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| {{Original research|date=September 2012}}
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| The '''coefficient of performance''' or '''COP''' (sometimes CP) of a [[heat pump]] is a ratio of heating or cooling provided to electrical energy consumed.<ref>http://www.tetech.com/temodules/graphs/instructions.pdf</ref><ref>http://us.grundfos.com/service-support/encyclopedia-search/cop-coefficient-ofperformance.html</ref> Higher COPs equate to lower operating costs. The COP may exceed 1, because it is a ratio of output:loss, unlike the [[thermal efficiency]] ratio of output:input energy. For complete systems, COP should include energy consumption of all auxiliaries. COP is highly dependent on operating conditions, especially absolute temperature and relative temperature between sink and system, and is often graphed or averaged against expected conditions.<ref>http://www.tetech.com/temodules/graphs/HP-199-1.4-0.8.pdf</ref>
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| == Equation ==
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| The equation is:
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| :<math>COP = \frac{ Q}{ W}</math>
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| where
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| * <math> Q \ </math> is the [[heat]] supplied to or removed from the reservoir.
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| * <math>W \ </math> is the [[Mechanical work|work]] consumed by the heat pump.
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| The COP for heating and cooling are thus different, because the heat reservoir of interest is different. When one is interested in how well a machine cools, the COP is the ratio of the heat removed from the cold reservoir to input work. However, for heating, the COP is the ratio of the heat removed from the cold reservoir plus the heat added to the hot reservoir to the input work:
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| :<math> COP_{heating}=\frac{| Q_{H}|}{ W}=\frac{| Q_{C}| + W}{ W}</math>
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| :<math> COP_{cooling}=\frac{| Q_{C}|}{ W}</math>
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| where
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| *<math> Q_{C} \ </math> is the heat removed from the cold reservoir.
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| *<math> Q_{H} \ </math> is the heat supplied to the hot reservoir.
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| ==Derivation==
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| {{Unreferenced section|date=January 2011}}
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| According to the [[first law of thermodynamics]], in a reversible system we can show that <math>Q_{hot}=Q_{cold}+W </math> and <math>W=Q_{hot}-Q_{cold}</math>, where <math>Q_{hot}</math> is the heat transferred to the hot reservoir and <math>Q_{cold}</math> is the heat collected from the cold heat reservoir.<br>
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| Therefore, by substituting for W,<br>
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| :<math> COP_{heating}=\frac{Q_{hot}}{Q_{hot}-Q_{cold}}</math>
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| For a heat pump operating at maximum theoretical efficiency (i.e. Carnot efficiency), it can be shown that
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| :<math> \frac{Q_{hot}}{T_{hot}}=\frac{Q_{cold}}{T_{cold}}</math> and <math>Q_{cold}=\frac{Q_{hot}T_{cold}}{T_{hot}}</math>
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| where <math>T_{hot} </math> and <math>T_{cold}</math> are the temperatures of the hot and cold heat reservoirs respectively. Note that these equations must use an absolute temperature scale, for example, Kelvin or Rankine.
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| At maximum theoretical efficiency, <br>
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| :<math> COP_{heating}=\frac{T_{hot}}{T_{hot}-T_{cold}} </math>
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| which is equal to the reciprocal of the ideal efficiency for a heat engine, because a heat pump is a heat engine operating in reverse. Similarly, <br>
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| :<math> COP_{cooling}=\frac{Q_{cold}}{Q_{hot}-Q_{cold}} =\frac{T_{cold}}{T_{hot}-T_{cold}}</math>
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| Note that the COP of a heat pump depends on its duty the heat rejected to the hot sink is greater than the heat absorbed from the cold source, so the heating COP is 1 greater than the cooling COP.
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| <math>COP_{heating}</math> applies to heat pumps and <math>COP_{cooling}</math> applies to air conditioners or refrigerators. For heat engines, see [[Thermodynamic efficiency|Efficiency]]. Values for actual systems will always be less than these theoretical maximums. In Europe, the standard tests for ground source heat pump units use 35 °C (95 °F) for <math>{T_{hot}}</math> and 0 °C (32 °F) for <math>{T_{cold}}</math>. According to the above formula, the maximum achievable COP would be 7.8. Test results of the best systems are around 4.5. When measuring installed units over a whole season and accounting for the energy needed to pump water through the piping systems, seasonal COP's are around 3.5 or less. This indicates room for improvement.
