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The Optimal Use of Entropy and Enthalpy

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The Optimal Use of Entropy and Enthalpy GENERAL I ARTICLE The Optimal Use of Entropy and Enthalpy M S Ananth and R Ravi Chemical engineers juggle entropy and enthalpy changes to produce chemicals with the minimal expenditure of work. In a free market, the prices of common chemicals correlate very well with the thermodynamic work required to produce them! M S Ananth is a Professor Introduction of Chemical Engineering at the Indian Institute of The majority of the elements on earth are present in the form of Technology, Madras. His compounds, mainly oxides. Oil, natural gas, coal, biomass, rock, research interests are in salt, sulphur, air and water are the primary raw materials that th~ thermodynamics and chemical industry depends on. From distillation of crude oil mathematical modelling. He is deeply concerned chemical engineers produce the major fuels such as LPG, gaso­ about the quality and line, diesel and kerosene. There are about 20 base chemicals reach of engineering including ethene, propene, butene, benzene, synthesis gas, am­ education in India. monia, methanol, sulphuric acid and chlorine and 300 interme­ diates like acetic acid, formaldehyde, urea, acrylonitrile, acetal­ dehyde and terephthalic acid. These base and intermediate chemicals are often referred to as bulk chemicals. The very large number of speciality chemicals are manufactured using these bulk chemicals as the raw materials [1]. R Ravi is an Associate Professor in the Depart­ Figure 1 indicates schematically the typical components of the ment of Chemical chemical industry: reactors, separators, heat exchangers and Engineering at the Indian Institute of Technology, utilities. Industrial separation processes represent a major por­ Madras. His research tion of the manufacturing cost for most chemicals. Of these interests are in thermody­ (Figure 2) about 55% can be described as equilibrium separation namics and statistical processes and are, as the name implies, amenable to quantitative mechanics. thermodynamic analysis. It is estimated that, on the average, 70% of the capital investment in the petroleum and petro­ chemical industry is on separation equipment alone. The energy consu.med by such prqcesses in the USA in 1976 was of the order of 1016 Joules! --------~~------ RESONANCE I September 2001 67 alNlttAL I ARTICLE Rate governed separation process separation process process Figure 1. (left) Components In any chemical industry the raw materials enter at room tem­ ofa typical chemical indus­ try. perature and the products leave at room temperature. We can Figure 2. (right) Broad clas­ therefore look upon each chemical industry as a black box sification ofindustrial sepa­ representing an isothermal process for converting a set of raw ration process. materials into a set of finished products. Thermodynamics en­ ables us to calculate the minimum work that has to be put into the industry in order to achieve the change of state from raw materials to finished products. In the following section we discuss some thermodynamic pre­ liminaries. Then we derive expressions for extrema in work which exhibit explicitly the central role of the Gibbs free energy. In order to apply these results to engineering systems we then describe the model for the Gibbs free energy of an ideal mixture. The calculation of the work of separation and the relative importance of enthalpic and entropic contributions are The major then illustrated using examples. The major component of the component of the cost of many chemicals arises from the separation steps involved cost of many in their manufacture. For a few such chemicals it is shown that chemicals arises the thermodynamic calculation of the work required to extract from the them from their naturally occurring state correlates well with separation steps their prices in a free market. We also describe briefly the concept involved in their of 'zero work' cycles. We then derive criteria of equilibrium in manufacture. terms of the Gibbs free energy and use examples to demonstrate -68-------------------------------~-------------------------------- RESONANCE I September 2001 GENERAL I ARTICLE the role of energy and entropy in the attainment of equilibrium in some reacting systems. We touch upon the interpretation of energy and entropy in statistical thermodynamics in order to help visualise mixing processes. Finally we trace the history of the development of the concept of entropy for the sake of completeness. Thermodynamic Preliminaries We shall recall the definitions of a few basic terms. A system is simply a region of interest. It is separated from the surroundings by boundaries. Systems are conveniently classified into isolated, closed or open systems depending on their interaction with the surroundings. An isolated system has no interaction whatever with its surroundings; a 'closed' system exchanges energy but no mass with its surroundings; an open system