Thermodynamics Carnot engine efficiency

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. 

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. 

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. 

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. 

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 ... 

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. 

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... 

Figure 3.11 Comparison between the thermodynamic efficiency of a heat engine (Carnot cycle efficiency) and the ideal efficiency of an H2-O2 fuel cell.

The amount of heat addition (Qh), heat rejection (QJ, and turbine work output (Wnet) in a heat engine cycle is estimated by applying the first law of thermodynamics. The thermal efficiency of a real heat engine cycle is less than the reversible Carnot cycle efficiency given by Equation 4.3. 

Entropy has both macroscopic and molecular aspects, as we have seen. The thermodynamic entropy is defined in terms of heat transferred in a reversible process. When heat is transferred from a higher to a lower temperature, the entropy of the universe increases. Heat at a lower temperature is less efficient in driving a Carnot engine, so entropy has some connection with the efficiency with which heat can be turned into work. In a later chapter we will discuss free energy, which is closely associated with the thermodynamic entropy. 

For combustion engines, steps A and B are combined in the well known way. The efficiency of step B is limited since the efficiency of a closed-cycle heat engine cannot surpass a certain value at given temperatures for the input and output of heat as derived by Carnot on thermodynamic grounds. Total efficiencies of up to 41% have been achieved for the conversion of chemical energy into electric energy in modern units. 

Carnot, Nicolas Leonard Sadi (1796-1832)AFrenchphysicistwhobeganhlscareer as a military engineer before turning to scientific research. In 1824 he published a book Reflections on the Motive Power of Fire, which provided for the first lime a general theoretical approach to understanding the conditions under which the efficiency of heat engines could be maximized. The thermodynamic Carnot cycle eventoally led to the concept of entropy. He died aged 36 from cholera. 

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 ... 

The second law of thermodynamics may be used to show that a cyclic heat power plant (or cyclic heat engine) achieves maximum efficiency by operating on a reversible cycle called the Carnot cycle for a given (maximum) temperature of supply (T ax) and given (minimum) temperature of heat rejection (T jn). Such a Carnot power plant receives all its heat (Qq) at the maximum temperature (i.e. Tq = and rejects all its heat (Q ) at the minimum temperature (i.e. 7 = 7, in) the other processes are reversible and adiabatic and therefore isentropic (see the temperature-entropy diagram of Fig. 1.8). Its thermal efficiency is... 

France was a center for the development of thermodynamics, the study of heat and its conversion to other forms of energy. A few years before Ril-lieux s arrival in Paris, the French physicist Sadi Carnot had published his studies of steam engines and described the principles that became the second law of thermodynamics, placing fundamental limits on how efficiently heat can be used. Within a few years, James Prescott Joule of England would lay the basis for the first law of thermodynamics stating the equivalence of heat and energy. 

It is commonly expressed that a fuel cell is more efficient than a heat engine because it is not subject to Carnot Cycle limitations, or a fuel cell is more efficient because it is not subject to the second law of thermodynamics. These statements are misleading. A more suitable statement for... 

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