Reversible cyclic engines

Consider a process shown in Figure 2.14 in which a quantity of heat q2 flows from a high temperature reservoir T2 into a reversible cyclic engine. Part of the heat is converted into work ir while the remainder q flows into a low temperature reservoir. The efficiency of this process is defined asqq r) = -w/q2, and it is a function of the reservoir temperatures. The relationship can be derived as follows ... 

Figure 6.1 Any cyclic reversible heat engine can be seen as comprising a large number of Carnot s Cycles...

Suppose that we run engine E in its reverse cycle and couple it to engine E running in its forward cycle. This gives us a composite cyclic engine that produces heat and work effects that are simply the sum of the individual effects of the appropriate cycles ... 

A "heat engine" is any cyclic device that takes heat from a high-temperature reservoir, does useful work, and expels xmused heat to a low-temperature reservoir. For a specified amount of heat into the engine, show that any real (i.e., irreversible) heat engine always produces less useful work than would a reversible heat engine operating between the same two reservoirs. 

Since the cyclic engine returns to its initial state, whether it is reversible or irreversible, there is no change in its entropy. On the other hand, since the heat transferred to the reservoirs and the irreversible engine have opposite sign, the total change of entropy of the reservoirs is... 

The second law of thermodynamics may be used to show that a cyclic heat power plant (or cyclic heat engine) achieves maximum efficiency by operating on a reversible cycle called the Carnot cycle for a given (maximum) temperature of supply (T ax) and given (minimum) temperature of heat rejection (T jn). Such a Carnot power plant receives all its heat (Qq) at the maximum temperature (i.e. Tq = and rejects all its heat (Q ) at the minimum temperature (i.e. 7 = 7, in) the other processes are reversible and adiabatic and therefore isentropic (see the temperature-entropy diagram of Fig. 1.8). Its thermal efficiency is... 

Considering an ideal heat engine as the system, the first law as applied to the engine undergoing a series of reversible changes in a cyclical fashion becomes... 

The reverse direction of a spontaneous process requires that some work must be done on the system. In 1824, Sadi Carnot, an engineer in Napoleon s army, presented an ideal engine in which the heat could not be completely converted into work. The engine had an ideal gas in a cylinder with a frictionless piston and employed a cyclic operation. In Figure 1.5, the pressure and volume are related to the four steps of the cycle. Initially, the engine contains an initial pressure of P, an initial volume of V, and an initial temperature of TH as the initial state A. 

A thermodynamic engine operates cyclically and reversibly between two temperature reservoirs, absorbing heat from the high-temperature bath at 450 K and discharging heat to the low-temperature bath at 300 K. 

If a molecular-level device has to work by inputs of chemical energy, it will need addition of fresh reactants ( fuel ) at any step of its working cycle, with the concomitant formation of waste products [11]. Accumulation of such waste products, however, will compromise the cyclic operation of the device unless they are removed from the system, as it happens in our body as well as in macroscopic internal combustion engines. The need to remove waste products introduces noticeable limitations in the design and construction of artificial molecular-level devices based on chemical fuel inputs. In any case, since a molecular device has to work by repeating cycles [point (c)], a fundamental requirement is that any chemical process taking place in the system has to be reversible. 

Che, Y., and Marshall, G. R. (2006) Engineering cyclic tetrapeptides containing chimeric amino acids as preferred reverse-turn scaffolds. J. Med. Chem. 49, 111-124. 

T . This may require Carnot engines or heat pumps internal to the system that provide for the reversible transfer of heat from the temperature of the flowing fluid to that of the surroundings. Since Carnot engines and heat pumps are cyclic, they undergo no net change of state. 

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