Ideal work of separation

The mechanisms for the embrittling effects are not completely tmder-stood. The fundamental thermodynamic quantity is the work of separation. As a grain-boundary crack propagates grain-boundary area is destroyed and two free surfaces are created. The work associated with this process is the ideal work of separation. 

Generally the experimental work of fracture is much larger than the ideal work of separation (except for an ideally brittle solid) because of plastic deformation of the solid prior to fracture. However, it has been found that the experimental work of fracture scales with w. ... 

Note that as the amount of a component becomes smaller in a mixture, more work is required to reversibly separate that component in the pure state. On the other hand, if only one component is separated from the mixture and all the other components remain mixed, the ideal work of separation is considerably smaller than when all the components of the mixture are individually separated. 

A natural gas stream has a volumetric composition of 84% methane, 8% ethane, 3% propane, 1% butane, and 4% nitrogen. Assuming that the behavior of all gases in the mixture follows the ideal-gas equation of state, evaluate the ideal work of separation at 300 K in kJ/kg of ethane and kJ/kg of propane if (a) all the gases are separated and (b) only the ethane and the propane are separated individually from the other gases that remain mixed. Does it make any difference whether the ethane or the propane is separated first from the gas mixture ... 

Several cases will be examined. Thus, for an ideal mixture at low pressure the minimum work of separation is ... 

Solution The ideal work for separation is equal to the lost work of mixing ... 

These concepts refer to an ideal elastic solid. Since rubbers and polymers are viscoelastic materials, their deformation properties are not reversible. In pulling surfaces apart some deformation energy will also be expended and the observed work of separation... 

An important property connected to interfacial tensions is the thermodynamic or ideal work of adhesion, which is defined as the work needed to separate an interface into two separate surfaces (in contact with air). 

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. 

A simple thermodynamic analysis provides considerably more data to work with. The required task is to separate propylene from propane. On a theoretical basis the ideal work (the minimum availability change) required for this separation is about 400 k BTU s/hr, of which an appreciable fraction is needed to raise the temperature of the products to the final values shown. The available energy (availability, exergy) supplied to this process from the condensing low pressure (20 psig) steam is 18.6 M BTU s/hr. 

In view of the fact that the most important goal of the CHP systems described here is to achieve the interconversions of chemical, thermal, and mechanical energies with the highest efficiency and the lowest losses, these systems are ideal subjects of thermodynamic analyses. Since there are no chemical raw materials consumed and since the only delivered products are heat and work, thermodynamic efficiency of the overall process plays a vital role in the design and economics of such systems. It 1s the purpose of this report to present the results of two separate applications of the second law analysis to these chemical energy systems. 

What is the ideal work for the separation of an equimolar mixture of methane and ethane 150°C and 5 bar in a steady-flow process into product streams of the pure gases at 35°C and 1 if T0 = 300 K ... 

We are rarely able to extract much work from chemical reactors. WTe mostly take out energy from the reactor in the form of heat. Also, when we let a hot stream heat up a cold stream in a heat exchanger we lose some of the work potential of the hot stream. The same is true for mixing and material flow across a pressure drop we take advantage of the spontaneity of the process and make no attempt to recover work from it. In contrast, we often want to perform operations that are the reverse to the spontaneous direction. This always requires work. For example, separation is the opposite of mixing. The work demand of separating an ideal mixture of n components into pure products at constant temperature T is... 

The net work of 0.52 MW for the separation section assumes that we perform all separations mechanically, i.e., with compressors and semipermeable membranes. In reality we use evaporation, partial condensation, and distillation to separate the components. We can use Eq. (5.8) to estimate how much heat, from 75 psia steam, we must supply to an ideal separation device to provide the necessary separation work. Again, this is only a rough estimate of the required heat. 

We can summarize the HDA example as follows. The process converts 132 kmobh of toluene. If it were possible to extract all the work contained in the reactants we could generate 1.58 MWT of electric power at standard conditions. When forced to generate power from steam we would obtain much less than 0.65 MW of electric power. When none of the reaction energy is converted to work we need to dissipate about 1.55 MW of heat to utilities. On the separation side we need 0.52 MW of mechanical power at standard conditions. If ideal heat-driven separation devices were... 

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