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Thermodynamic Entropy As an Indicator for Urban Sustainability?

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Thermodynamic Entropy As an Indicator for Urban Sustainability? Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 00 (2017) 000–000 www.elsevier.com/locate/procedia Urban Transitions Conference, Shanghai, September 2016 Thermodynamic entropy as an indicator for urban sustainability? Ben Purvisa,*, Yong Maoa, Darren Robinsona aLaboratory of Urban Complexity and Sustainability, University of Nottingham, NG7 2RD, UK bSecond affiliation, Address, City and Postcode, Country Abstract As foci of economic activity, resource consumption, and the production of material waste and pollution, cities represent both a major hurdle and yet also a source of great potential for achieving the goal of sustainability. Motivated by the desire to better understand and measure sustainability in quantitative terms we explore the applicability of thermodynamic entropy to urban systems as a tool for evaluating sustainability. Having comprehensively reviewed the application of thermodynamic entropy to urban systems we argue that the role it can hope to play in characterising sustainability is limited. We show that thermodynamic entropy may be considered as a measure of energy efficiency, but must be complimented by other indices to form part of a broader measure of urban sustainability. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of the Urban Transitions Conference. Keywords: entropy; sustainability; thermodynamics; city; indicators; exergy; second law 1. Introduction The notion of using thermodynamic concepts as a tool for better understanding the problems relating to “sustainability” is not a new one. Ayres and Kneese (1969) [1] are credited with popularising the use of physical conservation principles in economic thinking. Georgescu-Roegen was the first to consider the relationship between the second law of thermodynamics and the degradation of natural resources [2]. Despite the controversial nature of Georgescu-Roegen's work, the idea that the second law, in particular the concepts of entropy and exergy, can be successfully utilised to better understand sustainability remains prominent in the literature [3-8]. * Corresponding author. E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of the Urban Transitions Conference. 2 B. Purvis, Y. Mao, D. Robinson / Procedia Engineering 00 (2017) 000–000 Cities are highly complex dynamic entities. They form thermodynamically open systems which facilitate huge flows of mass and energy both within the urban system itself, and across its boundaries. They are also responsible for around 75% of global resource consumption, 50% of global waste, and 60-80% of global greenhouse gas emissions [9]. Work by Wolman [10] and others in the study of urban metabolism has emphasised the similarities of cities to living organisms. This thinking naturally leads to the analogy of thermodynamic dissipative systems which maintain their structure through the constant dissipation of entropy [6, 11-13]. Thermodynamics if properly applied can thus have great potential to bring physical rigour and understanding to the impact our cities have on the environment within the upcoming paradigm of sustainability science. But can it be properly applied? Such a complex system as a city is after all very different to an ideal thermodynamic scenario. In this work we present a review of the literature, identifying where and how thermodynamic entropy and the second law of thermodynamics have been applied to urban sustainability and related concepts. We believe that the relationship of the second law to urban sustainability has not yet been adequately addressed, something which we hope to achieve in this paper. The term entropy outside of thermodynamics has long been applied in urban contexts, for example, the spatial entropies of Batty [14] and Wilson [15], as well as the Shannon-like entropy measure used as a recycling metric by Rechberger [16]. Whilst these methods present potential avenues and applications of entropy to urban sustainability, they remain broadly separate from the thermodynamic entropy we focus on in this paper. 2. Entropy and exergy We first present a brief outline of the concepts of entropy and exergy, and their definitions within the thermodynamic literature. 