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18 Copyright: John Bryant, VOCAT International Ltd 2012, for personal use only. be understated. Nevertheless, excluding resource exergy losses, monetary economic cycles by themselves can be quite efficient, for if consumers agree to buy products and services from suppliers with an agreed productive content between the two parties, but with low inflation, one might expect only a small rise in money entropy during the exchange. Once consumers have bought their product/service, however, then a large increase in entropy occurs, as the products go through their useful life with consumers, or are consigned to waste. This part of the cycle is not efficient, and is to be regarded as a Second Law loss. A special case of the polytropic form (PNV n =Constant) is the Isentropic case where entropy change through the process is zero. It has the form PNV γ =Constant, where the index γ is a constant. Thus the structure for an isentropic case remains the same as that for the polytropic case (equations (5.7) and (5.8)), but with the elastic index n replaced by another index γ. While in our monetary process the index γ is unknown, clearly, from figure 5.7 of this chapter, the elastic indices n for the UK and USA economies have followed significantly variable paths, and isentropic conditions, have not existed over the periods examined. It was shown in chapter 3 that an expression stating the change in entropy in a polytropic process could be set out as in equation (5.13) below. While this held for a single unit of stock (s=S/N), we have effectively also arranged the same here by dividing price by money stock PN=P/N). Thus: ⎛ 1 ⎞ dT ds = k⎜ω + ⎟ (5.13) ⎝ 1− n ⎠ T rev Where the expression in the brackets was called the Entropic Index λ. The entropic index λ was related both to the elastic index n and the value capacity coefficient ω, which represented the amount of value required to raise the index of trading value (the velocity of circulation) T by a given increment, here for a nominal currency value k of 1. The relationship of the entropic index λ to the elastic index n and the value capacity coefficient ω with respect to changes in the velocity of circulation T is shown at figures (3.13), (3.14) and (3.15) at chapter 3. Remembering that for a polytropic case (equation (5.9) the following equation applies: dT dV = ( 1 − n) (5.14) T V
Copyright: John Bryant, VOCAT International Ltd 2012, for personal use only. Then an alternative expression for the entropy change is: dV ds = k( ω − ωn + 1) (5.15) V rev It was shown at equation (3.24) that the value capacity coefficient ω is a function of the lifetime length and perhaps other unquantifiable aesthetic factors. In the case of money, however, aesthetic factors are unlikely to be of significant importance and the lifetime length is likely to be the key factor. For money in the form of cash or electronic transfers, ω will be short – much less than a year. For money in the wider M2 or M4 definition, ω will be longer, and will be an average of a number of different constituents, up to 5 years. Thus ω is dependent upon the nature of the money instrument. While ostensibly for a given mix of money instruments ω might be fixed, it should be noted that changes in money mix, for instance a move towards electronic money, can change this value. From the charts at figure 5.5, the velocity of circulation of the UK and USA economies has varied about 1-2 times a year, suggesting a lifetime value for M2 and M4 money in the region of 0.5 – 1 year, with a value capacity coefficient ω also at about this level. A wider definition of money would entail a longer lifetime. In the UK, the lifetime appears to have lengthened from 1963 – 2011 as the velocity of circulation has reduced. In the USA, the lifetime of M2 money appears to have remained fairly constant 1959 – 1989, shortened to 1994, and then lengthened further to 2011. Figures of M3 for the US to 2006 have tended more towards the UK model. By combining equations (5.13 and (5.14), a third expression for the entropy change for a polytropic process could be stated as: ⎛ dT dV ⎞ ds = k⎜ω + ⎟ (5.16) ⎝ T V ⎠ rev Now for an isentropic condition, the expression in the brackets at equation (5.16) must be zero. Hence: dT dV ω = − (5.17) T V Figure 5.10 illustrates quarterly estimated values of money entropy change ds calculated from equation (5.16) for assumed values of value capacity 19
Page 1 and 2: THERMOECONOMICS A Thermodynamic App
Page 3 and 4: Contents Preface 1 Introduction 1 1
Page 5 and 6: Preface This book, first published
Page 7 and 8: Copyright: John Bryant, VOCAT Inter
Page 23: Copyright: John Bryant, VOCAT Inter
Page 49 and 50: INDEX Copyright: John Bryant, VOCAT
Page 51: Copyright: John Bryant, VOCAT Inter

THERMOECONOMICS - Vocat International Ltd

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