Carnot heat engine

Fig. 1. Schematic representation of (a) Carnot heat engine and (b) Carnot refrigerator used as a heat pump.

Whenever energy is transformed from one form to another, an iaefficiency of conversion occurs. Electrochemical reactions having efficiencies of 90% or greater are common. In contrast, Carnot heat engine conversions operate at about 40% efficiency. The operation of practical cells always results ia less than theoretical thermodynamic prediction for release of useful energy because of irreversible (polarization) losses of the electrode reactions. The overall electrochemical efficiency is, therefore, defined by ... 

Considering the concepts of reversible processes, a reversible cycle can be carried out for given thermal reservoirs at temperatures and Tl. The Carnot heat engine cycle on a p-V diagram and a T-S diagram, as shown in Fig. 1.4 is composed of the following four reversible processes ... 

Referring to Fig. 1.4, the system undergoes a Carnot heat engine cycle in the following manner ... 

Figure 1.4 Carnot heat engine cycle on p-v and T-s diagram.

According to the definition of heat engine efficiency, the efficiency of the Carnot heat engine is = output/6input = [area l-2-3-4-l]/[area... 

If the Carnot cycle for a heat engine is carried out in the reverse direction, the result will be either a Carnot heat pump or a Carnot refrigerator. Such a cycle is shown in Fig. 1.5. Using the same graphical explanation that was used in the Carnot heat engine, the heat added from the low-temperature reservoir at Tl is area 1-4-5-6-1 g4i is the amount of heat added to the Carnot cycle from a low-temperature thermal reservoir. 

The efficiency of the Carnot heat engine operating between a fixed high-temperature heat source thermal reservoir at Th and a fixed low-temperature heat sink thermal reservoir at Tl is irrespective of the working substance. 

The Carnot cycle is a reversible cycle. Reversing the cycle will also reverse the directions of heat and work interactions. The reversed Carnot heat engine cycles are Carnot refrigeration and heat pump cycles. Therefore, a reversed Carnot vapor heat engine is either a Carnot vapor refrigerator or a Carnot vapor heat pump, depending on the function of the cycle. 

Are the heat transfers between the Carnot heat engine and its surrounding heat source and heat sink reversible ... 

Equation (7.21) is the optimal performance characteristics of the endoreversible Carnot heat engine. It indicates that P = 0 when y = 0 and iy = iyc = 1 — Pl/Ph- Taking the derivative of P with respect to y and setting it equal to zero (dP/diy = 0) gives... 

The power versus efficiency characteristics of the endoreversible Carnot heat engine is a parabolic curve. The endoreversible heat engine is a simple model, which considers the external heat-transfer irreversibility between the heat engine and its surrounding heat reservoirs only. 

Wu, C., Power optimization of a finite-time Carnot heat engine. Energy The International Journal, 13(9), 681-687, 1988. 

This perfect result can be achieved by operating a Carnot heat engine between the temperatures TH and T0 (Figure 5.2). In this operation, heat is isothermally transferred from the heat source at a temperature TH to a working fluid, whereas an amount of heat Qin - V iix = Qo is isothermally transferred from the working fluid to the environment at temperature T0. 

As shown in Sec. 5.2, the efficiency of a Carnot heat engine is independent of the working medium of the engine. Similarly, the coefficient of perfomianee of a Carnot refrigerator is... 

Note that if the Carnot heat engine is operated as shown in Fig. 4.3-2 it absorbs heat from the high-temperamre bath, exhausts heat to the low-temperature bath, and produces work. However, if the engine is operated in reverse, it accepts work, absorbs heat from the low-temperature bath, and exhausts heat to the high-temperature bath. In this mode it is operating as a refrigerator, air conditioner, or heat pump. 

Thus, the thermodynamic efficiency of the Carnot heat engine is at a maximnm when the engine is operating reversibly and can never be 1, or 100 percent, because T,. can never be zero and cannot be infinite. In other words, we can never convert heat totally into work some of it escapes into the surroundings as waste heat. 

Notice that the ecological criterion proposed by Angulo-Brown for finite-time Carnot heat engines. Equation (3), represents a compromise between the high power output P and a loss power output, T a. However Yan (1993) showed that it might be more reasonable to use Eg = P - Tq(T if the cold reservoir temperature Tq is not equal to the environments temperature Tg because in the definition of E two different quantities, exergy outpnit, P, and... 

Chen, J. (1994). The Maximum Power Output and Maximum Efficiency of an Irreversible Carnot Heat Engine, /, Phys. D Appl. Phys., Vol. 27, pp. 1144-1149 Chen, J. (1996). The Efficiency of an Irreversible Combined Cycle at Maximum Specific Power Output, /, Phys. D Appl. Phys. Vol. 29, pp. 2818-2822 Chen, L. . Zhang, W. Sun, F. (2007). Power, efficiency, entropy generation rate and ecological optimization for a class of generalized universal heat engine cycles. Applied Energy, Vol. 84, pp. 512-525... 

The direct combustion of hydrogen in an oxygen atmosphere follows the same reaction as in Equation 1.7. In this process, AH is transformed completely into thermal energy (heat), which can be converted into mechanical work using a steam turbine. Thereafter, it can be transformed into electrical work in an electric generator. The upper limit of the thermodynamic efficiency for any heat or steam cycle corresponds to the efficiency of the hypothetical Carnot heat engine ... 

Data presented in Table 4.3 shows variations in enthalpy of reaction and entropy of reaction with increase in temperature. The change in Gibbs function is estimated based on Equation 4.30a, and results show a decrease in negative of Gibbs energy of formation. Thus, the reversible work of a fuel cell also decreases with increase in temperature. This is in contrast to the reversible work of a Carnot heat engine where the net reversible work and, hence, the thermal efficiency increase with increase in high-temperature heat somce. 

A Carnot heat pump is a Carnot heat engine that is driven backwards by another engine. It removes heat from the cool reservoir and exhausts heat into the hot reservoir. Figure 3.3 represents a Carnot heat pump cycle, which is the reverse of the cycle of Figure 3.2. The steps are numbered with a prime ( ) and are numbered in the order in which they occur. Since we are considering the same Carnot engine run backwards,... 

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