exchanges both energy and mass with its surroundings. A certain minimum number of variables must be specified in order to describe a system completely. These variables, which describe the present state of the system without any reference to its history, are called state variables (or functions of state or simply properties of the system). It follows that the change in the value of any state variable between two given states of the system is independent of the path. The most common examples are the measurable properties like pressure, volume, tempera­ ture, and composition. Functions of state playa very important role in thermodynam­ The discovery of ics. For all practical purposes the discovery of the laws of the laws of thermodynamics can be looked upon as the discovery of two thermodynamics important functions of state, the internal energy U and the can be looked entropy S. upon as the discovery of two Indeed Gibbs [2] introduced the 'fundamental thermodynamic important functions equation' and its differential form of state, the U=U(S, V) (1) internal energy U dU=TdS-PdV (2) and the entropy S. -R-ES-O-N-A-N--C-E-I--se-p-te-m-b-e-r--2-0-0-1------~-~-------------------------------6-9 GENERAL I ARTICLE Thermodynamics from which 'may be derived all the thermodynamic properties of provides criteria for the fluid (so for as reversible processes are concerned),. equilibrium, In chemical engineering applications the most important func­ typically telling tions are the enthalpy H defined as U + PVand the Gibbs free chemical energy G defined as H - TS. engineers when a reaction or a The concepts of heat (Q) and work (W') are central to thermody­ separation can namic analysis and are as difficult to define precisely as they are progress no familiar. Unlike the functions of state discussed above they are further. 'energies in transit' and are path dependent quantities. There are primarily two concerns, central to chemical engineers, that thermodynamics addresses. Firstly, thermodynamics en­ ables us to identify reversible paths, along which Q and W take on maximum or minimum values. Secondly thermodynamics provides criteria for equilibrium, typically telling chemical en­ gineers when a reaction or a separation can progress no further. Extrema in Work Consider a closed system. The two laws of thermodynamics can be expressed mathematically as follows. dU= 8Q-bW 8Q ~ TdS. Combining the two laws, rearranging and integrating between any two states of the system we deduce that the maximum work that can be done by a closed system in the isentropic case is given by w' max = -IJ.U. Conversely the minimum work that must be put into a system for an isentropic change of state is clearly given by (-W)min = ~U. While the work done by a closed system during an adiabatic process is always given by -~U, the maximum work is obtained --------~-------- 70 RESONANCE I September 2001 GENERAL I ARTICLE from the reversible case i.e. the isentropic process. Another case The total mass of practical interest is that of a process in which the system of inflow is effectively interest exchanges just enough heat with the surroundings so as equal to the total to remain at constant temperature. In this case the correspond­ mass outflow. ing results are: Wmax=-M (-W)min = M, where A = U - TS is the Helmholtz free energy, the adjective 'free' emphasising the fact that, in an isothermal process, a part of the change -t1U in the internal energy namely + Tt1S is 'unavailable', while the remainder, -M, is 'free' for conversion to useful work. The discussion following the equations for closed systems can be easily extended, mutadis mutandis, to open systems for two special cases: systems operating at steady state or with mass hold-up that is negligibly small compared to the mass flowing through the system. In either case the total mass inflow is effectively equal to the total mass outflow. In the isentropic and isothermal cases the results are simply W s max / m =-M W smaxm=-g/ . t1 (3) where Ws is mechanical 'shaft' work defined as work other than that due to changes in P or V. Small case letters refer to pro­ perties per unit mass and t1 denotes the difference in values between outlet and inlet. The left hand side of these equations represents the rate of work done divided by the mass flow rate or simply the work done per unit mass flowing through the system. Gibbs Free Energy of a Mixture In order to apply (3) it is necessary to relate changes in the Gibbs free energy to changes in measurable quantities. This involves the repeated use of differential calculus and the two laws. These relations are derived in standard textbooks [3]. We will merely -R-ES-O-N-A-N--CE--I-s-e-p-te-m-b-e-r--2-0-0-1--------~~-------------------------------n- GENERAL I ARTICLE Thermodynamics state a few results that help explain some typical chemical does not specify engineering applications. The Gibbs free energy of a mixture is the composition given by dependence of the chemical potential completely [3].
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