Net work

This can be illustrated by showing the net work involved in various adiabatic paths by which one mole of helium gas (4.00 g) is brought from an initial state in whichp = 1.000 atm, V= 24.62 1 [T= 300.0 K], to a final state in whichp = 1.200 atm, V= 30.7791 [T= 450.0 K]. Ideal-gas behaviour is assumed (actual experimental measurements on a slightly non-ideal real gas would be slightly different). Infomiation shown in brackets could be measured or calculated, but is not essential to the experimental verification of the first law. 

For all of these adiabatic processes, the total (net) work is exactly the same. 

The high T] values above conflict with the common behef that distillation is always inherendy inefficient. This behef arises mainly because past distillation practices utilized such high driving forces for pressure drop, tedux ratio, and temperature differentials in teboilets and condensers. A teal example utilizing an ethane—ethylene sphtter follows, in which the relative number for the theoretical work of separation is 1.0, and that for the net work potential used before considering driving forces is 1.4. 

Funds Statement A typical funds statement is shown in Table 9-32. It displays the change in net working capital and can be obtained from a statement of changes in working capital, such as the one shown in Table 9-33. A funds statement shows where the cash came from and how it was used. 

Transactions that change the character of the net working capital but do not affect its value occur in a company. For example, a cash payment of 10,000 for accounts payable reduces both the current asset of cash by 10,000 and the current liabihty of accounts payable by 10,000, leaving the net working capital unchanged. However, this transac tion affects Doth the current and the quick ratios. 

Mechanical work equal to Q /0.9 is returned by the expander to the compressor, so the net work to the compressor is... 

Over the time increment dt, the force applied on the left-hand side of the element acts over a distance u dt, so the work done on the element from the left is Pu dt. The force on the right-hand boundary of the element k P + (dPIdh), dh, and it travels a distance (u + (dufdh), dh) dt, so the work done by the element on the surrounding fluid to the right is (P + (dP/dh), dh)(u + (dujdh), dh) dt. The net work done on the fluid element is the difference... 

There are two work terms to consider when a nucleus forms from the liquid. Equations (6.1) and (6.2) show that work of the type AH (T, - T)/T, is available to help the nucleus form. If AH is expressed as the latent heat given out when unit volume of the solid forms, then the total available energy is (4/3)ot AH (T, - T)/T, . But this is offset by the work 4 rr ysL needed to create the solid-liquid interface around the crystal. The net work needed to form the crystal is then... 

The term pump head represents the net work performed on the liquid by the pump. It is eomposed of four parts. They are the statie head (Hs), or elevation the pre.ssure head (Hp) or the pre.ssures to be overcome the friction head (Hf) and velocity head (Hf), which are frictions and other resistances in the piping system. These heads are discussed in Chapter 8. The head formula is the following ... 

Intercooling and Reheat Effects. The net work of a gas turbine cycle is given by... 

Therefore, if a simple gas turbine cycle is modified with the compression accomplished in two or more adiabatic processes with intercooling between them, the net work of the cycle is increased with no change in the turbine work. 

The reheat cycle increases the turbine work, and consequently the net work of the cycle, can be increased without changing the compressor work or the turbine inlet temperature by dividing the turbine expansion into two... 

This system, as can be seen from Figure 2-27, indicates that the net work is about the same as one would expect in a steam injection cycle, but the efficiencies are much higher. The disadvantages of this system are its high initial cost. However, just as in the steam injection cycle, the NO content of its exhaust remains the same and is dependent on the gas turbine used. This system is being used widely because of its high efficiency. 

Figure 2-28. Comparison of net work output of various oyoies temperature.

It has already been shown that a measure of the total work available is given by the magnitude of -A A. Since some of the work may be absorbed in expansion (FAT) the magnitude of -AF gives an estimate of the net work or free energy available. 

Net work done by the system ineluding both meehanieal and eleetrieal work, W,. 

Here W is the net work output, i.e. the difference between the turbine work output (W-r) and the work required to drive the compressor (Wc ), W = Wy — Wq-. 

The first modification, involving n and is important and affects the Hawthorne-Davis chart. The compressor work is unchanged but the turbine work, and hence the non-dimensional net work NDNW, are increased. The heat supplied term NDHT is also changed. It should be noted here that the assumption n = (n-I-I )/2, used by Horlock and Woods, is not generally valid, except at very low pressure ratios. 

Lloyd argues that for a plant with fixed pressure ratio and top temperature, the turbine work output (and hence the net work output) is increased linearly with the. steam quantity 5 that is injected, but the (2n and Qa terms increase more slowly. Thus, the efficiency similarly increases with S. but also more slowly. 

The rea.son for this choice of low pressure ratio is illustrated by an approximate analysis [12], which extends the graphical method of calculating gas turbine pierformance described in Chapter 3. If the gas turbine higher plant is assumed to ojjerate on an air standard cycle (i.e. the working fluid is a perfect gas with a constant ratio of specific heats, y), then the compressor work, the turbine work, the net work output and the heat supplied may be written as... 

---