Expansion, work done

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. 

Expansion work done during a chemical reaction is calculated by the formula w = —PAV, where P is the external pressure opposing the change in volume. In this instance, P = 5.0 atm and Ay = (14.5 — 12.0) L = 2.5 L. Remember that an expanding system loses work energy and thus has a negative sign. 

A 19.2-g quantity of dry ice (solid carbon dioxide) is allowed to sublime (evaporate) in an apparatus like the one shown in Figure 6.10. Calculate the expansion work done against a constant external pressure of 0.995 atm and at a constant temperature of 22°C. Assume that the initial volume of dry ice is negligible and that CO2 behaves like an ideal gas. 

The thermal efficiency of the process (QE) should be compared with a thermodynamically ideal Carnot cycle, which can be done by comparing the respective indicator diagrams. These show the variation of temperamre, volume and pressure in the combustion chamber during the operating cycle. In the Carnot cycle one mole of gas is subjected to alternate isothermal and adiabatic compression or expansion at two temperatures. By die first law of thermodynamics the isothermal work done on (compression) or by the gas (expansion) is accompanied by the absorption or evolution of heat (Figure 2.2). 

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. 

AA is sometimes referred to as the change in work function. This equation simply states that energy will be available to do work only when the heat absorbed exceeds the increase in internal energy. For proeesses at constant temperature and pressure there will be a rise in the heat content (enthalpy) due both to a rise in the internal energy and to work done on expansion. This can be expressed as... 

The first term is due to the irreversible expansion from V, to Vj, and the second term to the isentropic expansion from Vj to Vj. Adamczyk does not actually say how p3 should be chosen. A reasonable choice for seems to be the initial-peak shock overpressure, as calculated from Eq. (6.3.22). The equation presented above can be compared to the results of Guirao et al. (1979). They numerically evaluated the work done by the expanding contact surface. When the difference between... 

Wiedermatm (1986b) presents an alternative method for calculating work done by a fluid. The method uses the lambda model to describe isentropic expansion, and permits work to be expressed as a function of initial conditions and only one fluid parameter, lambda. Unfortunately, this parameter is known for very few fluids. 

It is not clear which measure of explosion energy is most suitable. Note that, in the method presented in Section 6.3, the energy of gas-filled pressure vessel bursts is calculated by use of Brode s formula, and for vessels filled with vapor, by use of the formula for work done in expansion. 

The specific work done by a fluid in expansion is calculated with Eq. (6.3.25) as follows ... 

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... 

Ausdehnungs-arbeit,/. work done in expanding, -koeflizient, m. expansion coefficient, -messer, m. dilatometer extensometer. -vermOgen, n. expansibility extensibility dilatability. -zahl, /. expansion coefficient, ausdenken, v.t. think out. devise, conceive, ausdeuten, v.t. interpret, explain, ausdorren, v.t. dry up, desiccate season (timber). 

J. R. Mayer (1842) made the first calculation of the mechanical equivalent of heat by comparing the work done on expansion of air with the heat absorbed. 

If a fluid contained in a cylinder expands so that its pressure remains constant (e.g.9 saturated steam in contact with water), the work done is that of raising the piston, of area a, which supports a weight W just sufficient to keep the expansive force indefinitely near equilibrium. If s = distance of outward motion of piston work A = W. s = pa. s = p. as = p v, where Av is the increase of volume. 

Any continuous change of volume is represented (Fig. 3) by a curve AB, and the work done by an infinitesimal expansion Bv is represented by a narrow rectangle with base Bv and mean altitude pv. The work done in a finite expansion from volume v to volume v2 is therefore the area enclosed between the v axis, the ordinates v = and v = r2, and p the part of the curve intercepted v2... 

A convenient unit for gaseous expansion is obtained by measuring p in standard atmospheres and v in litres the work done by expansion through a volume of 1 litre under a constant pressure of one atmosphere is called a litre-atmosphere (1. atm,). Its value in ergs or other units may be calculated as follows ... 

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 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. 

The adiabatic expansion of a gas is an example of (b). In the reversible adiabatic expansion of one mole of an ideal monatomic gas, initially at 298.15 K, from a volume of 25 dm3 to a final volume of 50 dm3, 2343 J of energy are added into the surroundings from the work done in the expansion. Since no heat can be exchanged (in an adiabatic process, q = 0), the internal energy of the gas must decrease by 2343 J. As a result, the temperature of the gas falls to 188 K. 

Thus, theoretically, the clearance volume does not affect the work done per unit mass of gas, since Vi — V4 is the volume admitted per cycle. It does, however, influence the quantity of gas admitted and therefore the work done per cycle. In practice, however, compression and expansion are not reversible, and losses arise from the compression and expansion of the clearance gases. This effect is particularly serious at high compression ratios. 

Therefore, the work done by the expanding gas is PexAV. At this point, we match the signs to our convention. When a system expands, it loses energy as work so, when A V is positive (an expansion), tv is negative. Therefore,... 

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