Isothermic processes Carnot cycle

The Intercooled Regenerative Reheat Cycle The Carnot cycle is the optimum cycle between two temperatures, and all cycles try to approach this optimum. Maximum thermal efficiency is achieved by approaching the isothermal compression and expansion of the Carnot cycle or by intercoohng in compression and reheating in the expansion process. The intercooled regenerative reheat cycle approaches this optimum cycle in a practical fashion. This cycle achieves the maximum efficiency and work output of any of the cycles described to this point. With the insertion of an intercooler in the compressor, the pressure ratio for maximum efficiency moves to a much higher ratio, as indicated in Fig. 29-36. 

The thermal efficiency of the process (QE) should be compared with a thermodynamically ideal Carnot cycle, which can be done by comparing the respective indicator diagrams. These show the variation of temperamre, volume and pressure in the combustion chamber during the operating cycle. In the Carnot cycle one mole of gas is subjected to alternate isothermal and adiabatic compression or expansion at two temperatures. By die first law of thermodynamics the isothermal work done on (compression) or by the gas (expansion) is accompanied by the absorption or evolution of heat (Figure 2.2). 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

Figure 2.10 (a) A schematic Carnot cycle in which isotherms at empirical temperatures 6 and 62 alternate with adiabatics in a reversible closed path. The enclosed area gives the net work produced in the cycle, (b) The area enclosed by a reversible cyclic process can be approximated by the zig-zag closed path of the isothermal and adiabatic lines of many small Carnot cycles. 

Figure 3.4 Carnot cycle for the expansion and compression of an ideal gas. Isotherms alternate with adiabats in a reversible closed path. The shaded area enclosed by the curves gives the net work in the cyclic process.

During process 4-1, heat is transferred isothermally from the working substance to the low-temperature reservoir at Tl. This process is accomplished reversibly by bringing the system in contact with the low-temperature reservoir whose temperature is equal to or infinitesimally lower than that of the working substance. The amount of heat transfer during the process is 641= f TdS = Ti Si — S4), which can be represented by the area 1-4-5-6-1 Q41 is the amount of heat removed from the Carnot cycle to a low-temperature thermal reservoir. 

A reversible isothermal heat-transfer process between the Carnot cycle and its surrounding thermal reservoirs is impossible to achieve... 

In order to achieve the isothermal heat addition and isothermal heat rejection processes, the Carnot simple vapor cycle must operate inside the vapor dome. The T-S diagram of a Carnot cycle operating inside the vapor dome is shown in Fig. 2.2. Saturated water at state 2 is evaporated isothermally to state 3, where it is saturated vapor. The steam enters a turbine at state 3 and expands isentropically, producing work, until state 4 is reached. The vapor-liquid mixture would then be partially condensed isothermally until state 1 is reached. At state 1, a pump would isentropically compress the vapor-liquid mixture to state 2. 

The working fluid for vapor cycles is alternately condensed and vaporized. When a working fluid remains in the saturation region at constant pressure, its temperature is also constant. Thus, the condensation or evaporation of a fluid in a heat exchanger is a process that closely approximates the isothermal heat-transfer processes of the Carnot cycle. Owing to this fact, vapor cycles closely approximate the behavior of the Carnot cycle. Thus, in general, they tend to perform efficiently. 

The simple Rankine cycle is inherently efficient. Heat is added and rejected isothermally and, therefore, the ideal Rankine cycle can achieve a high percentage of Carnot cycle efficiency between the same temperatures. Pressure rise in the cycle is accomplished by pumping a liquid, which is an efficient process requiring small work input. The back-work ratio is large. 

CARNOT CYCLE. An ideal cycle or four reversible changes in the physical condition of a substance, useful in thermodynamic theory. Starting with specified values of die variable temperature, specific volume, and pressure, the substance undergoes, in succession, an isothermal (constant temperature) expansion, an adiabatic expansion (see also Adiabatic Process), and an isothermal compression to such a point that a further adiabatic compression will return the substance to its original condition. These changes are represented on the volume-pressure diagram respectively by ub. he. ctl. and da in Fig. I. Or the cycle may he reversed ad c h a. 

Figure 4.3 Reversible Carnot cycle, showing steps (1) reversible isothermal expansion at th (2) reversible adiabatic expansion and cooling from th to tc (3) reversible isothermal compression at tc (4) reversible adiabatic compression and heating back to the original starting point. The total area of the Carnot cycle, P dV, is the net useful work w performed in the cyclic process (see text).

For a single reversible process between two sets of fixed conditions, the work is independent of the reversible path. However, in a network of reversible processes, such as Figure A.l, alteration of the pressure and temperature of the isothermal enclosure alters the pressure ratio of, for example, the fuel isothermal expander. The power output of Figure A.l is therefore variable and not a constant, merely because it is reversible. The maximum power, the fuel chemical exergy, is obtained from an electrochemical reaction at standard temperature, Tq, and sum of reactant and product pressures, Pg, with isothermal expanders only and without a Carnot cycle. 

In the classical equilibrium thermodynamics, Stirling and Ericsson cycles have an efficiency that goes to the Carnot efficiency, as it is shown in some textbooks. These three cycles have the common characteristics, including two isothermal processes. The objection to the classical point of view is that reservoirs coupled to the engine modeled by any of these cycles do not have the same temperature as the working fluid because this working fluid is not in direct thermal contact with the reservoir. Thus, an alternative study of these cycles is using finite... 

