Power and Efficiency of Heat Engines

On the first isothermal branch a quantity of heat, Qi, Hows reversibly from the heat reservoir to the engine, both being a Ti similarly, on the second isothermal branch a quantity of heat Q2 Hows from the engine to the heat reservoir, both at T2. A total amount of work W is done in one cycle. For the isothermal steps we have the entropy changes 

The reversible Carnot engine has no power output, since the reversible work done takes an infinite time. The power is the work done in a finite time, and hence here is zero. To achieve power output [1] there must be some spontaneous, naturai, irreversible process [2,3]. We shall assume that heat flows spontaneously from the reservoir at T to the heat engine at T, see Fig. 13.1, according to a simple linear rate law 

Our system consists of the working fluid, the cylinder and the piston of mass m. To calculate the entropy change of the system in an irreversible 

By including the piston in the system we see that the entropy change of the system can be written in the same form for reversible and irreversible processes. With inclusion of the piston in the system we insure that on expansion, reversible or irreversible, there is no dissipation and hence (13.17) applies in both cases. 

We turn next to the calculation of the rates of all the steps in the irreversible cycle. For the first isothermal step heat flows from the reservoir to the system and may change the internal energy of the system and the kinetic energy of the piston, and may be used to produce work in the surroundings. We may write 

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Gutkowics-Krusin, D., Procaccia, I., Ross, J. (1978) On the efficiency of rate processes. Power and efficiency of heat engines. /. Chem. Phys., Vol. 69, pp 3898-3906. 

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. 

Glaebrook, W. (1982) Efficiencies of heat engines and fuel cells the methanol fuel cell as a competitor to otto and diesel engines. Journal of Power Sources, 7 (3), 215 256. 

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... 

Two additional aspects of efficiency are of interest 1) the effects of integrating a fuel cell into a complete system that accepts readily available fuels like natural gas and produces grid quality ac power (see Section 9), and 2) issues arising when comparing fuel cell efficiency with heat engine efficiency (see below). 

The answers are rate of heat added in the low-temperature heat exchanger = 125.6 kW, rate of heat added in the high-temperature heat exchanger = 2501 kW, net power produced by the Rankine cycle = 357 kW, and efficiency of the solar heat engine = 357/(125.6-I-2501)= 13.59%. 

Display the T s diagram and cycle properties results. The cycle is a heat engine. The answers are power required for the first compressor = —6.60 kW, power required for the second compressor 14.64 kW, maximum temperature of the cycle = 1169°C, power produced by the first turbine = 47.34 kW, rate of heat added in the reheater = 47.29 kW, power produced by the second turbine = 26.00 kW, net power produced = 52.11 kW, back-work ratio = 28.95%, and efficiency of the cycle 7 = 35.38%. 

Determine the maximum power output of the cycle. Find the heat-transfer added, heat transfer removed, heat transfer surface area of the low-temperature side heat exchanger between the heat engine and the heat sink, and efficiency of the cycle at the maximum power output condition. 

Single-cycle fuel cell efficiencies range from 47 to 50%. The efficiency of combined-cycle fuel cells is about 60%, and if the generated heat is also recovered (in the form of hot water), the total efficiency can be around 80%. In comparison, the efficiency of gasoline engines is around 25%, of nuclear power plants about 35%, and of subcritical fossil fuel power plants, 37%. 

Power for industrial operations is supplied at present by electricity from coal, natural gas, and oil, working heat engines at overall efficiencies of < 35%. All can be replaced by fuel cells of various kinds operating for the next two to three decades on hydrogen from re-formed fossil fuels and as soon as possible by hydrogen from photovoltaics and the decomposition of water.20... 

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. 

In traditional fnel technology, the same fnel wonld be burned in air, producing an amonnt of heat = AH, the enthalpy of combnstion. The heat would then be nsed to rnn a heat engine-generator system to prodnce electrical power. The efficiency of conversion of heat to work is limited by the laws of thermodynamics. If the heat is supplied at temperature Th and if the lower operating temperature is T , the maximum work obtainable (see Section 13.4) is... 

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