Heat engines transform
thermal energy, or heat,
Qin into
mechanical energy, or
work,
Wnet. They cannot do this task perfectly, so some of the input heat energy is not converted into work, but is dissipated as
waste heat Qout
Q_{in} = |W_{\rm net}| + |Q_{\rm out}| The thermal efficiency of a heat engine is the percentage of heat energy that is transformed into
work. Thermal efficiency is defined as :\eta_{\rm th} \equiv \frac{Q_{\rm in}} = \frac{ {Q_{\rm in}} - |Q_{\rm out}|} {Q_{\rm in}} = 1 - \frac{Q_{\rm in}} The efficiency of even the best heat engines is low; usually below 50% and often far below. So the energy lost to the environment by heat engines is a major waste of energy resources. Since a large fraction of the fuels produced worldwide go to powering heat engines, perhaps up to half of the useful energy produced worldwide is wasted in engine inefficiency, although modern
cogeneration,
combined cycle and
energy recycling schemes are beginning to use this heat for other purposes. This inefficiency can be attributed to three causes. There is an overall theoretical limit to the efficiency of any heat engine due to temperature, called the Carnot efficiency. Second, specific types of engines have lower limits on the ideal efficiency of the
engine cycle they use. Thirdly, the nonideal behavior of real engines, such as mechanical
friction and losses in the
combustion process, causes further efficiency losses.
Carnot efficiency The
second law of thermodynamics puts a fundamental limit on the thermal efficiency of all heat engines. Even an ideal, frictionless engine can't convert anywhere near 100% of its input heat into work. The limiting factors are the temperature at which the heat enters the engine, T_{\rm H}\,, and the temperature of the environment into which the engine exhausts its waste heat, T_{\rm C}\,, measured in an absolute scale, such as the
Kelvin or
Rankine scale. From
Carnot's theorem, for any engine working between these two temperatures: :\eta_{\rm th} \le 1 - \frac{T_{\rm C}}{T_{\rm H}} This limiting value is called the
Carnot cycle efficiency because it is the efficiency of an unattainable, ideal,
reversible engine cycle called the
Carnot cycle. No device converting heat into mechanical energy, regardless of its construction, can exceed this efficiency. Examples of T_{\rm H}\, are the temperature of hot steam entering the turbine of a
steam power plant, or the temperature at which the fuel burns in an
internal combustion engine. T_{\rm C} is usually the ambient temperature where the engine is located, or the temperature of a lake or river into which the waste heat is discharged. For example, if an automobile engine burns gasoline at a temperature of T_{\rm H} = 816^\circ \text{C} = 1500^\circ \text{F} = 1089 \text{K} and the ambient temperature is T_{\rm C} = 21^\circ \text{C} = 70^\circ \text{F} = 294 \text{K}, then its maximum possible efficiency is: :\eta_{\rm th} \le \left (1 - \frac{294 K}{1089 K} \right ) 100\% = 73.0\% Due to the other causes detailed below, practical engines have efficiencies far below the Carnot limit. For example, the average automobile engine is less than 35% efficient. Carnot's theorem applies to thermodynamic cycles, where thermal energy is converted to mechanical work. Devices that convert a fuel's chemical energy directly into electrical work, such as
fuel cells, can exceed the Carnot efficiency.
Engine cycle efficiency The Carnot cycle is
reversible and thus represents the upper limit on efficiency of an engine cycle. Practical engine cycles are irreversible and thus have inherently lower efficiency than the Carnot efficiency when operated between the same temperatures T_{\rm H} and T_{\rm C}. One of the factors determining efficiency is how heat is added to the working fluid in the cycle, and how it is removed. The Carnot cycle achieves maximum efficiency because all the heat is added to the working fluid at the maximum temperature T_{\rm H}, and removed at the minimum temperature T_{\rm C}. In contrast, in an internal combustion engine, the temperature of the fuel-air mixture in the cylinder is nowhere near its peak temperature as the fuel starts to burn, and only reaches the peak temperature as all the fuel is consumed, so the average temperature at which heat is added is lower, reducing efficiency. An important parameter in the efficiency of combustion engines is the
specific heat ratio of the air-fuel mixture,
γ. This varies somewhat with the fuel, but is generally close to the air value of 1.4. This standard value is usually used in the engine cycle equations below, and when this approximation is made the cycle is called an
air-standard cycle. •
Otto cycle: automobiles The
Otto cycle is the name for the cycle used in spark-ignition
internal combustion engines such as gasoline and
hydrogen fuelled
automobile engines. Its theoretical efficiency depends on the
compression ratio r of the engine and the
specific heat ratio γ of the gas in the combustion chamber. This is because, since the fuel is not introduced to the combustion chamber until it is required for ignition, the compression ratio is not limited by the need to avoid knocking, so higher ratios are used than in spark ignition engines. •
Rankine cycle: steam power plants The
Rankine cycle is the cycle used in steam turbine power plants. The majority of the world's electric power is produced with this cycle. Since the cycle's working fluid, water, changes from liquid to vapor and back during the cycle, their efficiencies depend on the thermodynamic properties of water. The thermal efficiency of modern steam turbine plants with reheat cycles can reach 47%, and in
combined cycle plants, in which a steam turbine is powered by exhaust heat from a gas turbine, it can approach 60%. •
Brayton cycle: gas turbines and jet engines The
Brayton cycle is the cycle used in
gas turbines and
jet engines. It consists of a compressor that increases pressure of the incoming air, then fuel is continuously added to the flow and burned, and the hot exhaust gasses are expanded in a turbine. The efficiency depends largely on the ratio of the pressure inside the combustion chamber
p2 to the pressure outside
p1 \eta_{\rm th} = 1 - \left(\frac{p_2}{p_1}\right)^\frac{1-\gamma}{\gamma}
Other inefficiencies One should not confuse thermal efficiency with other efficiencies that are used when discussing engines. The above efficiency formulas are based on simple idealized mathematical models of engines, with no friction and working fluids that obey simplified thermodynamic models. Real engines have many departures from ideal behavior that waste energy, reducing actual efficiencies below the theoretical values given above. Examples are: •
friction of moving parts • inefficient combustion • heat loss from the combustion chamber • departure of the working fluid from the thermodynamic properties of an
ideal gas • aerodynamic drag of air moving through the engine • energy used by auxiliary equipment like oil and water pumps. • inefficient compressors and turbines • imperfect valve timing These factors may be accounted when analyzing thermodynamic cycles, however discussion of how to do so is outside the scope of this article. ==Energy conversion==