In thermodynamics, the thermal
efficiency ()
is a dimensionless performance
measure of a device that uses thermal energy, such
as an internal combustion engine,
a boiler, a furnace, or a refrigerator for example. The input, ,
to the device is heat, or the
heatcontent of a fuel that is consumed. The desired output is
mechanical work, ,
or heat, ,
or possibly both. Because the input heat normally has a real
financial cost, a memorable, generic definition of thermal
efficiency is^{[1]}
From the first law of
thermodynamics, the energy output can't exceed the input,
so
When expressed as a percentage, the thermal efficiency must be between 0% and 100%. Due to inefficiencies such as friction, heat loss, and other factors, thermal engines' efficiencies are typically much less than 100%. For example, a typical gasoline automobile engine operates at around 25% efficiency, and a large coalfueled electrical generating plant peaks at about 46%. The largest diesel engine in the world peaks at 51.7%. In a combined cycle plant, thermal efficiencies are approaching 60%.^{[2]}
There are two types of thermal efficiency 1.Indicated thermal efficiency 2.Brake thermal efficiency
Contents 
Heat engines transform thermal energy, or heat, Q_{in} into mechanical energy, or work, W_{out}. 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} into the environment
The thermal efficiency of a heat engine is the percentage of heat
energy that is transformed into work. Thermal efficiency is
defined as
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, although modern cogeneration, combined cycle and energy recycling schemes are beginning to use this heat for other purposes. 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. 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 and losses in the combustion process causes further efficiency losses.
To complicate matters, there are at least two different definitions of Calorific Value in wide use, and wich one is being used significantly affects any quoted efficiency. Not stating whether an efficiency is HCV or LCv renders such numbers very misleading.^{[3]}
The second law of thermodynamics puts a fundamental limit on the thermal efficiency of all heat engines. Surprisingly, 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, , and the temperature of the environment into which the engine exhausts its waste heat, , measured in an absolute scale, such as the Kelvin or Rankine scale. From Carnot's theorem, for any engine working between these two temperatures:^{[4]}
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 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. is usually the ambient temperature where the engine is located, or the temperature of a lake or river that waste heat is discharged into. For example, if an automobile engine burns gasoline at a temperature of and the ambient temperature is , then its maximum possible efficiency is:
As Carnot's theorem only applies to heat engines, devices that convert the fuel's energy directly into work without burning it, such as fuel cells, can exceed the Carnot efficiency.
It can be seen that since is fixed by the environment, the only way for a designer to increase the Carnot efficiency of an engine is to increase , the operating temperature of the engine. This is a general principle that applies to all heat engines. For this reason the operating temperatures of engines have increased greatly over the long term, and new materials such as ceramics to enable engines to stand higher temperatures are an active area of research.
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 and . 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 , and removed at the minimum temperature . In contrast, in an internal combustion engine, the temperature of the fuelair 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.
The above efficiency formulas are based on simple idealized mathematical models of engines, with no friction and working fluids that obey simple thermodynamic rules called the ideal gas law. Real engines have many departures from ideal behavior that waste energy, reducing actual efficiencies far below the theoretical values given above. Examples are:
Another source of inefficiency is that engines must be optimized for other goals besides efficiency, such as low pollution. The requirements for vehicle engines are particularly stringent: they must be designed for low emissions, adequate acceleration, fast starting, light weight, low noise, etc. These require compromises in design (such as altered valve timing) that reduce efficiency. The average automobile engine is only about 35% efficient, and must also be kept idling at stoplights, wasting an additional 17% of the energy, resulting in an overall efficiency of 18%.^{[5]} Large stationary electric generating plants have fewer of these competing requirements as well as more efficient Rankine cycles, so they are significantly more efficient than vehicle engines, around 50% Therefore, replacing internal combustion vehicles with electric vehicles, which run on a battery that is charged with electricity generated by burning fuel in a power plant, can greatly increase the thermal efficiency of energy use in transportation, thus decreasing the demand for fossil fuels.
For an energy conversion device like a boiler or furnace, the
thermal efficiency is
So, for a boiler that produces 210 kW (or 700,000 BTU/h) output for each 300 kW (or 1,000,000 BTU/h) heatequivalent input, its thermal efficiency is 210/300 = 0.70, or 70%. This means that the 30% of the energy is lost to the environment.
An electric resistance heater has a thermal efficiency of at or very near 100%, so, for example, 1500W of heat are produced for 1500W of electrical input. When comparing heating units, such as a 100% efficient electric resistance heater to an 80% efficient natural gasfueled furnace, an economic analysis is needed to determine the most costeffective choice.
