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thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
, the thermal efficiency (\eta_) is a
dimensionless Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...
performance measure of a device that uses
thermal energy The term "thermal energy" is often used ambiguously in physics and engineering. It can denote several different physical concepts, including: * Internal energy: The energy contained within a body of matter or radiation, excluding the potential en ...
, such as an
internal combustion engine An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal comb ...
,
steam turbine A steam turbine or steam turbine engine is a machine or heat engine that extracts thermal energy from pressurized steam and uses it to do mechanical work utilising a rotating output shaft. Its modern manifestation was invented by Sir Charles Par ...
,
steam engine A steam engine is a heat engine that performs Work (physics), mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cyl ...
,
boiler A boiler is a closed vessel in which fluid (generally water) is heated. The fluid does not necessarily boil. The heated or vaporized fluid exits the boiler for use in various processes or heating applications, including water heating, centra ...
, furnace,
refrigerator A refrigerator, commonly shortened to fridge, is a commercial and home appliance consisting of a thermal insulation, thermally insulated compartment and a heat pump (mechanical, electronic or chemical) that transfers heat from its inside to ...
, ACs etc. For a
heat engine A heat engine is a system that transfers thermal energy to do mechanical or electrical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, pa ...
, thermal efficiency is the ratio of the net work output to the heat input; in the case of a
heat pump A heat pump is a device that uses electricity to transfer heat from a colder place to a warmer place. Specifically, the heat pump transfers thermal energy using a heat pump and refrigeration cycle, cooling the cool space and warming the warm s ...
, thermal efficiency (known as the '' coefficient of performance'' or COP) is the ratio of net heat output (for heating), or the net heat removed (for cooling) to the energy input (external work). The efficiency of a heat engine is fractional as the output is always less than the input while the COP of a heat pump is more than 1. These values are further restricted by the Carnot theorem.


Overview

In general, energy conversion efficiency is the
ratio In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
between the useful output of a device and the input, in
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
terms. For thermal efficiency, the input, Q_, to the device is
heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...
, or the heat-content of a fuel that is consumed. The desired output is mechanical work, W_, or heat, Q_, or possibly both. Because the input heat normally has a real financial cost, a memorable, generic definition of thermal efficiency is \eta_ \equiv \frac. From the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. For a thermodynamic process affecting a thermodynamic system without transfer of matter, the law distinguishes two ...
, the energy output cannot exceed the input, and by the
second law of thermodynamics The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...
it cannot be equal in a non-ideal process, so 0 \le \eta_ < 1 When expressed as a percentage, the thermal efficiency must be between 0% and 100%. Efficiency must be less than 100% because there are inefficiencies such as friction and heat loss that convert the energy into alternative forms. For example, a typical gasoline automobile engine operates at around 25% efficiency, and a large coal-fuelled electrical generating plant peaks at about 46%. However, advances in Formula 1 motorsport regulations have pushed teams to develop highly efficient power units which peak around 45–50% thermal efficiency. The largest diesel engine in the world peaks at 51.7%. In a combined cycle plant, thermal efficiencies approach 60%. Such a real-world value may be used as a
figure of merit A figure of merit (FOM) is a performance metric that characterizes the performance of a device, system, or method, relative to its alternatives. Examples *Absolute alcohol content per currency unit in an alcoholic beverage *accurizing, Accuracy o ...
for the device. For engines where a fuel is burned, there are two types of thermal efficiency: indicated thermal efficiency and brake thermal efficiency. This form of efficiency is only appropriate when comparing similar types or similar devices. For other systems, the specifics of the calculations of efficiency vary, but the non-dimensional input is still the same:
Efficiency = Output energy / input energy.


Heat engines

Heat engines transform
thermal energy The term "thermal energy" is often used ambiguously in physics and engineering. It can denote several different physical concepts, including: * Internal energy: The energy contained within a body of matter or radiation, excluding the potential en ...
, or heat, ''Q''in into
mechanical energy In physical sciences, mechanical energy is the sum of macroscopic potential and kinetic energies. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical ...
, or work, ''W''net. They cannot do this task perfectly, so some of the input heat energy is not converted into work, but is dissipated as waste heat ''Q''out < 0 into the surroundings: :Q_ = , W_, + , Q_, The thermal efficiency of a
heat engine A heat engine is a system that transfers thermal energy to do mechanical or electrical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, pa ...
is the percentage of heat energy that is transformed into work. Thermal efficiency is defined as :\eta_ \equiv \frac = \frac = 1 - \frac 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 their efficiency due to the inherent irreversibility of the engine cycle they use. Thirdly, the nonideal behavior of real engines, such as mechanical
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
and losses in the
combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion ...
process causes further efficiency losses.


