THE NATURAL HEAT ENGINE by John C. Wheatley, Gregory W. Swift, and Albert Migliori eat engines are a compromise reversible in the sense that it can be made limit for the coefficient of performance between the crisp ideals dis- to operate in either of two modes: prime (C. O. P.) of a heat pump (the amount of cussed in thermodynamic mover or heat pump* (Fig. 1). In a prime heat rejected at the higher temperature per H textbooks and the clanking, mover, heat flows from high to low unit of work). Both theoretical limits de- hissing realities of irreversible processes, temperatures, and the engine converts a pend only on the temperatures involved. This compromise produces wonderful ma- portion of that heat to work. In a heat chines, such as the automobile engine and pump, the flows of heat and work are Carnot. The most fundamental engine the household refrigerator. In designing reversed; that is, work done on the engine cycle operating between two temperatures real devices, the goal is not to approach causes it to pump heat from low to high is the functionally and thermodynamically thermodynamic ideals by reducing ir- temperatures. Few practical engines are reversible cycle propounded by Sadi reversibilities but to balance cost, effi- functionally reversible. The internal com- Carnot in 1824. The cycle consists of alter- ciency, size, power, reliability, simplicity, bustion engine is a prime mover only; the nating adiabatic and isothermal steps and other factors important to the needs of household refrigerator is a heat pump (Fig. 2). During an adiabatic step, no heat particular applications. only: neither engine is ever operated in Simplicity is the most striking feature of both modes, remains constant. Thus any flow of work a natural engine, a reciprocating heat en- Figure 1 shows how the first and second causes a corresponding change in the tem- gine with no moving parts. As we will see, laws of thermodynamics place an upper perature of the working medium. During the basic operating cycle of the natural limit on the efficiency of a prime mover- an isothermal step, the temperature re- engine is so straightforward it can be ap- (the fraction of the heat input converted to mains constant, and flows of entropy, plied to a wide variety of systems with work), The efficiency of a thermodynam- work, and heat occur. working media that range from air to ically reversible cycle-that is, one in In the Carnot cycle, the entropy change paramagnetic disks. which all parts of the system are always in of one isothermal step exactly balances the Although the natural engine is new in thermodynamic equilibrium—is equal to entropy change of the other isothermal concept, the underlying thermodynamic that upper limit. (One statement of the step. Over a complete cycle, no entropy is principles and processes are shared with second law of thermodynamics is that all generated. If- an engine could be made to conventional engines, such as the Stirling reversible engines operating between the follow a Carnot cycle, its efficiency would and Rankine engines. To set the stage for same two temperatures have the same effi- equal the theoretical upper limit given in natural engines, we will first discuss a few ciency.) Figure 1 also shows the upper Fig. 1. Although the upper limit applies to conventional idealized thermodynamic any reversible engine, this efficiency is cycles and the practical engines they sug- usually called the Carnot efficiency. gest. *A prime mover is often called an engine and a Building an engine that approximates a heat pump a refrigerator. Here we use the term engine to denote both thermodynamic func- Carnot cycle requires that all processes in Conventional Heat Engines tions, and our use of the term heat pump in- its cycle are carried out very near equi- and Cycles cludes the refrigerator. Strictly speaking, how librium. If not, the resulting ir- ever, the purpose of a heat pump is to reject heat reversibilities due to temperature and at the higher temperature, whereas the purpose In principle, any idealized thermody- of a refrigerator is to extract heat at the lower pressure gradients generate entropy and namic heat engine cycle is functionally temperature. cause a loss of efficiency, For example, the 2 Fall 1986 LOS ALAMOS SCIENCE The release of acoustic energy by a simple natural heat engine, the Hofler tube, made evident by the white plume at the upper end. The device consists of a two-piece copper tube, closed at the bottom, and a short set of fiber glass plates that run parallel to the tube ‘s axis in the region of the flanges. The acous- tic energy results spontaneously when a temperature gradient is applied iacross the plates. In this case, the gradient was produced by holding one end of tube tube while