Efficiency, Carnot cycle heat engine

Stirling engines also have the maximum theoretical possible efficiency because their power cycle (their theoretical pressure volume diagram) matches the Carnot cycle. The Carnot cycle, first described by the French physicist Sadi Carnot, determines the maximum theoretical efficiency of any heat engine operating between a hot and a cold reservoir. The Carnot efficiency formula is... 

An estimate of the efficiency of a heat engine working between two temperatures T and T - can be obtained by assuming the Carnot cycle is used. By combining the results from applying the first and second laws to the Carnot cycle, the Carnot efficiency e, may be written ... 

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... 

Students are reminded of the upper thermodynamic limit set on the efficiency of a heat engine, for example the internal combustion and gas-turbine engines. The ideal and totally unrealistic engine would operate on the so-called Carnot cycle where the working substance (e.g. the gas) is taken in at the high temperature (Th) and pressure and after doing external work is exhausted at the lower temperature (Tc) and lower pressure. The Carnot efficiency, /, is given by... 

Carnot s analysis of efficiency for a heat engine operating reversibly showed that in each cycle q/T at the high temperature reservoir and q/T at the low tem-peratnre environment snmmed to zero ... 

By definition, the efficiency of a heat engine is equal to the ratio of the total work W done in the cycle to the heat Qi taken in at the upper temperature hence, by equations (18.2) and (18.7), the efficiency of the hypothetical Carnot engine is... 

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 maximum possible performance of a heat engine set by that given by a reversible heat engine operating on a Carnot cycle, which involves four reversible processes (i) reversible isothermal heat addition, Qh, (ii) reversible adiabatic expansion (work), W, (iii) reversible isothermal heat rejection, Ql, and (iv) reversible adiabatic compression. Thermal efficiency of the heat engine is given by... 

Thus, we obtain the same formula for the efficiency of a heat engine as from the Carnot cycle. Along the way, we realized that when heat flows from hot to cold, the environment wUl gain the exhaust heat 1 1 so that the environment gains enfropy. A profound result of this sort of analysis is that entropy tends to increase in the environment unless there is some other condition and the overall entropy in the universe tends to increase. Especially for biology majors and generally for aU of us. 

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 s cycle A hypothetical scheme for an ideal heat machine. Shows that the maximum efficiency for the conversion of heat into work depends only on the two temperatures between which the heat engine works, and not at all on the nature of the substance employed. 

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 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... 

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. 

As the magnirnde of the heat exchanged in an isothermal step of a Carnot cycle is proportional to a function of an empirical temperature scale, the magnitude of the heat exchanged can be used as a thermometric property. An important advantage of this approach is that the measurement is independent of the properties of any particular material, because the efficiency of a Carnot cycle is independent of the working substance in the engine. Thus we define a thermodynamic temperature scale (symbol T) such that... 

The Carnot cycle is not a practical model for vapor power cycles because of cavitation and corrosion problems. The modified Carnot model for vapor power cycles is the basic Rankine cycle, which consists of two isobaric and two isentropic processes. The basic elements of the basic Rankine cycle are pump, boiler, turbine, and condenser. The Rankine cycle is the most popular heat engine to produce commercial power. The thermal cycle efficiency of the basic Rankine cycle can be improved by adding a superheater, regenerating, and reheater, among other means. 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

Just as the Carnot cycle C of Fig. 4.3 can be claimed to be the most efficient possible heat engine ( reai < fcamot = 1 — c/ h )> so too can the reverse Carnot cycle C be claimed to be the most efficient possible refrigerator ... 

Carnot s cycle is the most efficient possible heat engine. 

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