Carnot heat engine thermodynamic efficiency

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 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... 

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. 

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 ... 

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. 

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. 

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... 

One hundred fifty years ago, the two classic laws of thermodynamics were formulated independently by Kelvin and by Clausius, essentially by making the Carnot theorem and the Joule-Mayer-Helmholtz principle of conservation of energy concordant with each other. At first the physicists of the middle 1800s focused primarily on heat engines, in part because of the pressing need for efficient sources of power. At that time, chemists, who are rarely at ease with the calculus, shied away from... 

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... 

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 Carnot cycle engine is actually the only reversible engine that we can design with two heat reservoirs. We see that because of the need to reject heat when returning the engine to its initial state, the engine cannot operate with unit efficiency. In Chapter 3, we will elevate this observation to one of the basic tenets of thermodynamics—the second law. 

In Chapter 2, we have analyzed one particular type of heat engine, the reversible Carnot cycle engine with an ideal gas as the working substance, and found that its efficiency is e = 1 — Tc/Th. For both practical and theoretical reasons, we ask if it is possible, with the same two heat reservoirs, to design an engine that achieves a higher efficiency than the reversible Carnot cycle, ideal gas engine. What can thermodynamics tell us about this possibility ... 

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... 

Since all reversible heat engines working between the same two temperatures will have the same efficiencies, we can conclude that their efficiencies depend only upon the two temperatures between which they work. For further thermodynamic consideration it is, therefore, sufficient that we consider that type of reversible machine, which will lend itself to simple thermodynamic treatment. A machine employing Carnot s cycle is of such a type. 

An internal combustion engine, as well as a major electrical power station are both "heat engines" in the thermodynamic sense, and their theoretical maximum efficiency is that of the Carnot cycle. 

The steam generation and condensing cycle is, by itself, not highly efficient as may be predicted by the fundamental thermodynamic theory of a reversible heat engine (Carnot Cycle) which gives ... 

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. 

In tire hydrogen production by nuclear heat, there is the limitation by thermodynamic law (the Carnot efficiency at the highest), because either the electrolysis or the thermochemical water splitting process has to go through the "heat engine path. 

The second law of thermodynamics postulates It is impossible for a device operating in a cyclic manner to completely convert heat into work. If the heat flows spontaneously from higher to tower temperature, the opposite process requires a heat engine. Carnot demonstrated that the maximum work from a heat engine is given by a cycle formed by two adiabates and two isotherms whose efficiency is ... 

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