Thermodynamics Carnot engine

Rankine Cycle Thermodynamics. Carnot cycles provide the highest theoretical efficiency possible, but these are entirely gas phase. A drawback to a Carnot cycle is the need for gas compression. Producing efficient, large-volume compressors has been such a problem that combustion turbines and jet engines were not practical until the late 1940s. 

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. 

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. 

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 thermodynamic 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 the 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. 

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

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

We may define the right side of Eq. (5.4) as the ratio of two thermodynamic temperatures they are to each other as the absolute values of the heats absorbed and rejected by Carnot engines operating between reservoirs at these temperatures, quite independent of the properties of any substance. However, Eq. (5.4) still leaves us arbitrary choice of the empirical temperature represented by 9 once this choice is made, we must determine the function ifi. If 6 is chosen as the Kelvin temperature T, then Eq. (5.4) becomes... 

Carnot engine, 147, 249 compressor and turbine, 226-227, 235 of heat engines 140-141 of internal-combustion engines, 262-269 of irreversible processes, 69 qf power plants, 252-254 thermal, 140-141, 147, 249 thermodynamic, 551 Electrolytic cell, 42, 248 Energy, 12-17... 

Eor estimation purposes we need not be concerned with the design of the heat engine, but assume that a suitable engine can be built to deliver 30 percent of the work of a Carnot engine operating between the temperatures of 300 and 115 K. The equations that apply to Carnot engines can be found in any thermodynamics text. 

The first conclusion is that a Thermodynamic temperature scale exists which has fixed ratios of temperature between any two equilibrium states. Fixing the temperature of any one equilibrium state then fixes the temperature of all others. This follows from the fact that q /92 is a fixed number for any two equilibrium states, being independent of the size, shape, or working substance of the (hypothetical) Carnot engine used. These conclusions follow from the derivations we have omitted. 

From the characteristics of a particularly simple kind of heat engine, the Carnot engine, and from universal experience that certain kinds of engine cannot be constructed, we concluded that all reversible heat engines operating between the same two heat reservoirs have the same efficiency, which depends only on the temperatures of the reservoirs. Thus it was possible to establish the thermodynamic scale of temperature, which is independent of the properties of any individual substance, and to relate the efficiency of the engine to the temperatures on this scale ... 

The highest thermodynamic effici cy is achieved in the Carnot cycle in which energy input (heating the working medium) and work both occur at differrat but constant temperatures, Tjj, and T. For a "Carnot engine ... 

Thus, Sadi Carnot s analysis of Carnot cycle provided the theory for the formulation of the first and the second law of thermodynamics. His concept is that for a system undergoing a cycle, the net heat transfer is equal to the net work done, which led to the first law of thermodynamics. Similarly, the concept that a heat engine cannot convert all the heat absorbed from a heat source at a single temperature into work even under ideal condition led to the second law of thermodynamics. Carnot cycle efficiency gives the idea about the maximmn theoretical efficiency of an engine. Sadi Carnot was rightly honored with the title Father of Thermodynamics for his invaluable contribution to thermodynamics. 

French physicist, who first worked as a miiitary engineer. He then turned to scientific research and in 1824 published his analysis of the efficiency of heat engines. The key to this analysis is the thermodynamic Carnot cycle. He died at an early age of cholera. 

The father of thermodynamics is Sadi Carnot. He wrote Reflections on the Motive Power of Fire in 1824. This was a discourse on heat, power, and engine efficiency. The Carnot engine, Carnot cycle, and Carnot equations are named after him. 

Two particular temperature scales are used extensively. The ideal-gas temperature scale is defined by gas thermometry measurements, as described on page 42. The thermodynamic temperature scale is defined by the behavior of a theoretical Carnot engine, as explained in Sec. 4.3.4. These temperature scales correspond to the physical quantities called ideal-gas temperature and thermodynamic temperature, respectively. Although the two scales have different definitions, the two temperatures turn out (Sec. 4.3.4) to be proportional to one another. Their values become identical when the same unit of temperature is used for both. Thus, the kelvin is defined by specifying that a system containing the solid, liquid, and gaseous phases of H2O coexisting at equilibrium with one another (the triple point of water) has a thermodynamic temperature of exactly 273.16 kelvins. We... 

The plan of the remaining sections of this chapter is as follows. In Sec. 4.3, a h)q)o-thetical device called a Carnot engine is introduced and used to prove that the two physical statements of the second law (the Clausius statement and the Kelvin-Planck statement) are equivalent, in the sense that if one is true, so is the other. An expression is also derived for the efficiency of a Carnol engine for Ihe purpose of defining thermodynamic temperature. Section 4.4 combines Carnot cycles and the Kelvin-Planck statement to derive the existence... 

---