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Encyclopedia > Thermal efficiency

The thermal efficiency (eta_{th} ,) 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} ,, to the device is heat, or the heat-content of a fuel that is consumed. The desired output is mechanical work, W_{out} ,, or heat, Q_{out} ,, or possibly both. Because the input heat normally has a real financial cost, a memorable, generic definition of thermal efficiency is:[1]

A colorized automobile engine The internal combustion engine is a heat engine in which the burning of a fuel occurs in a confined space called a combustion chamber. ... A boiler is a closed vessel in which water or other fluid is heated under pressure. ... A furnace is a device for heating air or any other fluid. ... In physics, heat, symbolized by Q, is defined as energy in transit. ... In thermodynamics, thermodynamic work is a generalisation of the concept of mechanical work in mechanics. ...

From the first and second law of thermodynamics, the output can't exceed what is input, so:

The second law of thermodynamics is a theorem in physics regarding the directional flow of heat in relation to work and which accounts for the phenomenon of irreversibility in thermodynamic systems. ...

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 that 100%. For example, a typical gasoline automobile engine operates at around 25% thermal efficiency, and a large coal-fueled electrical generating plant peaks at about 36%. In a combined cycle plant, where both heat and work are desired products, thermal efficiencies can exceed 70% or so.


Heat engines

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

To meet Wikipedias quality standards, this article or section may require cleanup. ... In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... In engineering and thermodynamics, a heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot source and a cold sink. Heat is transferred from the source, through the working body of the engine, to the sink, and in this process some... In thermodynamics, thermodynamic work is a generalisation of the concept of mechanical work in mechanics. ...

eta_{th} equiv frac{W_{out}}{Q_{in}},

or via the first law of thermodynamics to substitute waste heat rejection for the work produced,

The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ...

eta_{th} = 1 - frac{Q_{out}}{Q_{in}}.

For example, when 1000 joules of thermal energy is transformed in 300 joules of mechanical energy (with the remaining 700 joules dissipated as waste heat), the thermal efficiency is 30%. The joule (symbol: J) is the SI unit of energy, which is defined as the potential to do work. ... Waste heat is the by-product heat of machines and technical processes for which no useful application is found. ...

Energy conversion

For an energy conversion device like a boiler or furnace, the thermal efficiency is:

eta_{th} equiv frac{Q_{out}}{Q_{in}}.

So, for a boiler that produces 700,000 Btu/h output for each 1,000,000 Btu/h heat-equivalent input, its thermal efficiency is 7/10 = 0.70, or 70%.

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 gas-fueled furnace, an economic analysis is needed to determine the most cost-effective choice. An electric heater is an electrical appliance that converts electrical energy into heat. ... Engineering economics, previously known as engineering economy, is a subset of economics for application to engineering projects. ...

Heat pumps

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 Coefficient-of-performance (COP), Energy Efficiency Ratio (EER), and Seasonal Energy Efficiency Ratio (SEER). A heat pump is a machine, which moves heat from a low temperature reservoir to a higher temperature reservoir under supply of work. ... It has been suggested that Freezer be merged into this article or section. ... Note: in the broadest sense, air conditioning can refer to any form of heating, ventilation, and air-conditioning. ...

Energy efficiency

While the 'thermal efficiency' it is sometimes called the energy efficiency. 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 the 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 Utilization Efficiency (AFUE).[2]

See also

Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... The Carnot heat engine uses a particular thermodynamic cycle studied by Nicolas Léonard Sadi Carnot in the 1820s and expanded upon by Thomas Benoit in the 1840s and 50s. ... The coefficient of performance, or COP (sometimes CP), of a heat pump is the ratio of the output heat to the supplied work or where Q is the useful heat supplied by the condenser and W is the work consumed by the compressor. ... The efficiency of air conditioners are often (but not always) rated by the Seasonal Energy Efficiency Ratio (SEER). ... Seasonal Energy Efficiency Ratio (SEER) is a measurement of efficiency for cooling devices such as heat pumps and air conditioners. ... The efficiency of an entity (a device, component, or system) in electronics and electrical engineering is defined as useful power output divided by the total electrical power consumed (a fractional expression). ... In physics, mechanical efficiency is the effectiveness of a machine and is defined as Efficiency is often indicated by a percentage, the efficiency of an ideal machine is 100%. Due to the fact that energy cannot emerge from nothing and the Second law of thermodynamics which states that the quality...


  1. ^ Fundamentals of Engineering Thermodynamics, by Howell and Buckius, McGraw-Hill, New York, 1987
  2. ^ HVAC Systems and Equipment volume of the ASHRAE Handbook, ASHRAE, Inc., Atlanta, GA, USA, 2004

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