Efficiency, Carnot engine

Would the Carnot engine efficiency be increased more by (a) increasing at fixed Tj or (b) decreasing Tj at fixed Tj Explain. 

Perhaps one of the earliest attempts at representing fluid properties centered around the concept of the ideal gas. Experiments on gases at low pressures and densities had led to the following observations at a given temperature, the volume of a gas is inversely proportional to its absolute pressure and, at a given pressure, the volume of a gas is directly proportional to its temperature, if the latter is measured on an appropriate scale. Later work showed that this scale coincides with the absolute temperature scale associated with the Carnot engine efficiency (Section 1.1.1). The two observations were combined to form the ideal gas equation of state. An equation of state is a fluid behavior model that relates the temperature, pressure, and volume of the fluid in an equation form. The ideal gas equation of state takes the form... 

Fuel cells produce electricity directly from fuel through electrochemical processes, and hence bypass Carnot engine efficiency constraints. This could deliver unparalleled levels of efficiency in electricity generation. The downside is that the chemical reactions in themselves are a source of irreversibihty, which mitigates fuel cell efficiency to some extent. 

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. 

From his study of this cycle, Carnot concluded that the engine efficiency was independent of the working substance (e.g., steam or air). He also found... 

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. 

Here Tc is the temperature of the cooling reservoir, i.e. the surroundings, while Th is the temperature of the process, i.e. the temperature of combustion. The Carnot efficiency is applicable for conventional heat pump engines. Efficiencies of more than 100 % correspond to converting heat from the surroundings into electricity and is only of academic interest, as is the high efficiency listed in Tab. 8.10. 

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. 

By a similar argument, it can be shown that the assumption of an efficiency less than a also leads to a contradiction of the second law. Thus, any reversible Carnot engine operating between the same pair of reservoirs has the same efficiency, and that efficiency must be a function only of the temperatures of the reservoirs. 

Thus, we have obtained the specific functional relationship between the efficiency of a reversible Carnot engine and the thermodynamic temperatures of the heat reservoirs. 

In the synthesis of sucrose, 23,000 J of the 29,300 J available from the hydrolysis of ATP are used for synthetic work. If we call 23,000/29,300 the efficiency of this pair of reactions carried out at 37°C, and if we consider 37°C equivalent to the temperamre of the high-temperature reservoir of a heat engine, what would the temperature of the low-temperature reservoir have to be to attain a comparable efficiency for a reversible Carnot engine ... 

According to the definition of heat engine efficiency, the efficiency of the Carnot heat engine is = output/6input = [area l-2-3-4-l]/[area... 

A Carnot engine with a steady flow rate of 1 kg/sec uses water as the working fluid. Water changes phase from saturated liquid to saturated vapor as heat is added from a heat source at 300° C. Heat rejection takes place at a pressure of lOkPa. Determine (1) the quality at the exit of the turbine, (2) the quality at the inlet of the pump, (3) the heat transfer added in the boiler, (4) the power required for the pump, (5) the power produced by the turbine, (6) the heat transfer rejected in the condenser, and (7) the cycle efficiency. 

A Diesel cycle has a compression ratio of 18. Air-intake conditions (prior to compression) are 72°F and 14.7 psia, and the highest temperature in the cycle is limited to 2500° F to avoid damaging the engine block. Calculate (a) thermal efficiency, (b) net work, and (c) mean effective pressure (d) compare engine efficiency with that of a Carnot cycle engine operating between the same temperatures. 

The T-s diagram and schematic diagram of the Curzon and Ahlborn (endoreversible Carnot) cycle are shown in Figs. 7.5 and 7.6, respectively (Cuzon, F.L. and Ahlborn, B., Efficiency of a Carnot engine at maximum... 

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

The Carnot engine operating between these temperatures T3 and T4 with heat absorbed at a rate Qin and rejected at a rate Qout will have an efficiency... 

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