Maximum efficiency, heat engine

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. 

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... 

For a heat engine like a steam turbine in an electric power plant the low temperature is determined by the outdoor environment. This temperature is about 300 K. Engineering considerations limit the high temperature to about 800 K. The maximum efficiency according to Carnot is 0.63 or 63 percent. No matter how skilled the builders of a steam turbine, if the temperatures are 300 K and 800 K, the efficiency will never exceed 63 percent. When you realize that the efficiency can never be larger than about 63 percent, a realizable efficiency of 50 percent looks quite good. 

The maximum possible efficiency at which a heat engine can work is defined by the Carnot efficiency equation E = (T2—Tl)/T2, where E is the efficiency of the heat engine, T1 is the temperature of the cold... 

Stirling engines also have the maximum theoretical possible efficiency because their power cycle (their theoretical pressure volume diagram) matches the Carnot cycle. The Carnot cycle, first described by the French physicist Sadi Carnot, determines the maximum theoretical efficiency of any heat engine operating between a hot and a cold reservoir. The Carnot efficiency formula 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. 

The reversible process (for which the equal sign applies) gives the maximum efficiency for the conversion of heat into work, but even the reversible engine is limited in the extent to which heat can be converted into work. 

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. 

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... 

A conventional power plant fired by fossil fuels converts the chemical energy of combustion of the fuel first to heat, which is used to raise steam, which in turn is used to drive the turbines that turn the electrical generators. Quite apart from the mechanical and thermal energy losses in this sequence, the maximum thermodynamic efficiency e for any heat engine is limited by the relative temperatures of the heat source (That) and heat sink (Tcoid) ... 

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

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... 

No creation of entropy and uncompensated heat occurs in the reversible heat engine and pomp, and hence Eq. 3.45 gives the maximum efficiency theoretically attainable for heat engines and heat pumps. This equation also shows that thermal energy (heat) can not be... 

The conventional generation of electrical energy from a fuel requires the use of a heat engine which converts thermal energy to mechanical energy. All heat engines operate by the Carnot cycle, and their maximum efficiency is about 40-50% (for the modern gas-fired power stations, the efficiency is about 55%). 

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. 

---