Law of diminishing returns

Most observations in chemistry come from ex periments If we do enough experiments we may see a pattern running through our observations A /aw is a mathematical (the law of gravity) or verbal (the law of diminishing returns) description of that pattern Establishing a law can lead to the framing of a rule that lets us predict the results of future experiments This IS what the 1870 version of Markovnikov s rule is a statement based on experimental observations that has predictive value... 

The law of diminishing returns ensures that heat exchangers near the end of the heat path require increasingly larger heating surfaces to extract heat from the lower temperature gases than those at the beginning of the heat path. 

Basicity also may be regarded as a measure of amine hydrolysis, and it governs the increase in pH level, per additional unit measure of amine. The law of diminishing returns applies of course, and beyond a certain point there is little further increase in system pH. Also, the basicity constant for individual amines varies considerably with temperature, so it is important to consider Kb at the relevant operating temperature, rather than simply at ambient temperature. 

Data for the model are given below in Table 4.6. The variable y represents yields of wheat corresponding to six rates of application of fertilizer, x, on a coded scale. The model equation is often called Mitcherlisch s law of diminishing returns. 

The industry continues its efforts to reduce even these emissions still further. The law of diminishing returns does of course apply, and we are now reaching levels close to the limits of detection where it is difficult to be sure what measurements actually mean. At these very low levels there are also significant relative differences between... 

An important factor to keep in mind when designing reinjection wells or systems is that eventually they will have to be redeveloped. Reinjection wells and the redevelopment of these wells unfortunately follow the law of diminishing returns. Constant reinjection of coproduced groundwater without regular development results in irreversible clogging and ultimately the abandonment of the well. 

Because of the law of diminishing returns, their assumption of sharply increasing marginal costs of emissions reduction is not controversial. 

Also, the law of diminishing returns is evident, as to gain additional performance usually requires progressively increased levels of actives to be present, drawn from higher cost, specialty inhibitor components. 

C. Lees, Environmental Policy The Law of Diminishing Returns PAS Annual Conference, University of Lincoln, Lincoln, UK, 2004. 

Although refractionation may narrow the molecular weight distributions of primary fractions such operations are subject to a law of diminishing returns because of the complications of Eq. (12-30) which have just been mentioned. 

Fig. 56.2 Exam marks as a function of time. The marks awarded in a single answer will follow the law of diminishing returns - it will be far more difficult to achieve the final 25% of the available marks than the initial 25%. Do not spend too long on any one question.

Searches not made for a patent department may also have date boundaries, but here date limits are often dictated by the law of diminishing returns. 

R6a. Robinson, R., Tedium and the law of diminishing returns in clinical biochemistry laboratories. Lancet I, 433-434 (1967). 

Clearly the synthesis of menthadienes is now following the law of diminishing returns, but a few aspects, particularly concerning chirality, still arise from time to time. 

These problems are more complex and are within the reach of modern science if science is allowed to be interpreted by its rules and not those of legal or historical precedence. We must adopt systems that rank relative risks and factor in known benefits. The law of diminishing returns will always oper-... 

A solar DHW system could be designed to provide 100% of the hot water requirement (i.e., a solar fraction of 1), but it worrld not be econorrtical except in the most favorable situatiorts. Figure 8 shows the solar fraction as a function of collector area for a typical DHW installation, and it is a clear illustration of the law of diminishing returns. Most designers firrd the economic limit to be between a solar fraction of 0.6 and 0.8. 

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