Carnot efficiency

The
second law of thermodynamics The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...
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_\,, and the temperature of the environment into which the engine exhausts its waste heat, T_\,, measured in an absolute scale, such as the
Kelvin The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...
or Rankine scale. From Carnot's theorem, for any engine working between these two temperatures: :\eta_ \le 1 - \frac 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_\, 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 An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal comb ...
. T_ 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_ = 816^\circ \text = 1500^\circ \text = 1089 \text and the ambient temperature is T_ = 21^\circ \text = 70^\circ \text = 294 \text, then its maximum possible efficiency is: :\eta_ \le \left (1 - \frac \right ) 100\% = 73.0\% It can be seen that since T_ is fixed by the environment, the only way for a designer to increase the Carnot efficiency of an engine is to increase T_, the temperature at which the heat is added to the engine. The efficiency of ordinary heat engines also generally increases with
operating temperature An operating temperature is the allowable temperature range of the local ambient environment at which an electrical or mechanical device operates. The device will operate effectively within a specified temperature range which varies based on the de ...
, and advanced structural materials that allow engines to operate at higher temperatures is an active area of research. 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 A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most batteries in req ...
, 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_ and T_. 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_, and removed at the minimum temperature T_. 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 engine An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal comb ...
s such as gasoline and hydrogen fuelled
automobile engine There are a wide variety of propulsion systems available or potentially available for automobiles and other vehicles. Options included internal combustion engines fueled by petrol, diesel, propane, or natural gas; hybrid vehicles, plug-in hybr ...
s. 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. \eta_ = 1 - \frac Thus, the efficiency increases with the compression ratio. However the compression ratio of Otto cycle engines is limited by the need to prevent the uncontrolled combustion known as knocking. Modern engines have compression ratios in the range 8 to 11, resulting in ideal cycle efficiencies of 56% to 61%. *Diesel cycle: trucks and trains In the Diesel cycle used in diesel truck and train engines, the fuel is ignited by compression in the cylinder. The efficiency of the Diesel cycle is dependent on ''r'' and ''γ'' like the Otto cycle, and also by the ''cutoff ratio'', ''rc'', which is the ratio of the cylinder volume at the beginning and end of the combustion process: \eta_ = 1-\frac The Diesel cycle is less efficient than the Otto cycle when using the same compression ratio. However, practical Diesel engines are 30% - 35% more efficient than gasoline engines. 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 overwhelming 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 turbine A gas turbine or gas turbine engine is a type of Internal combustion engine#Continuous combustion, continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas gene ...
s and
jet engine A jet engine is a type of reaction engine, discharging a fast-moving jet (fluid), jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition may include Rocket engine, rocket, Pump-jet, water jet, and ...
s. 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 ''p''2 to the pressure outside ''p''1 \eta_ = 1 - \left(\frac\right)^\frac


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 Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
of moving parts *inefficient combustion *heat loss from the combustion chamber *departure of the working fluid from the thermodynamic properties of an
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...
*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

For a device that converts energy from another form into thermal energy (such as an electric heater, boiler, or furnace), the thermal efficiency is :\eta_ \equiv \frac where the Q quantities are heat-equivalent values. So, for a boiler that produces 210 kW (or 700,000 BTU/h) output for each 300 kW (or 1,000,000 BTU/h) heat-equivalent input, its thermal efficiency is 210/300 = 0.70, or 70%. This means that 30% of the energy is lost to the environment. An electric resistance heater has a thermal efficiency close to 100%. When comparing heating units, such as a highly efficient electric resistance heater to an 80% efficient natural gas-fuelled furnace, an economic analysis is needed to determine the most cost-effective choice.


Effects of fuel heating value

The heating value of a
fuel A fuel is any material that can be made to react with other substances so that it releases energy as thermal energy or to be used for work (physics), work. The concept was originally applied solely to those materials capable of releasing chem ...
is the amount of
heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...
released during an
exothermic reaction In thermochemistry, an exothermic reaction is a "reaction for which the overall standard enthalpy change Δ''H''⚬ is negative." Exothermic reactions usually release heat. The term is often confused with exergonic reaction, which IUPAC define ...
(e.g.,
combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion ...
) and is a characteristic of each substance. It is measured in units of
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
per unit of the substance, usually
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
, such as: kJ/kg, J/ mol. The heating value for
fuel A fuel is any material that can be made to react with other substances so that it releases energy as thermal energy or to be used for work (physics), work. The concept was originally applied solely to those materials capable of releasing chem ...
s is expressed as the HHV, LHV, or GHV to distinguish treatment of the heat of phase changes: *
Higher heating value The heating value (or energy value or calorific value) of a substance, usually a fuel or food (see food energy), is the amount of heat released during the combustion of a specified amount of it. The ''calorific value'' is the total energy release ...
(HHV) is determined by bringing all the products of combustion back to the original pre-combustion temperature, and in particular condensing any vapor produced. This is the same as the thermodynamic
heat of combustion The heating value (or energy value or calorific value) of a substance, usually a fuel or food (see food energy), is the amount of heat released during the combustion of a specified amount of it. The ''calorific value'' is the total energy relea ...
. * Lower heating value (LHV) (or ''net calorific value'') is determined by subtracting the heat of vaporization of the water vapor from the higher heating value. The energy required to vaporize the water therefore is not realized as heat. * Gross heating value accounts for water in the exhaust leaving as vapor, and includes liquid water in the fuel prior to combustion. This value is important for fuels like
wood Wood is a structural tissue/material found as xylem in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulosic fibers that are strong in tension and embedded in a matrix of lignin t ...
or
coal Coal is a combustible black or brownish-black sedimentary rock, formed as rock strata called coal seams. Coal is mostly carbon with variable amounts of other Chemical element, elements, chiefly hydrogen, sulfur, oxygen, and nitrogen. Coal i ...
, which will usually contain some amount of water prior to burning. Which definition of heating value is being used significantly affects any quoted efficiency. Not stating whether an efficiency is HHV or LHV renders such numbers very misleading.


