Available energy Shaft work

This contrasts with the engine cycles studied for these, net area measured shaft work output, but for compressed-air systems, net area measures work lost. Remember, completely available energy, shaft work, runs compressed-air systems higher-temperature heat runs engine cycles. 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

The system s Second Law efficiency rises as the work/heat ratio increases (Figure 7). This is partially due to improved performance of the turbine, pump, and condenser and the higher temperature steam from the boiler. This considerably decreases the available-energy destruction due to heat transfer in the boiler. Thus, the turbine can take advantage of this for the production of shaft work. 

As a consequence, the conclusion can be drawn, from the second law, that "the available energy is the maximum shaft work obtainable." This statement is usually used to define available energy. Unfortunately such a definition gives the impressions (i) that available energy is relevant only to "work processes," and (ii) that work is the ultimate commodity of value. Actually,... 

If Q represents the energy supplied at a temperature Tq to a steady-state or cyclic "heat engine" (Figure 2), it follows rrom an available energy balance that the net rate of available energy flowing from the cycle in the form of shaft work can at most be equal to the thermal available energy supplied to the cycle i.e.,... 

The amount of available energy which a substance has is relative and depends upon the choice of a dead state. The fundamental dead state is the state that would be attained if each constituent of the substance were reduced to complete stable equilibrium with the components (8,9,10) in the environment—a component-equilibrium dead state. (Thus, one may visualize the available energy as the maximum net work obtainable upon allowing the constituents to come to complete equilibrium with the environment.) The equilibrium is dictated by the dead state temperature T0 and, for ideal gas components, by the dead state partial pressure p-jg of each component j. (The available energy could be completely obtained, say in the form of shaft work, if equilibrium were reached via an ideal process—no dissipations or losses—involving such artifices as perfectly-selective semi-permeable membranes, reversible expanders, etc. (9,10,11).)... 

The method used in the previous example, called the extraction method, assumes that the sole purpose of the turbine is to produce shaft power. Therefore, the shaft work is charged for the capital cost of the turbine and for the steam available energy used by the turbine to produce the work. With this rationale, the additional equation is obtained by equating the unit costs of high- and low-pressure steam available-energy, cLp = cHp. The result is that the shaft work bears the entire burden of the costs associated with the turbine process and capital expense. 

It should be mentioned that other methods of design optimization, employing the Second Law for costing, have been used. For example, without explicitly determining the cost of available energy at each juncture of a system, in 1949 Benedict (see 19) employed the Second Law for optimal design. He determined the "work penalties" associated with the irreversibilities in an air separation plant. That is, the additional input of shaft power to the compressors required as a consequence of irreversibilities was determined from the entropy production in each subsystem. Associated with additional shaft power requirements are the costs of the power itself and the increased capital for larger compressors. 

The state of each stream can be manipulated through C mole numbers, a thermal interaction, and a shaft-work mode hence, the term (C + 2). In addition, energy can enter or leave the control volume through a thermal interaction and a shaft-work mode hence, the 2 on the rhs of (3.6.12). And we might impose external constraints by blocking interactions. If no external constraints are imposed, then we have the maximum number of available interactions. 

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