The existence of a finite heat transfer in the isothermal processes is affected with the assumption of a non-endoreversible cycle with ideal gas as working substance. Power output and ecological function have also an issue that shows direct dependence on the temperature of the working substance. Expressions obtained with the changes of variables have the virtue of leading directly to the shape of the efficiency through Z, function. Thus, in classical equilibrium thermodynamics, the Stirling cycle has its efficiency like the Carnot cycle efficiency in finite time thermodynamics, this cycle has an efficiency in their limit cases as the Curzon-Ahlborn cycle efficiency. 

Carnot cycle Composed of four reversible processes—two isothermal and two adiabatic—and can be executed either in a closed or a steady-flow system. First proposed in 1824 by French engineer Sadi Carnot (1796-1832). 

Assume that the system used to carry out the Carnot cycle is an amount of ideal gas contained in a cylinder fitted with a frictionless piston. The concept of an ideal gas is introduced in Section 1.2. Of consequence at this point is the premise that for an ideal gas the internal energy, U, is a function of temperature only. The Carnot cycle consists of reversible isothermal and adiabatic processes. An isothermal process is one in which the system temperature is kept constant. An adiabatic process requires that no heat be transferred between the system and its surroundings. The steps are as follows ... 

The Carnot cycle is a reversible process that is carried out using an ideal gas as working fluid. It involves consecutive isothermal and adiabatic steps. At the end of the cycle, the system has the same state (defined by V and p) and internal energy as at the start. At/ = 0. 

In the Carnot cycle, the process indicated in Eq. (2.25) occurs twice. First, the gas is expanded isothermally in contact with the reservoir at high temperature (h) and after the adiabatic step, the gas is compressed isothermally in contact with the reservoir at lower temperature (/). We place now formally the indices to indicate the two steps and get... 

Equation (5.25) is the condition of the Gay - Lussac experiment. The isodynamic lines must be at the same time isotherms. Conversely, an isothermal process of an ideal gas is an isodynamic process. Such a process is taking place in the Carnot cycle. This means that the amount of energy is taken up from a thermal reservoir as thermal energy is released as expansion energy and vice versa. The situation is different in the Gay - Lussac experiment. Here the gas itself converts internally. When we write the energy as... 

Carnot Cycle - The most efficient heat engine cycle Is the Carnot cycle, consisting of two isothermal processes and two adiabatic processes. The Carnot cycle can be thought of as the most efficient heat engine cycle allowed by physical laws... 

Namely, we discuss two examples of equilibrium reversible processes the isothermal and then those which are adiabatic. Such processes with ideal gas (i.e., with real stable gas at sufficiently low pressures) are used in the Carnot cycle in Appendix A.l. 

In the remaining part of this AppendixA.1, we obtain the important result (A.9) using an ideal cyclic process from subset C of Sect. 1.2, namely the Carnot cycle [1, 2, 4, 5]. Carnot cycle is a cyclic process with (fixed number of mols, n, of) uniform ideal gas composed from isothermal and adiabatic (no heat exchange) expansions followed by isothermal (at lower temperature) and adiabatic compressions back to the starting state. All these processes pass the equilibrium (stable) states and they are reversible (cf. definition in Sect. 1.2), see also Rem. 48 in Chap. 3. 

But, generally, such a cycle with adiabatic and isothermal irreversible processes may be realized with real gas (or even liquid). Those with real gas approximate the reversible Carnot cycle with ideal gas by a double limiting process as follows (i.e., we form the ideal cyclic process from set A (and also B and C), see motivation of postulate U2 in Sect. 1.2) running this cycle slower and slower... 

Problem 4.20 A Carnot cycle operates in a closed system using steam saturated liquid at 20 bar (state A) is heated isothermally until it becomes saturated vapor (state B), expanded by reversible adiabatic process to 10 bar (state C), partially condensed to state D, and finally compressed by reversible adiabatic process to initial state A. 

As we have just seen, the flow of energy as heat does not indicate whether or not a process will occur spontaneously. So we must also consider another thermodynamic state function, called entropy. Historically, entropy was first introduced in considering the efficiency of steam engines. Figure 10.2 illustrates the Carnot cycle, which uses a combination of adiabatic processes (in which no heat is exchanged) and isothermal, or constant temperature, processes. The Carnot cycle demonstrated that a previously unknown state function existed because the sum of q/T (heat divided by temperature) around the closed path is zero. This new state... 

Carnot cycle, an ideal gas undergoes a series of four processes. Two of these (labeled 1 and 3 in the figure) are isothermal, which means they occur at constant temperamre. The other two steps (2 and 4) are adiabatic, meaning that = 0 for those parts of the cycle. Carnot showed that the sum of the quantity q/T for the entire cycle is equal to zero. 

During each stage of the experimental process with nonzero heat, we allow the Carnot engine to undergo many infinitesimal Carnot cycles with infinitesimal quantities of heat and work. In one of the isothermal steps of each Carnot cycle, the Carnot engine is in thermal contact with the heat reservoir, as depicted in Fig. 4.8(a). In this step the Carnot engine has the same temperature as the heat reservoir, and reversibly exchanges heat dg with it. 

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