Thermodynamic efficiency equation

This equation expresses the law of the conservation of mass, overall and for each chemical element separately The combustion reaction as written in Equation 13.12 is still short of (440 + Vi x 20-50 - Vi x 410) = 195 kj. So theoretically, the work available in another /i mol of C is required, corrected for the work available in another /i mol of C02. Theoretically, the amount of waste is now 1 mol of C02 per mole of product. But suppose that the thermodynamic efficiency of the overall scheme is 50%. In that case, 1 mol more of C will be required, resulting in total of 2 mol of C02, that is, a fourfold of the C02 emission of the reaction in Equation 13.12. 

According to this equation, the maximum efficiency change with increasing temperature depends on the entropy change of the fuel cell reactions. For example, for H2/air (02) fuel cells, the thermodynamic efficiency decreases with increasing... 

The above equation implies that for a given total reaction rate and a given total volume, entropy production is minimal when the driving force A GIT is equal in all n subsystems. According to the linear duality theory, the results of the optimization will be the same if we maximize the total reaction speed for a given entropy production. Therefore, a thermodynamically efficient reactor has a uniform A GIT in all parts of the reactor volume. This result is independent of the local variations in the reaction rate. 

The theoretical thermodynamic efficiency of an Otto cycle engine is based on the compression ratio of the engine and the specific-heat ratio of the fuel as shown in the equation ... 

The Photochemical Thermodynamic Efficiency Factor (PTEF) is an energy ratio equating the energy used to achieve the photocatalytic conversion of organic molecules over the energy absorbed by the photocatalyst. This parameter was first introduced by Serrano and de Lasa (1997) and evaluates the performance of photocatalytic reactors on a thermodynamic basis. 

Thermodynamic analysis of power plants seeks to characterize efficiency and identify sources of losses. First law analysis assesses performance based on energy balance equations, while second law analysis uses exergy balances and looks for locations of exergy destruction. In this section, analysis methods are developed to apply thermodynamic balance equations to analyze heat engines and power plant components. Results are summarized in Appendix B of this chapter and detailed examples are provided in Section 23.6. 

The theoretical efficiency is sometimes also known as the thermodynamic efficiency or the maximum efficiency limit. The theoretical efficiency at different temperatures and standard pressure is shown in Figure 1.25. The data are also given in Table 1.7. It is clear that there is a conneetion between the reversible OCV of a cell and its theoretical efficiency (or maximum efficiency) based on the above equation. 

The thermodynamic efficiency of the proton pump is defined by the equation... 

The direct combustion of hydrogen in an oxygen atmosphere follows the same reaction as in Equation 1.7. In this process, AH is transformed completely into thermal energy (heat), which can be converted into mechanical work using a steam turbine. Thereafter, it can be transformed into electrical work in an electric generator. The upper limit of the thermodynamic efficiency for any heat or steam cycle corresponds to the efficiency of the hypothetical Carnot heat engine ... 

Mol fraction ethanol in feed Minimum heat requirement, B.t.u. per lb. mol of feed Thermodynamic work equation (7-44), B.t.u. per lb. mol Available work equation (7-47), B.t.u. per lb. mol of feed Thermodynamic efficiency, per cent... 

The benzene-toluene system shows a maximum thermodynamic efficiency of about 80 per cent for a feed composition of 40 per cent benzene. The efficiency decreases for feeds both weaker and stronger, but in the range of feed compositions from 0.1 to 0.8 it is good. Equation (7-44) shows that the efficiency is zero both for xf approaching 0 and 1.0. In the case of the ethanol-water system, the heat requirement per mol of distillate is essentially independent of the feed composition over the range shown because the minimum reflux ratio condition corresponds to a tangency with the equilibrium curve at about 84 mol per cent alcohol. Thus the reflux ratio is the same over the whole concentration region considered. This reflux ratio corre-... 

This maximum efficiency limit is sometimes known as the thermodynamic efficiency . Table 2.2 gives the valnes of the efficiency limit, relative to the HHV, for a hydrogen fuel cell. The maximum voltage, from equation 2.1, is also given. 

This also corresponds to the condition of open circuit reversible voltage, with no current flowing through the external circuit. Such a condition leads to the maximum electrical energy conversion and Equation 4.57 for reversible thermodynamic efficiency of a fuel cell can also be expressed as... 

However, in some cases. Equation 8.13 could not be an accurate approximation, particularly in a case when concentrated aqueous solutions are the participating chemicals. An example of a dramatic difference between thermodynamic efficiency and its standard value is given in Ref. [7] for an electrolytic systan where highly concentrated aqueous solutions are used. 

Another implementation of homotopy-continuation methods is the use of problem-dependent homotopies that exploit some physical aspect of the problem. Vickeiy and Taylor [AIChE J., 32, 547 (1986)] utilized thermodynamic homotopies for K values and enthalpies to gradually move these properties from ideal to ac tual values so as to solve the MESH equations when veiy nonideal hquid solutions were involved. Taylor, Wayburn, and Vickeiy [I. Chem. E. Symp. Sen No. 104, B305 (1987)] used a pseudo-Murphree efficiency homotopy to move the solution of the MESH equations from a low efficiency, where httle separation occurs, to a higher and more reasonable efficiency. 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

The function f(k ) is shown plotted against the thermodynamic capacity ratio in Figure 1. It is seen that for peaks having capacity ratios greater than about 2, the magnitude of (k ) has only a small effect on the optimum particle diameter because the efficiency required to effect the separation tends to a constant value for strongly retained peaks. From equation (1) it is seen that the optimum particle diameter varies as the square root of the solute diffusivity and the solvent viscosity. As, in... 

In evaluating and/or designing compressors the main quantities that need to be calculated are the outlet (discharge) gas temperature, and the energy required to drive the motor or other prime mover. The latter is then corrected for the various efficiencies in the system. The differential equations for changes of state of any fluid in terms of the common independent variable are derived from the first two laws of thermodynamics ... 

---