2.1. Entropy The concept of entropy is fundamentally rooted in thermodynamics, specifically the second law of thermodynamics, which Clausius stated in 1854 as: “heat cannot by itself pass from a colder to a warmer body” [17]. This law tells us that all real processes are irreversible, capturing what Eddington described as the “arrow of time”, something hitherto absent from classical physics. The Second Law describes what we know from experience, but how do we quantify the notion of irreversibility? For a thermodynamic process, the quantity of heat, Q, absorbed by a system depends on the path the process takes from the initial state of the system A to the final state B. Clausius showed however that division of Q by the temperature T at which the heat is supplied, produces a quantity which is path independent, depending only on the initial and final states, he called this quantity entropy, S. The change in entropy of the system being heated is thus given for a reversible process by: B dQ SSS . (1) AB A T For a reversible process the total entropy change of the universe is zero, since the entropy gain of the system being heated is equal to the reduction in entropy of the system from which the heat is transferred. In an irreversible process, work is lost resulting in an additional production of entropy. Thus for an irreversible process, the total entropy change of the universe is always positive. This is a restatement of the second law, sometimes known as Clausius’ inequality, ΔS ≥ 0, and applies to any isolated system which cannot exchange energy with its surroundings. For a system that can exchange matter and energy with its surroundings, i.e. one that is not isolated, the system's entropy change consists of the entropy flux due to the exchange of energy and matter with the surroundings ΔSE, and Author name / Procedia Engineering 00 (2017) 000–000 3 the internal entropy production due to irreversible processes ΔSI. Since the system can exchange energy with its surroundings, Clausius’ inequality no longer applies, in this case the second law only means that the internal entropy production has to be greater than or equal to zero, ΔSI ≥ 0. In the 1870s Boltzmann developed statistical mechanics by considering entropy at the molecular level. Each molecule in a system has a set of discretised energy levels, the higher the temperature of the system, the greater the number of energy states that are available to each molecule. Each potential distribution of energy within the system is called a microstate. The relation between entropy and the number of microstates, W, accessible to the specified system at a given temperature and volume, the macrostate, is given by Boltzmann's equation: b WkS .ln (2) In this context, an increase in entropy means that the number of accessible microstates increases, and the probability that the system will be found in a certain energy state is reduced. 2.2. Exergy The exergy of a system is defined as the maximum amount of work that may theoretically be obtained from it by bringing the system into equilibrium with an environmental reference state [18]. The concept of exergy has its roots in the early conceptions of classical thermodynamics, and is equivalent to what Gibbs in 1873 described as “available energy”, but it wasn’t until the 1960s and 1970s that the modern concept of exergy began to take off [19]. The development of exergy was driven by the inadequacies of energy accounting methods in capturing both the transformation of energy, and the concept of energy ‘quality’, or capacity to cause change [19]. For example 1kJ of electricity has a higher quality, or potential for performing work, than 1kJ of heat at ambient temperature. Exergy analysis is thus a common technique used within engineering to identify the thermodynamic imperfections of various systems by locating processes where exergy is “destroyed” [20,21]. Kotas [20] distinguishes between four types of exergy relating to possible sources of energy within a system: kinetic, potential, physical, and chemical. Physical exergy relates to processes involving thermal interaction with the environment and is thus related to the system’s pressure and temperature. Chemical exergy refers to the chemical properties of the substance in question such as its chemical potential and concentration relative to the environment. By definition, exergy requires a reference environment to be specified before any analysis can be performed. This requirement can be problematic, in part due to the lack of consensus on the definition of a reference environment [Szargut05, SGR]. The difficulties are most prominent when it comes to chemical exergy; some authors prescribe the need for a universal reference environment [Gool, Rivero, Szargut05, Sato] based upon standard compositions of atmosphere, crust etc, however it seems as of yet whilst most methods are similar, no universal method has been adopted. Despite this, exergy remains an important and widely used tool in the application of thermodynamics to the analysis of real world systems. 2.3. Exergy vs entropy The Gouy-Stodola relation [Bejan96] tells us that the destruction of exergy and production of entropy are two sides of the same coin: 0 STEx produceddestroyed . (3) This equivalence means that the two quantities may be used interchangeably given the factor of environmental temperature, T0. The concepts of absolute exergy and entropy are however distinct, the exergy of a system can include 4 B. Purvis, Y. Mao, D. Robinson / Procedia Engineering 00 (2017) 000–000 kinetic and potential energy for example, this is still compatible with equation (3) because as soon as any of this potential energy is used, exergy is destroyed and entropy production occurs. Both entropy and exergy require a reference state.
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