Engines Carnot

Tc- 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 cychc, they undergo uo net change of state. 

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. 

The Carnot engine (or cyclic power plant) is a useful hypothetical device in the study of the thermodynamics of gas turbine cycles, for it provides a measure of the best performance that can be achieved under the given boundary conditions of temperature. 

Fig. 2..t. Rever. iibie process with heat trnnst er at temperature T(to Carnot engine) (after Ref. 151). 

The above analysis has been concerned with heat transfer from the control volume. Consider next heat [AQ] = [d REvlx transferred to the control volume. Then that heat could be reversibly pumped to CV (at temperature T) from the atmosphere (at temperature To) by a reversed Carnot engine. This would require work input... 

The exergy equation (2.26) enables useful information on the irreversibilities and lost work to be obtained, in comparison with a Carnot cycle operating within the same temperature limits (T ,ax = Ey and T in = To). Note first that if the heat supplied is the same to each of the two cycles (Carnot and IJB), then the work output from the Carnot engine (Wcar) is greater than that of the IJB cycle (Wijg), and the heat rejected from the former is less than that rejected by the latter. 

Carnot s research also made a major contribution to the second law of thermodynamics. Since the maximum efficiency of a Carnot engine is given by 1 -T( H, if the engine is to be 100 percent efficient (i.e., Cma = 1), Tc must equal zero. This led William Thomson (Lord Kelvin) to propose in 1848 that Tf must be the absolute zero of the temperature scale later known as the absolute scale or Kelvin scale. ... 

This remarkable result shows that the efficiency of a Carnot engine is simply related to the ratio of the two absolute temperatures used in the cycle. In normal applications in a power plant, the cold temperature is around room temperature T = 300 K while the hot temperature in a power plant is around T = fiOO K, and thus has an efficiency of 0.5, or 50 percent. This is approximately the maximum efficiency of a typical power plant. The heated steam in a power plant is used to drive a turbine and some such arrangement is used in most heat engines. A Carnot engine operating between 600 K and 300 K must be inefficient, only approximately 50 percent of the heat being converted to work, or the second law of thermodynamics would be violated. The actual efficiency of heat engines must be lower than the Carnot efficiency because they use different thermodynamic cycles and the processes are not reversible. 

In practice the situation is less favorable due to losses associated with overpotentials in the cell and the resistance of the membrane. Overpotential is an electrochemical term that, basically, can be seen as the usual potential energy barriers for the various steps of the reactions. Therefore, the practical efficiency of a fuel cell is around 40-60 %. For comparison, the Carnot efficiency of a modern turbine used to generate electricity is of order of 50 %. It is important to realize, though, that the efficiency of Carnot engines is in practice limited by thermodynamics, while that of fuel cells is largely set by material properties, which may be improved. 

A major way of supplying work to a process is by setting the temperature of the heat that is added to the process. It is known from the thermodynamic study of Carnot engines that heat at high temperature has the ability to do work, and the quality or the work potential depends on its temperature. Thus, when we add heat to a process we are equivalently adding a certain amount of work to the process that we could access if the process is designed for reversibility. 

Consider staging the CTL process, i.e., producing synthesis gas (CO and H2) and then converting the syngas into liquid. Work is added to the process since in this case the process itself becomes a Carnot engine, as shown in Figure 17.3. 

The two-stage process has Gibbs energies and enthalpies that allow much of the work to come in and out of the process as heat, i.e., via Carnot engines. 

Figure 6.1. Scheme of a Carnot engine as a) a heat engine and b) as a refrigerator or heat pump. 

By a similar argument, it can be shown that the assumption of an efficiency less than a also leads to a contradiction of the second law. Thus, any reversible Carnot engine operating between the same pair of reservoirs has the same efficiency, and that efficiency must be a function only of the temperatures of the reservoirs. 

Now consider a group of three heat reservoirs at temperatures fj < 2 < h and a reversible Carnot engine that operates successively between any pair of reservoirs. According to Equation (6.19)... 

Thus, we have obtained the specific functional relationship between the efficiency of a reversible Carnot engine and the thermodynamic temperatures of the heat reservoirs. 

In the synthesis of sucrose, 23,000 J of the 29,300 J available from the hydrolysis of ATP are used for synthetic work. If we call 23,000/29,300 the efficiency of this pair of reactions carried out at 37°C, and if we consider 37°C equivalent to the temperamre of the high-temperature reservoir of a heat engine, what would the temperature of the low-temperature reservoir have to be to attain a comparable efficiency for a reversible Carnot engine ... 

A Carnot engine with a steady flow rate of 1 kg/sec uses water as the working fluid. Water changes phase from saturated liquid to saturated vapor as heat is added from a heat source at 300° C. Heat rejection takes place at a pressure of lOkPa. Determine (1) the quality at the exit of the turbine, (2) the quality at the inlet of the pump, (3) the heat transfer added in the boiler, (4) the power required for the pump, (5) the power produced by the turbine, (6) the heat transfer rejected in the condenser, and (7) the cycle efficiency. 

The T-s diagram and schematic diagram of the Curzon and Ahlborn (endoreversible Carnot) cycle are shown in Figs. 7.5 and 7.6, respectively (Cuzon, F.L. and Ahlborn, B., Efficiency of a Carnot engine at maximum... 

Wu, C. and Kiang, R.L., Finite time thermodynamic analysis of a Carnot engine with internal irreversibility. Energy The International Journal, 17(12),... 

The clockwise direction in C corresponds to the clockwise direction in the Carnot cycle, with heat and work input/output as shown in Fig. 4.2. We can similarly envision a reverse Carnot engine ( heat pump ) C, which is obtained by reversing the directions of heat and work arrows and traversing the Carnot cycle in counterclockwise direction ... 

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