Carnot thermodynamic efficiency

Because batteries direcdy convert chemical energy to electrical energy ia an isothermal process, they are not limited by the Carnot efficiency. The thermodynamic efficiency S for electrochemical processes is given by ... 

Fuel cells such as the one shown on Fig. 3.4a convert H2 to H20 and produce electrical power with no intermediate combustion cycle. Thus their thermodynamic efficiency compares favorably with thermal power generation which is limited by Carnot-type constraints. One important advantage of solid electrolyte fuel cells is that, due to their high operating temperature (typically 700° to 1100°C), they offer the possibility of "internal reforming" which permits the use of fuels such as methane without a separate external reformer.33 36... 

Figure 13.3. Theoretical thermodynamic efficiency of fuel cells and Carnot machines as a function of temperature.

In the conversion of fossil and nuclear energy to electricity, the value of high temperature solution phase thermodynamics in improving plant reliability has been far less obvious than that of classical thermodynamics in predicting Carnot cycle efficiency. Experimental studies under conditions appropriate to modern boiler plant are difficult and with little pressure from designers for such studies this area of thermodynamic study has been seriously neglected until the last decade or two. 

The portion AQ = AH - AG = TAS of AH is transformed into heat. Ideal theoretical efficiencies % determined by the types and amounts of reactants and by the operating temperature. Fuel cells have an efficiency advantage over combustion engines because the latter are subdued to the Carnot limitation. High thermodynamic efficiencies are possible for typical fuel cell reactions (e.g., e,h = 0.83 (at 25°C) for H2 + I/2O2 -> H20(i)). The electrical potential difference between anode and cathode, = -AG/W(f, which is also called the electromotive force or open-circuit voltage, drives electrons through the external... 

Figure 13.6 schematically gives W, as a function of Qin and at the same time, the corresponding thermodynamic efficiency n = (Wout/Qm) has its highest value, the Carnot value, for an infinitely slow operation of the engine at a zero heat input rate Q but also at zero power output. Note that then T2 —> and T3 T0. The thermodynamic efficiency T is zero when Wout is zero, but now at the maximum possible heat input rate that the engine can absorb, namely, when T2 = T3. Somewhere between these extremes the power output... 

The thermodynamic efficiency of a fuel cell is defined as the ratio between AG° and the enthalpy of reaction, AH°, p = AG°IAH°, and is not, unlike thermal external or internal combustion engines, limited by the ideal Carnot cycle. 

THERMODYNAMIC EFFICIENCY THE CARNOT, OTTO, DIESEL, AND RANKINE CYCLES... 

PROBLEM 4.27.1. Prove that for the Carnot cycle using a perfect gas as the working fluid in reversible steps, the thermodynamic efficiency is given by Eq. (4.27.1). 

This result, called the Carnot efficiency or the thermodynamic efficiency, places a fundamental limit on the efficiency with which heat can be converted to mechanical work. Only if the high temperature, T, were infinite or the low temperature, T , were zero would it be possible to have a heat engine operate with 100% efficiency. To maximize efficiency, the greatest possible temperature difference should be used. Although we derived this result specifically for the ideal gas, we will show later in this section that it applies to any reversible engine operating between two temperatures. For a real engine, which must operate irreversibly, the actual efficiency must be lower than the thermodynamic efficiency. 

The existence of a finite heat transfer in the isothermal processes is affected with the assumption of a non-endoreversible cycle with ideal gas as working substance. Power output and ecological function have also an issue that shows direct dependence on the temperature of the working substance. Expressions obtained with the changes of variables have the virtue of leading directly to the shape of the efficiency through Z, function. Thus, in classical equilibrium thermodynamics, the Stirling cycle has its efficiency like the Carnot cycle efficiency in finite time thermodynamics, this cycle has an efficiency in their limit cases as the Curzon-Ahlborn cycle efficiency. 

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. 

Steam undergoes a Carnot cycle between temperatures 500 °C and 300 °C. During the isothermal heating step, the steam expands from pressure 50 bar to 30 bar. Determine the states in each of the four corners A, B, C, and D of the cycle (see Figure 4-f ). calculate the thermodynamic energy balances and determine the thermodynamic efficiency of the cycle. 

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. 

If instead of a rubberUke deformation a phase transition occurs, the isothermal processes are represented by horizontal lines (since the force is independent of the length), as is shown in Fig. 8.20b. If in each of the two cycles described the same adiabatics are involved, the net work performed is greater for the one with the phase transition. This is analogous to using a condensed vapor in the more conventional Carnot cycle. The thermodynamic efficiency remains the same since it depends only on the two temperatures at which the engine operates. The deliverance... 

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 ... 

For the simplest type of coolant cycle, the reversible Carnot cycle, the thermodynamic efficiency is defined by the relation... 

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. 

Note that Gibbs function decreases with increase in temperature. Thus, the reversible work and thermod5mamic efficiency of a fuel cell decrease wifh increase in temperafure. This is in contrast to the reversible thermodynamic efficiency of a Carnot heat engine where the efficiency or reversible work increases with increase in temperature. 

To identify optimization potentials within the thermodynamic cycle, in the following the basic definition of the thermal efficiency of the Rankine cycle is converted into an equivalent definition according to Carnot s efficiency, which depends only on the mean temperatures of the heat supplied and removed (Figure 6.3) ... 

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