Compression, work done

Wlien a spring is stretched or compressed, work is done. If the spring is the system, then the work done on it is simply... 

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). 

Compression may be from below atmospheric as in a vacuum pump or above atmospheric as for the majority of process applications. The work done by Scheeh - is useful. 

Horsepower is the work done in a cylinder on the gas by the piston connected to the driver during the complete compression cycle. The theoretical horsepower is that required to isen-tropically (adiabatically) compress a gas through a specified pressure range. The indicated horsepower is the actual work of compression developed in the compressor cylinder(s) as determined from an indicator card. Brake horsepower (bhp) is the actual horsepower input at the crankshaft of the compressor drive. It does not include the losses in the driver itself, but is rather the actual net horsepower that the driver must deliver to the compressor crankshaft. 

Everything is now in the initial state, and the total work done must vanish. By reason of the slight compressibility of the solution and solvent, the amounts of work done in (1) and (3) may be taken as equal and opposite. 

All the impervious diaphragms are now removed, and the two gases slowly compressed into the box under the constant pressures, the steam produced being removed as fast as it is formed through the third semipermeable diaphragm, so that the equilibrium mixture remains unchanged. The amounts of work done are — 2RT, — RT and + 2RT for the 2H2,02, and 2H20. respectively. 

If we remove the mol of gas from the low pressure space, compress it isothermally and reversibly until its pressure rises to 2h> and then introduce it into the high pressure space, the cycle will be completed. The work done with the gas is ... 

Now suppose this brought to unit concentration by compressing with an osmotic piston. Work done... 

The work done in a reversible compression will be considered first because this refers to the ideal condition for which the work of compression is a minimum a reversible compression would have to be carried out at an infinitesimal rate and therefore is not relevant in practice. The actual work done will be greater than that calculated, not only because of irreversibility, but also because of frictional loss and leakage in the compressor. These two factors are difficult to separate and will therefore be allowed for in the overall efficiency of the machine. 

These equations give the work done during a simple compression of gas in a cylinder but do not take account of the work done either during the admission of the gas prior to compression or during the expulsion of the compressed gas. 

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. 

It is seen that the overall work done on the gas is intermediate between that for a single stage isothermal compression and that for an isentropic compression. The net saving in energy is shown as the shaded area in Figure 8.34. 

From equation 8.36, the work done in isothermal compression of 1 kg of gas... 

In an experimental study of a small air-lift pump(6), (25 mm. diameter and 13.8 m overall height) the results were expressed by plotting the efficiency of the pump, defined as the useful work done on the water divided by the energy required for isothermal compression of the air, to a basis of energy input in the air. In each case, the curve was found to rise sharply to a maximum and then to fall off more gradually. Typical results are shown in Figure 8.37. 

Calculate the ideal intermediate pressures and the work required per kilogram of gas. Assume compression to be isentropic and the gas to behave as an ideal gas. Indicate on a temperature-entropy diagram the effect of imperfect imercooling on the work done at each stage. 

To integrate this function the relationship between pressure and volume must be known. In process design an estimate of the work done in compressing or expanding a gas is... 

When one plots force vs. displacement, the area under the curve thus represents work. In practice, the compression/decompression data take the form shown in Fig. 18. The area under the upward line represents the work done on the tableting mass during compaction, while that under the downward line arise from the fact work is done on the punch by the tablet as a result of the latter s elastic recovery on decompression. 

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