Carnot’s efficiency

Note that Carnot s efficiency (4.9) is definitely more restrictive than the first-law efficiency (4.2b), constrained by the ratio of heat expelled (at tc) to heat absorbed (at th). 

The energy efficiency of any heat engine is limited to the Carnot s efficiency ... 

Based on GTHTR3()0 [7], 2. Power efficiency for the carrier system is estimated by Carnot s efficiency ratio of turbines between the carrier system and the conventional electrolysis system. 3. Ref. 

Figure 1.5 describes basic galvanic elements discriminated according to energy density (per mass) and temperature. All those galvanic cells that directly convert chemical into electrical energy, without thermal detours, are hence not bound by Carnot s efficiency, and offer high theoretical efficiencies. The application of solid... 

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) ... 

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. 

There is a problem with Carnot s analysis, however, since at that time almost all physicists (including Carnot) thought heat consisted of a substance called caloric, which could not be created or destroyed. As a result, the amount of heat taken from the hot source at temperature T, would have to be the same as that delivered to the cold reservoir at temperature T(. Because no heat was converted into work, the efficiency of such an engine would be zero. 

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. ... 

Fuel cells are electrochemical devices transforming the heat of combustion of a fuel (hydrogen, natural gas, methanol, ethanol, hydrocarbons, etc.) directly into electricity. The fuel is electrochemically oxidized at the anode, whereas the oxidant (oxygen from the air) is reduced at the cathode. This process does not follow Carnot s theorem, so that higher energy efficiencies are expected up to 40-50% in electrical energy and 80-85% in total energy (heat production in addition to electricity). 

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... 

CARNOT S THEOREM EFFICIENCY THERMODYNAMICS CARNOT S THEOREM EFFICIENCY... 

The working of the cell under reversible thermodynamic conditions does not follow Carnot s theorem, so that the theoretical energy efficiency, deflned as the ratio between the electrical energy produced (—AG°) and the heat of combustion (—AH°) at constant pressure, is... 

This theoretical efficiency is much greater (by a factor of about 2) than that of a thermal combustion engine, producing the reversible work, according to Carnot s theorem ... 

CARNOT S ANALYSIS OF OPTIMAL HEAT-ENGINE EFFICIENCY 123... 

Carnot s ensuing analysis of the steam engine culminated in an idealized engine of highest possible efficiency that could be represented as an abstract mathematical Carnot cycle in a PV diagram. Understanding the logic of this supreme thermodynamic abstraction is our first task. 

Carnot s principle can be summarized as an inequality that limits the possible efficiency reai of any real engine ... 

Let us therefore begin by assuming that Carnot s principle is false, i.e., that there exists some new and improved model C whose efficiency exceeds that of the reversible Carnot cycle. The hypothetical C engine can be represented as... 

Carnot s cycle is the most efficient possible heat engine. 

Kelvin first suggested how the Carnot efficiency (4.9) might be used to define an absolute temperature scale. As Carnot s principle asserts, the efficiency... 

Carnot s theorem the maximum efficiency of reversible heat engines... 

We caution the reader that applying Carnot s analysis is based on the assumptions that the heat is available at temperature T and that the heat reservoir is infinite. This means that if we use the adiabatic flame temperature for T, we will end up with a maximum attainable efficiency, since the exchange of heat will inevitably lead to a reduction in the temperature of the reservoir. From our analysis, it is not clear whether we used an adiabatic flame temperature [11]. Note that the adiabatic temperature is the highest temperature that can be reached by the system if all the heat generated is used to elevate the flame temperature. However, we can safely state that at least 30% of the maximum work potential has been lost. We will return to this subtle point at a later stage, when we examine the combustion of natural gas. 

At this point, it is useful to point out that simply computing the efficiency based on the Carnot factor is an exercise that should be performed with care. The Carnot factor, C, is given by C = 1 - (T0/T). As shown in the example, we can compute the group -CArH/Exin to get the efficiency Strictly speaking, this is not always true, but why The answer is very subtle. Carnot s analysis holds only for infinite heat reservoirs, and if the heat (which can be viewed as the useful product) is transferred, the temperature of the reservoir (the product mixture) also changes So the correct way of computing the efficiency based on the heat is to take into account the fact that the temperature T is not constant, but is variable and will decrease to T0 ... 

Equations (5.7) and (5.8) are known as Carnot s equations. In Eq. (5.7) the smallest possible value of QC is zero the corresponding value of Tc is the absolute zero of temperature on the Kelvin scale. As mentioned in Sec. 1.4, this occurs at -273.15°C. Equation (5.8) shows that the thermal efficiency of a Carnot engine can approach unity only when TH approaches infinity or Tc approaches zero. On earth nature provides heat reservoirs at neither of these conditions all heat engines therefore operate at thermal efficiencies less than unity. The cold reservoirs naturally available are the atmosphere, lakes and rivers, and the oceans, for which Tc = 300 K. Practical hot reservoirs are objects such as furnaces maintained at high temperature by combustion of fossil fuels and nuclear reactors held at high temperature by fission of radioactive elements, for which T = 600 K. With these values,... 

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