immersing the other end (frosted) in liquid nitrogen LOS ALAMOS SCIENCE Fall 1986 3 The Natural Heat Engine temperature differences across the heat ex- changers that move heat in or out of the engine are frequently a source of ir- reversibility that greatly cuts efficiency. (See "The Fridge” for a quantitative ac- counting of this and other losses in a prac- tical heat pump. ) Although one may approach near-equi- librium conditions by designing the engine so as to reduce these gradients, the end result is a very slow cycling of the engine and a very low power output. An impor- tant point (originally made by F. L. Curzon and B. Ahlborn and generalized by S. Berry, J. Ross, and their collaborators) is that Carnot-like cycles operating be- tween two temperatures with imperfect heat exchangers have quite different effi- ciencies depending on whether work per cycle or power is being maximized, Real engines, especially high-speed reciprocat- ing engines, cannot approximate Carnot’s cycle closely, Stirling. The Stirling engine, invented in 1816 by the Reverend Robert Stirling some eighteen years before Carnot’s ideas were published and originally called the hot-air engine, is a reciprocating engine that is functionally reversible and, in prin- ciple, thermodynamically reversible. The ideal Stirling cycle has the Carnot effi- ciency. From a practical standpoint, im- Fig. 1. (a) A heat engine operating as limit for W/Qh, the efficiency of the en- plementing the Stirling cycle suffers from prime mover converts some of the heat gine. Note that a prime mover can only some of the problems of implementing the that is flowing from a hot temperature Th approach its highest efficiency of unity Carnot cycle. However, the introduction to a cold temperature TC into work. The when T c << Th. (b) In a heat engine of a second thermodynamic medium first law of thermodynamics tells us that operating as heat pump, all flows of provided the means by which high-speed Q h, the heat that passes into the engine heat and work are reversed. Thus work Stirling engines of good efficiency could be at the hot temperature, equals Q c, the done on the engine causes it to draw built. heat put back into the environment at heat out of the environment at the cold The Stirling cycle (the solid black curve the cold temperature, plus W, the work temperature and place it into the en- in Fig. 3) differs from the Carnot cycle in done by the engine. The second law vironment at the hot temperature. Con- that the adiabatic steps are replaced with tells us that the entropy per cycle gener- sideration here of the first and second steps that are reversible by virtue of being ated by the system must be positive or, laws leads to an upper limit on the coef- locally isothermal, This type of cycle is at best, zero. Since the engine is as- ficient of performance (C.O.P.), Q h/W, achieved by using two thermodynamic sumed to be in a steady state, the en- which is the reciprocal of the efficiency media. The first is the working fluid, tropy change in the environment due to of a prime mover. (For a refrigerator, the which typically can be either a gas or a the heat flow out of the engine, Q c/Tc, is C.O.P. is better defined as the ratio of liquid, (There are Stirling cycles that use greater than or equal to that due to the the heat extracted at the lower tempera- solids, but we do not discuss them here.) heat flow into the engine, Q h /Th . ture to the work done on the machine, continued on page 6 Together, these two laws give an upper that is, Qc/W.) 4 Fall 1986 LOS ALAMOS SCIENCE The Natural Heat Engine The Fridge he basis for the household refriger- ator is the Rankine cycle, which, as T shown in the figure, duplicates a portion of the Carnot cycle in that it has Condenser I one adiabatic step and two isothermal I steps. A key feature of this cycle is a phase change in the working fluid. and the two isothermal steps correspond to condensa- 0\ tion of the fluid at T h and evaporation at T . Also, the engine operates with continu- c I Evaporator I ous flow rather than by reciprocating: the working fluid cycles through its various thermodynamic states by being forced The Rankine cycle, used in the house- steps and, on the compression side, an around a closed loop. hold refrigerator, is based on a liquid- adiabatic step. The two parts of the cy- This cycle has intrinsic irreversibilities gas phase change. The cycle is shown cle (shown in red) that differ from the associated with the free expansion of the here superimposed on the phase dia- Carnot cycle—the cooling of the gas at liquid and the cooling of the gas to the gram for the working fluid; a schematic constant pressure to the condensation temperature at which condensation oc- of the heat pump is also shown.