Thermodynamical cycles

Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

Fig. 11.9 Thermodynamic cycle used to calculate absolute free energies [Jorgensen et al. 1988].

Power plants based on the Rankine thermodynamic cycle have served the majority of the world s electric power generation needs in the twentieth century. The most common heat sources employed by Rankine cycle power plants are either fossil fuel-fired or nuclear steam generators. The former are the most widely used. 

Other Refrigeration Methods. Cryocoolers provide low temperature refrigeration on a smaller scale by a variety of thermodynamic cycles. The Stirling cycle foUows a path of isothermal compression, heat transfer to a regenerator matrix at constant volume, isothermal expansion with heat transfer from the external load at the refrigerator temperature, and finally heat transfer to the fluid from the regenerator at constant volume. 

Figure 1 Thermodynamic cycles for solvation and binding, (a) Solutes S and S in the gas phase (g) and solution (w) and bound to the receptor R in solution, (b) Binding of S to the receptors R and R. The oblique arrows on the left remove S to the gas phase, then transfer it to its binding site on R. This pathway allows the calculation of absolute binding free energies.

Figure 3 Mutation of a ligand Asp into Asn in solution and bound to a protein, (a) Thermodynamic cycle, (b) Dual topology description a hybrid ligand with two side chains. Blocks are used to define the hybrid energy function [Eq. (14)]. Only the ligand is shown the environment is either solvent or the solvated protein, (c) Single-topology description.

In the present case, each endpoint involves—in addition to the fully interacting solute—an intact side chain fragment without any interactions with its environment. This fragment is equivalent to a molecule in the gas phase (acetamide or acetate) and contributes an additional term to the overall free energy that is easily calculated from ideal gas statistical mechanics [18]. This contribution is similar but not identical at the two endpoints. However, the corresponding contributions are the same for the transfonnation in solution and in complex with the protein therefore, they cancel exactly when the upper and lower legs of the thermodynamic cycle are subtracted (Fig. 3a). 

Figure 6 Thermodynamic cycle for multi-substate free energy calculation. System A has n substates system B has m. The free energy difference between A and B is related to the substate free energy differences through Eq. (41). A numerical example is shown in the graph (from Ref. 39), where A and B are two isomers of a surface loop of staphylococcal nuclease, related by cis-trans isomerization of proline 117. The cis trans free energy calculation took into account 20 substates for each isomer only the six or seven most stable are included in the plot.

The surprise was finally clarified by remembering that this was an air operated plant built in a thermodynamic cycle, (the Brayton or gas turbine cycle) with a 18,000 HP air compressor. This generated 5 MW of salable... 

Another reason for the increased use of gas turbines as prime movers in the process industry is the high thermodynamic cycle efficiencies and subsequent low operating cost. 

Active carbons can be used in both refrigeration and heat pumping cycles, but their potential for use in these applications does not necessarily merit the development of such systems. Before devoting research and development effort into active carbon-based thermodynamic cycles, the interest in both heat-driven cycles in general, and adsorption cycles in particular, must be justified. 

Because these stability measurements pertain to the gas phase, it is important to consider the effects that solvation might have on the structure-stability relationships. Hydride affinity values based on solution measurements can be derived from thermodynamic cycles that relate hydrocarbon p T, bond dissociation energy and electrochemical potentials. The hydride affinity, AG, for the reaction... 

It is important first to distinguish between a closed cyclic power plant (or heat engine) and an open circuit power plant. In the former, fluid passes continuously round a closed circuit, through a thermodynamic cycle in which heat ((2b) is received from a source at a high temperature, heat (Qa) >s rejected to a sink at low temperature and work output (IT) is delivered, usually to drive an electric generator. 

Usually, a gas turbine plant operates on open circuit , with internal combustion (Fig. 1.3). Air and fuel pass across the single control surface into the compressor and combustion chamber, respectively, and the combustion products leave the control surface after expansion through the turbine. The open circuit plant cannot be said to operate on a thermodynamic cycle however, its performance is often assessed by treating it as equivalent to a closed cyclic power plant, but care must be taken in such an approach. 

An important field of study for power plants is that of the combinedplant [ 1 ]. A broad definition of the combined power plant (Fig. 1.5) is one in which a higher (upper or topping) thermodynamic cycle produces power, but part or all of its heat rejection is used in supplying heat to a lower or bottoming cycle. The upper plant is frequently an open circuit gas turbine while the lower plant is a closed circuit steam turbine together they form a combined cycle gas turbine (CCGT) plant. 

It was pointed out in Chapter I that the desire for higher maximum temperature (T nx) in thermodynamic cycles, coupled with low heat rejection temperature (Tmin), is essentially based on attempting to emulate the Carnot cycle, in which the efficiency increases with... 

Figure 16.2 An exainple of a thermodynamic cycle for calculating differences in solvation energies...

This remarkable result shows that the efficiency of a Carnot engine is simply related to the ratio of the two absolute temperatures used in the cycle. In normal applications in a power plant, the cold temperature is around room temperature T = 300 K while the hot temperature in a power plant is around T = fiOO K, and thus has an efficiency of 0.5, or 50 percent. This is approximately the maximum efficiency of a typical power plant. The heated steam in a power plant is used to drive a turbine and some such arrangement is used in most heat engines. A Carnot engine operating between 600 K and 300 K must be inefficient, only approximately 50 percent of the heat being converted to work, or the second law of thermodynamics would be violated. The actual efficiency of heat engines must be lower than the Carnot efficiency because they use different thermodynamic cycles and the processes are not reversible. 

No thermodynamic cycle can be more efficient than a reversible cycle operating between the same temperature limits. 

For what is probably the earliest microscopic calculations of thermodynamic cycles in proteins see Ref. 12, that reported a PDLD study of the pKtt s of some groups in lysozyme. The use of FEP approaches for studies of proteins is more recent and early studies of catalysis and binding were reported in Refs. 11, 12, and 13 of Chapter 4. 

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