Expansion processes, work

The Intercooled Regenerative Reheat Cycle The Carnot cycle is the optimum cycle between two temperatures, and all cycles try to approach this optimum. Maximum thermal efficiency is achieved by approaching the isothermal compression and expansion of the Carnot cycle or by intercoohng in compression and reheating in the expansion process. The intercooled regenerative reheat cycle approaches this optimum cycle in a practical fashion. This cycle achieves the maximum efficiency and work output of any of the cycles described to this point. With the insertion of an intercooler in the compressor, the pressure ratio for maximum efficiency moves to a much higher ratio, as indicated in Fig. 29-36. 

Any work developed by the turboexpander is at the expense of the enthalpy of the process stream, and the latter is correspondingly cooleci. A low inlet temperature means a correspondingly lower outlet temperature, and the lower the temperature range, the more effective the expansion process becomes. 

If no Mollier diagram is available, it is more difficult to estimate the ideal work in compression or expansion processes. Schultz (1962) gives a method for the calculation of the polytropic work, based on two generalised compressibility functions, X and Y which supplement the familiar compressibility factor Z. 

There is no way to use the expansion process to raise or lower a weight in the surroundings, so there can be no work. 

An ideal Otto Cycle with air as the working fluid has a compression ratio of 9. At the beginning of the compression process, the air is at 290 K and 90kPa. The peak temperature in the cycle is 1800 K. Determine (a) the pressure and temperature at the end of the expansion process (power stroke), (b) the heat per unit mass added in kJ/kg during the combustion process, (c) net work, (d) thermal efficiency of the cycle, and (e) mean effective pressure in kPa. 

An ideal Diesel engine receives air at 103.4 kPa and 27°C. Heat added to the air is 1016.6 kJ/kg, and the compression ratio of the engine is 13. Determine (a) the work added during the compression process, (b) the cut-off ratio, (c) the work done during the expansion process, (d) the heat removed from the air during the cooling process, (e) the MEP (mean effective pressure), and (f) the thermal efficiency of the cycle. 

Find the pressure and temperature of each state of an ideal Atkinson cycle with a compression ratio of 8. The heat addition to the combustion chamber is 800Btu/lbm, the atmospheric air is at 14.7 psia and 60°F, and the cylinder contains 0.02 Ibm of air. Determine the maximum temperature, maximum pressure, heat supplied, heat removed, work added during the compression processes, work produced during the expansion... 

The isochoric heating process of a Lenoir engine receives air at 15°C and 101 kPa. The air is heated to 2000° C, and the mass of air contained in the cylinder is 0.01kg. Determine the pressure at the end of the isochoric heating process, the temperature at the end of the isentropic expansion process, heat added, heat removed, work added, work... 

COMMENTS. (1) The turbine work produced is very small. It does not pay to install an expansion device to produce a small amount of work. The expansion process can be achieved by a simple throttling valve. (2) The compressor handles the refrigerant as a mixture of saturated liquid and saturated vapor. It is not practical. Therefore, the compression process should be moved out of the mixture region to the superheated region. 

After anomerisation and before initiation of the ring-expansion process, the a-and p-glucofuranosides were found to be present in a -equilibrium in the ratio 1 1.7 which agrees with the value obtained by radiochemical methods and with that observed by Bishop and Cooper for the methyl xylofuranosides 4). However, the ratio for the xylosides was found in the isotope work to be 1 1.2 (1 1.3 for ethyl xylofuranosides) regardless of whether they were derived from xylose or either of its methyl furanosides. A further relevant observation made with these furanosides was that acetal was formed during their anomerisation indicating that pathways (C) and (E) (Scheme 3) are open. 

When the bubble shrinks, the volume change is 47cr dr. The gas within the bubble undergoes compression while the external atmosphere undergoes expansion. The net work associated with the compression and expansion processes is given by... 

The fraction of nonchemical work available in the gas that has been lost in the expansion process can now be calculated from W /Exj = 3.325/13.501 = 0.246. If we had included the chemical exergy of the gas, this number would have been reduced to 0.00393, but as the expansion step is strictly nonchemical, this result is meaningless. Of course, the calculation of Wlost itself would not be affected as the chemical exergy would have to be included in both Exj and Ex2 and would drop out. 

Step 3-1 Expansion process that produces work. Heat flows into the system. Since the PT product is constant,... 

We shall discuss adoption of a convention for the sign for work of expansion -(Frames 7, 9, 14 and 15) and use it when we discuss in more detail the gas expansion processes (Frame 9). Also (FIRST LAW OF THERMODYNAMICS - see Frames 2, 8) the internal energy change, A U for the overall process in Figure 1.1 (i.e. gas at Vf and 7j -> gas at Vf and Tf) (being a state function) is identical for both paths between the SAME initial and final states (and so is route independent). 

In Frame 9 we consider the expansion of an ideal gas along an isotherm (or constant temperature curve for which dT = 0) from (Pi, V ) to (Pf, Vf). Whilst the state functions P and V show identical changes in the two expansion processes considered (dP = Pf — Pi) dV = (Vf — V) the work done in the two cases is entirely different. Two routes (paths) are considered ... 

In other cases (Figure 8.2c) heat <73 (<73 > q > q2) can be supplied, part of which can be used to increase the internal energy of the system but some of which can be used by the water to increase its volume (by expanding). In this expansion process energy is needed to force back the external pressure imposed on its surface by the atmosphere thus doing work of expansion against the surroundings (= —wf). For this case ... 

The varying P is substituted by nRT/V and the integration then performed over the changing volume. wrev is the work done by the gas in expanding reversibly from (Vf Pi) to (Vf, Pf). It can be equated to the area enclosed between the curve of P plotted versus V and the V axis (i.e. the abscissa) (see Frame 2). wKV is larger than the work done, Win, during the irreversible process of expansion and it also represents the maximum work obtainable from any expansion process which takes the gas from the state (Vi, Pi) to the state (Vf, Pf). 

Suppose that in a second experiment the piston is no longer frictionless, again the temperature is constant, now to achieve the same expansion more heat will be needed to overcome the frictional forces which oppose the expansion. So here q > qlev(q = <7rev + q ) but the work performed will be the same for the expansion process. qlev is a particular value of the heat absorbed by the gas and it is only this value which defines the entropy change, AS. This shows, as was seen in Frame 1, that q and w depend on the specific parameters of the experiment or path and are not state functions in contrast to the entropy change, AS. 

For plastics at least examining systems are required most often for goods that are in continuous production (like film or sheet), and an example intended for work of this kind will be described. It evaluates the surface roughness of a product used widely in vehicle fittings the material undergoes an expansion process so the surface tends to be uneven—but a high degree of uniformity in fact is required. 

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