Reversible heat engines

Heat pump A reversed heat engine or refrigerator that takes in heat from a body at low temperature and by the expenditure of mechanical work rejects heat to a body at a higher temperature. 

Reversible heat engine A heat engine, which will convert a certain quantity of heat into an amount of work (W7), that will produce the original quantity of heat if the same amount of w ork is expended in driving the engine backwards. 

Fig. 2.3 shows such a fully reversible steady flow through the control volume CV. The heat transferred [GrevIx. supplies a reversible heat engine, delivering external work [( c)rev]x and rejecting heat [(2o)rev1x to the environment. 

All reversible heat engines operating between a fixed high-temperature heat source thermal reservoir and a fixed low-temperature heat sink thermal reservoir have the same efficiency. 

The combination of a SOFC with a heat engine allows highest electric efficiencies. This is caused by the comparable low entropy production within high temperature fuel cells. Generally, the combination of a reversible fuel cell and a reversible heat engine, as represented by the Carnot cycle, results in a reversible process at any operating temperature of the fuel cell. This combination can be used as refer-... 

In the development of the second law and the definition of the entropy function, we use the phenomenological approach as we did for the first law. First, the concept of reversible and irreversible processes is developed. The Carnot cycle is used as an example of a reversible heat engine, and the results obtained from the study of the Carnot cycle are generalized and shown to be the same for all reversible heat engines. The relations obtained permit the definition of a thermodynamic temperature scale. Finally, the entropy function is defined and its properties are discussed. 

The temperature scales that have been discussed earlier are quite arbitrary and depend upon the properties of a particular substance. Kelvin was the first to observe that the efficiency of a reversible heat engine operating between two temperatures is dependent only upon the two temperatures and not at all upon the working substance. Therefore, a temperature scale could be defined that is independent of the properties of any substance. 

The second law is independent of the first law. Historically, the second law was generally accepted and understood before acceptance of the first law. Therefore, we base the discussion on the efficiency of a reversible heat engine used in a Carnot cycle. If the efficiency of a reversible heat engine... 

The Kelvin scale is thus defined in terms of an ideal reversible heat engine. At first such a scale does not appear to be practical, because all natural processes are irreversible. In a few cases, particularly at very low temperatures, a reversible process can be approximated and a temperature actually measured. However, in most cases this method of measuring temperatures is extremely inconvenient. Fortunately, as is proved in Section 3.7, the Kelvin scale is identical to the ideal gas temperature scale. In actual practice we use the International Practical Temperature Scale, which is defined to be as identical as possible to the ideal gas scale. Thus, the thermodynamic scale, the ideal gas scale, and the International Practical Temperature Scale are all consistent scales. Henceforth, we use the symbol T for each of these three scales and reserve the symbol 9 for any other thermodynamic scale. 

We prove the identity of the Kelvin scale and the ideal gas scale by using an ideal gas as the fluid in a reversible heat engine operating in a Carnot cycle between the temperatures T2 and 7. An ideal gas has been defined by Equations (2.36) and (2.37). Then the energy of an ideal gas depends upon the temperature alone, and is independent of the volume. 

The efficiency of reversible heat engines two statements of the second law of thermodynamics... 

We now discuss the efficiency of a reversible heat engine operating in a Carnot cycle. The efficiency depends upon the difference between the two temperatures. The greater the difference for a fixed T2 is, the greater the... 

Carnot s theorem the maximum efficiency of reversible heat engines... 

We continue with a reversible heat engine operating in a Carnot cycle, but center our attention on the working substance rather than on the entire system consisting of the heat engine, the work reservoir, and the two heat reservoirs. For such a cycle we can write... 

Draw a work diagram for a reversible heat engine that operates with two isothermal steps and two constant-pressure steps. How many heat reservoirs are needed to operate this engine ... 

Equation (28) provides us with a means of defining a temperature scale that is as elegant as it is impractical. Our thermometer is a reversible heat engine, the efficiency of which we measure when it is operated between the temperature of interest and a reference temperature, defined as 273.15 K for an ice bath at 1 atm... 

The product of the efficiency of a reversible heat engine times the coefficient of performance of a reversible heat pump, both operating between... 

A thermometer is based on a reversible heat engine, which operates between a boiling water bath and a heat reservoir at a lower temperature. The boiling water bath is defined to be at 373°. The temperature of the low temperature bath is determined from the efficiency with which the engine converts heat withdrawn from the boiling water bath to mechanical energy. Derive an explicit equation, Tc = /(e), from which the temperature of the low-temperature bath can be calculated. 

From the first law (energy conservation) of thermodynamics we have dQi = dW + dQ2, and the second law (entropy creation) of thermodynamics gives us dQx Tx) + dQ2IT2) a 0, where equality is for a reversible heat engine and inequality for an irreversible one. We then have the efficiency dW/dQx) for the reversible heat engine and the efficiency... 

No creation of entropy and uncompensated heat occurs in the reversible heat engine and pomp, and hence Eq. 3.45 gives the maximum efficiency theoretically attainable for heat engines and heat pumps. This equation also shows that thermal energy (heat) can not be... 

The efficiency of the reversible heat engine, krev = (W JQ) as given in Eq. 3.45, represents the energy availability XQ of an amount of heat Q at a constant temperature T ... 

Fig. 10.1. Conversion of heat Q into work through a reversible heat engine between a high temperature T and the temperature T0 of our environment.

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