that case, we can use Eq. 3 (iv = —PCXAV) to write AH = q - PexAV + PAV... 

Self-Test 6.7A In an exothermic reaction at constant pressure, 50. kj of energy left the system as heat and 20. kj of energy left the system as expansion work. What are the values of (a) AH and (b) At/ for this process ... 

As explained in Section 6.5, the heat capacity of a substance is the constant of proportionality between the heat supplied to a substance and the temperature rise that results (q = CAT). However, the rise in temperature and therefore the heat capacity depend on the conditions under which the heating takes place because, at constant pressure, some of the heat is used to do expansion work rather than to raise the temperature of the system. We need to refine our definition of heat capacity. 

J-K 1 mol 1 =21.1 J-K -mol-1, a difference of 65%. The heat capacity at constant pressure is greater than that at constant volume because at constant pressure not all the heat supplied is used to raise the temperature some returns to the surroundings as expansion work and C = q/AT is larger (because AT is smaller) than at constant volume (when all the energy remains inside the system). 

For reactions in which no gas is generated or consumed, little expansion work is done as the reaction proceeds and the difference between AH and AU is negligible so we can set AH = AU. However, if a gas is formed in the reaction, so much expansion work is done to make room for the gaseous products that the difference can be significant. We can use the ideal gas law to relate the values of AH and AU for gases that behave ideally. 

Each of the pictures below shows a molecular view of a system undergoing a change. In each case, indicate whether heat is absorbed or given off by the system, whether expansion work is done on or by the system, and predict the signs of q and iv for the process. 

For a certain reaction at constant pressure, AU = —65 kj, and 48 kj of expansion work is done by the system. What is AH for this process ... 

At this point, we recognize that the system may do both expansion work and nonexpansion work ... 

Reversible expansion work (achieved by matching the external to the internal pressure) is given by the infinitesimal version of Eq. 3 of Chapter 6 (itzL.xpanNlon = — PKKAV, which becomes dtfcxpansion = —PexdV) and setting the external pressure equal to the pressure of the gas in the system at each stage of the expansion ... 

Examples freezing N2(g) + 3 H2(g) - 2 NH,(g). expanded valence shell A valence shell containing more than eight electrons. Also called an expanded octet. Examples the valence shells of P and S in PC1S and SFh. expansion work See work. experiment A test carried out under carefully controlled conditions. 

Expansion work against constant external pressure ... 

The cylinder and piston in Figure 6-18 illustrate expansion work. If the chemical system expands, it pushes the piston through a displacement (d). The opposing force is related to the pressure (P) on the piston. As described in... 

Because of this expansion work, a process at constant pressure involves both heat and work ... 

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