Heat pumps and refrigerators

Heat pump A heat pump is a device that uses electricity to transfer heat from a colder place to a warmer place. Specifically, the heat pump transfers thermal energy using a heat pump and refrigeration cycle, cooling the cool space and warming the warm s ...
s,
refrigerator A refrigerator, commonly shortened to fridge, is a commercial and home appliance consisting of a thermal insulation, thermally insulated compartment and a heat pump (mechanical, electronic or chemical) that transfers heat from its inside to ...
s and air conditioners use work to move heat from a colder to a warmer place, so their function is the opposite of a heat engine. The work energy (''W''in) that is applied to them is converted into heat, and the sum of this energy and the heat energy that is taken up from the cold reservoir (''Q''C) is equal to the magnitude of the total
heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...
energy given off to the hot reservoir (, ''Q''H, ) :, Q_, = Q_ + W_ Their efficiency is measured by a coefficient of performance (COP). Heat pumps are measured by the efficiency with which they give off heat to the hot reservoir, COPheating; refrigerators and air conditioners by the efficiency with which they take up heat from the cold space, COPcooling: :\mathrm_ \equiv \frac = \frac = \mathrm_+1\, :\mathrm_ \equiv \frac\, The reason the term "coefficient of performance" is used instead of "efficiency" is that, since these devices are moving heat, not creating it, the amount of heat they move can be greater than the input work, so the COP can be greater than 1 (100%). Therefore, heat pumps can be a more efficient way of heating than simply converting the input work into heat, as in an electric heater or furnace. Since they are heat engines, these devices are also limited by Carnot's theorem. The limiting value of the Carnot 'efficiency' for these processes, with the equality theoretically achievable only with an ideal 'reversible' cycle, is: :\mathrm_ \le \frac=\mathrm_\mathrm :\mathrm_ \le \frac=\mathrm_\mathrm The same device used between the same temperatures is more efficient when considered as a heat pump than when considered as a refrigerator since :\mathrm_ = \mathrm_ + 1 This is because when heating, the work used to run the device is converted to heat and adds to the desired effect, whereas if the desired effect is cooling the heat resulting from the input work is just an unwanted by-product. Sometimes, the term efficiency is used for the ratio of the achieved COP to the Carnot COP, which can not exceed 100%.


Energy efficiency

The 'thermal efficiency' is sometimes called the energy efficiency. In the United States, in everyday usage the SEER is the more common measure of energy efficiency for cooling devices, as well as for heat pumps when in their heating mode. For energy-conversion heating devices their peak steady-state thermal efficiency is often stated, e.g., 'this furnace is 90% efficient', but a more detailed measure of seasonal energy effectiveness is the annual fuel use efficiency (AFUE).


Heat exchangers

The role of a heat exchanger is to transfer heat between two mediums, so the performance of the heat exchanger is closely related to energy or thermal efficiency. A counter flow heat exchanger is the most efficient type of heat exchanger in transferring heat energy from one circuit to the other. However, for a more complete picture of heat exchanger efficiency, exergetic considerations must be taken into account. Thermal efficiencies of an internal combustion engine are typically higher than that of external combustion engines.


See also

* Kalina cycle *
Electrical efficiency The efficiency of a system in electronics and electrical engineering is defined as useful power output divided by the total electrical power consumed (a vulgar fraction, fractional Expression (mathematics), expression), typically denoted by the G ...
* Mechanical efficiency *
Heat engine A heat engine is a system that transfers thermal energy to do mechanical or electrical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, pa ...
* Federal roofing tax credit for energy efficiency (US) * Lower heating value *
Cost of electricity by source Different methods of electricity generation can incur a variety of different costs, which can be divided into three general categories: 1) wholesale costs, or all costs paid by utilities associated with acquiring and distributing electricity to ...
*
Higher heating value The heating value (or energy value or calorific value) of a substance, usually a fuel or food (see food energy), is the amount of heat released during the combustion of a specified amount of it. The ''calorific value'' is the total energy release ...
* Energy conversion efficiency


References

{{DEFAULTSORT:Thermal Efficiency Thermodynamic properties Heating, ventilation, and air conditioning Energy conversion Engineering thermodynamics