Heat pumps, refrigerators 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 moved from the cold reservoir (Q_{C}) is equal to the total heat energy added to the hot reservoir (Q_{H})
Their efficiency is measured by a coefficient of performance (COP). Heat pumps are measured by the efficiency with which they add heat to the hot reservoir, COP_{heating}; refrigerators and air conditioners by the efficiency with which they remove heat from the cold interior, COP_{cooling}:
The reason for not using the term 'efficiency' is that the coefficient of performance can often be greater than 100%. Since these devices are moving heat, not creating it, the amount of heat they move can be greater than the input work. 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:
The same device used between the same temperatures is more efficient when considered as a heat pump than when considered as a refrigerator:
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 byproduct.
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 energyconversion heating devices their peak steadystate 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 Utilization Efficiency (AFUE).^{[6]}
There are two types of thermal efficiency 1.Indicated thermal efficiency 2.Brake thermal efficiency
For heat engines the thermal efficiency is the mechanical work output for each unit of heat input. For the Carnot cycle it is
where
T_{0} = ambient absolute temperature
T_{max} = maximum cycle absolute temperature
Actual engines using other cycles will have lower efficiencies than the Carnot cycle since they have irreversible processes such as heat flow across finite temperature differences and nonadiabatic compression and expansions, as well as friction.
Heat engines use as high a temperature as possible to maximize the efficiency and are limited by temperature capabilities of real materials used to make the engines.
The thermal efficiency ($\backslash eta\_\{th\}\; \backslash ,$) is a dimensionless performance measure of a thermal device such as an internal combustion engine, a boiler, or a furnace, for example.
The input, $Q\_\{in\}\; \backslash ,$, to the device is heat, or the heatcontent of a fuel that is consumed. The desired output is mechanical work, $W\_\{out\}\; \backslash ,$, or heat, $Q\_\{out\}\; \backslash ,$, or possibly both. Because the input heat normally has a real financial cost, a memorable, generic definition of thermal efficiency is^{[1]}
$\backslash eta\_\{th\}\; \backslash equiv\; \backslash frac\{\backslash text\{What\; you\; get\}\}\{\backslash text\{What\; you\; pay\; for\}\}.$
From the first and second law of thermodynamics, the output can not exceed what is input, so
$0\; \backslash le\; \backslash eta\_\{th\}\; \backslash le\; 1.0.$
When expressed as a percentage, the thermal efficiency must be between 0% and 100%. Due to inefficiencies such as friction, heat loss, and other factors, thermal efficiencies are typically much less than 100%. For example, a typical gasoline automobile engine operates at around 25% thermal efficiency, and a large coalfueled electrical generating plant peaks at about 36%. In a combined cycle plant thermal efficiencies are approaching 60%.
Contents 
When transforming thermal energy into mechanical energy, the thermal efficiency of a heat engine is the percentage of energy that is transformed into work. Thermal efficiency is defined as
$\backslash eta\_\{th\}\; \backslash equiv\; \backslash frac\{W\_\{out\}\}\{Q\_\{in\}\}$,
or via the first law of thermodynamics to substitute waste heat rejection for the work produced,
$\backslash eta\_\{th\}\; =\; 1\; \; \backslash frac\{Q\_\{out\}\}\{Q\_\{in\}\}$.
For example, when 1000 joules of thermal energy is transformed into 300 joules of mechanical energy (with the remaining 700 joules dissipated as waste heat), the thermal efficiency is 30%.
For an energy conversion device like a boiler or furnace, the thermal efficiency is
$\backslash eta\_\{th\}\; \backslash equiv\; \backslash frac\{Q\_\{out\}\}\{Q\_\{in\}\}$.
So, for a boiler that produces 210 kW (or 700,000 BTU/h) output for each 300 kW (or 1,000,000 BTU/h) heatequivalent input, its thermal efficiency is 210/300 = 0.70, or 70%. This means that the 30% of the energy is lost to the environment.
An electric resistance heater has a thermal efficiency of at or very near 100%, so, for example, 1500W of heat are produced for 1500W of electrical input. When comparing heating units, such as a 100% efficient electric resistance heater to an 80% efficient natural gasfueled furnace, an economic analysis is needed to determine the most costeffective choice.
Heat pumps, refrigerators, and air conditioners, for example, move heat, rather than convert it, so other measures are needed to describe their thermal performance. The common measures are the coefficientofperformance (COP), energyefficiency ratio (EER), and seasonalenergyefficiency ratio (SEER).
The Efficiency of a Heat pump (HP) and Refrigerators (R)*:
$E\_\{HP\}=\backslash frac\{Q\_H\}\{W\}$
$E\_\{R\}=\backslash frac\{Q\_L\}\{W\}$
$\backslash displaystyle\; E\_\{HP\}\; \; E\_\{R\}\; =\; 1$
If temperatures at both ends of the Heat Pump or Refrigerator are constant and their processes reversible:
$E\_\{HP\}=\backslash frac\{T\_H\}\{T\_H\; \; T\_L\}$
$E\_\{R\}=\backslash frac\{T\_L\}\{T\_H\; \; T\_L\}$
*H=high (temperature/heat source), L=low (temperature/heat source)
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 energyconversion heating devices their peak steadystate 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 Utilization Efficiency (AFUE).^{[2]}
