Ideal 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. 

In sununary, for an idealized, reversible heat engine that absorbs heat Q from a hot reservoir at absolute temperature T and discards heat Qz to a cold reservoir at absolute temperature Tz, firom (3.2.3) we have... 

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. 

What happens when such real processes are carried out in an ideal mode Let us imagine that a reversible heat engine is operating between two temperatures Tj and T2, i.e., the heat source is at T, and the heat sink is at T. In a complete cycle of operation the system of heat engine returns to its original temperature (or original state) after taking, say quantity of... 

Let us consider one mole of an ideal gas contained in a cylinder with a frictionless piston. Statement (//) of second law requires that if this assembly is to be used as a reversible heat engine, it must work at least between two temperatures. Let those temperatures be (higher) and (Lower). It is obvious that such an engine cannot work only in adiabatic cycles. An adiabatic cycle will not pick up any energy and therefore cannot give out energy in the form of work. 

In this expression for the efficiency, 0 is the temperature defined by one particular property (such as volUfne at a constant pressure) and we assume that it satisfies the ideal gas equation. The temperature t, measured by any other empirical means such as measuring the volume of mercury, is related to 0. We may denote this relation by 0(t), i.e. t measured by one means is equal to 0 = 0(t), measured by another means. In terms of any other temperature t, the efficiency may take a more complex form. In terms of the temperature 9 that obeys the ideal gas equation, however, the efficiency of the reversible heat engine takes a particularly simple form (3.1.9). 

Discussion of the conversion of heat to work with a reversible heat engine - the Carnot cycle - essential for the development of an analytical statement of the second law (and, to bring this ideal engine closer to reality, the very real power plant cycle - for the production of electricity from fuels - is described briefly). 

We have arrived, thus, at a new temperature, established by the second law and not arbitrarily through, for example, the Celsius scale or even through an ideal gas. Rather, it is defined in terms of the ratio of the heats absorbed and rejected in a reversible heat engine ... 

Show, using the verbal statement of the second law, that if two reversible heat engines operate between the same temperatures, they have equal efficiencies. 3.52.a.What is the difference between the thermodynamic and the ideal gas temperature ... 

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... 

As the efficiency of a Camot engine is independent of the working substance, the efficiency given in Equation (6.42) for an ideal gas must be equal to that given in Equation (6.29) for any reversible Camot engine operating between the same heat reservoirs. Thus,... 

Although the two scales are identical numerically, their conceptual bases are different. The ideal gas scale is based on the properties of gases in the limit of zero pressure, whereas the thermodynamic scale is based on the properties of heat engines in the limit of reversible operation. That we can relate them so satisfactorily is an illustration of the usefulness of the concepts so far defined. 

An ideal reciprocating Stirling refrigeration cycle is shown in Fig. 6.30. It is the reversible Stirling heat engine cycle, which is composed of two isothermal processes and two isochoric processes. Working fluid is... 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

In Chapter 2, we have analyzed one particular type of heat engine, the reversible Carnot cycle engine with an ideal gas as the working substance, and found that its efficiency is e = 1 — Tc/Th. For both practical and theoretical reasons, we ask if it is possible, with the same two heat reservoirs, to design an engine that achieves a higher efficiency than the reversible Carnot cycle, ideal gas engine. What can thermodynamics tell us about this possibility ... 

The effect of increasing the compression ratio, defined as the ratio of the volumes at the beginning and end of the compression stroke, is to increase the efficiency of the engine, i.e., to increase the work produced per unit quantity of fuel. We demonstrate this for an idealized cycle, called the air-standard cycle, shown in Fig. 8.9. It consists of two adiabatic and two constant-volume steps, which comprise a heat-engine cycle for which air is the working fluid. In step DA, sufficient heat is absorbed by the air at constant volume to raise its temperature and pressure to the values resulting from combustion in an actual Otto engine. Then the air is expanded adiabatically and reversibly (step AB), cooled... 

This derivation makes clear the difference between W , the shaft work of the turbine, and Wideal. The ideal work includes not only the shaft work, but also all work obtainable by the operation of heat engines for the reversible transfer of heat to the surroundings at T0. 

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