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| ==Improving COP==
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| As the formula shows, the COP of a heat pump system can be improved by reducing the temperature gap <math>T_{hot} </math> minus <math>T_{cold}</math> at which the system works. For a heating system this would mean two things: 1) reducing the output temperature to around {{convert|30|C|F}} which requires piped floor, wall or ceiling heating, or oversized water to air heaters and 2) increasing the input temperature (e.g. by using an oversized ground source or by access to a solar-assisted thermal bank <ref>Thermalbanks and Thermal Energy Storage, http://www.icax.co.uk/ThermalBanks.html</ref> ). For an air cooler, COP could be improved by using ground water as an input instead of air, and by reducing temperature drop on output side through increasing air flow. For both systems, also increasing the size of pipes and air canals would help to reduce noise and the energy consumption of pumps (and ventilators).{{OR|date=September 2012}}
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| The heat pump itself can be improved by increasing the size of the internal heat exchangers relative to the power of the compressor, and to reduce the system's internal temperature gap over the compressor. This latter measure, however, makes such heat pumps unsuitable to produce output above roughly 40 °C (104 °F) which means that a separate machine is needed for producing hot tap water.{{OR|date=September 2012}}
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| ==Example==
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| {{Unreferenced section|date=September 2012|comment=Note that the footnotes aren't refs}}
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| A [[geothermal heat pump]] operating at <math>COP_{heating}</math> 3.5 provides 3.5 units of heat for each unit of energy consumed (i.e. 1 kWh consumed would provide 3.5 kWh of output heat). The output heat comes from both the heat source and 1 kWh of input energy, so the heat-source is cooled by 2.5 kWh, not 3.5 kWh.
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| A heat pump of <math>COP_{heating}</math> 3.5, such as in the example above, could be less expensive to use than even the most efficient gas furnace except in areas where the electricity cost per unit is higher than 3.5 times the cost of natural gas (i.e. [[Connecticut]] or [[New York City]]).
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| A heat pump cooler operating at <math>COP_{cooling}</math> 2.0 removes 2 units of heat for each unit of energy consumed (e.g. an [[air conditioner]] consuming 1 kWh would remove 2 kWh of heat from a building's air).
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| Given the same energy source and operating conditions, a higher COP heat pump will consume less purchased energy than one with a lower COP. The overall environmental impact of a heating or air conditioning installation depends on the source of energy used as well as the COP of the equipment. The operating cost to the consumer depends on the cost of energy as well as the COP or efficiency of the unit. Some areas provide two or more sources of energy, for example, natural gas and electricity. A high COP of a heat pump may not entirely overcome a relatively high cost for electricity compared with the same heating value from natural gas.
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| For example, the 2009 US average price per therm (100,000 BTU) of electricity was $3.38 while the average price per therm of natural gas was $1.16.<ref>Based on average prices of 11.55 cents per kWh for electricity [http://www.eia.doe.gov/cneaf/electricity/epm/table5_3.html] and $13.68 per thousand cubic feet for natural gas [http://tonto.eia.doe.gov/dnav/ng/hist/n3010us3a.htm], and conversion factors of 29.308 kWh per therm and 97.2763 cubic feet per therm [http://www.eia.doe.gov/kids/energyfacts/science/energy_calculator.html].</ref> Using these prices, a heat pump with a COP of 3.5 in moderate climate would cost $0.97<ref>$3.38/3.5~$0.97</ref> to provide one therm of heat, while a high efficiency gas furnace with 95% efficiency would cost $1.22<ref>$1.16/.95~$1.22</ref> to provide one therm of heat. With these average prices, the heat pump costs 20% less<ref>($1.16-$0.95)/$1.16~20%</ref> to provide the same amount of heat. At 0 °F (-18 °C) COP is much lower. Then, the same system costs as much to operate as an efficient gas heater. The yearly savings will depend on the actual cost of electricity and natural gas, which can both vary widely.
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| However, a COP may help make a determination of system choice based on carbon contribution. Although a heat pump may cost more to operate than a conventional natural gas or electric heater, depending on the source of [[electricity generation]] in one's area, it may contribute less net [[carbon dioxide]] to the atmosphere than burning natural gas or heating fuel. If locally no green electricity is available, then carbon wise the best option would be to drive a heat pump on piped gas or oil, to store excess heat in the ground source for use in winter, while using the same machine also for producing electricity with a built-in [[Stirling engine]]. {{Citation needed|date=February 2011}}
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| Please see Modern Geothermal HVAC Engineering and Control Applications by Jay Egg, Greg Cunniff, and Carl Orio.
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| ==Conditions of use==
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| {{Unreferenced section|date=September 2012}}
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| While the COP is partly a measure of the efficiency of a heat pump, it is also a measure of the conditions under which it is operating: the COP of a given heat pump will rise as the input temperature increases or the output temperature decreases because it is linked to a warm temperature distribution system like [[underfloor heating]].
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| ==See also==
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| * [[Seasonal energy efficiency ratio]] (SEER)
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| * [[Seasonal thermal energy storage]] (STES)
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| * [[Heating seasonal performance factor]] (HSPF)
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| * [[Thermal efficiency]]
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| * [[Vapor-compression refrigeration]]
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| * [[Air conditioner]]
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| * [[HVAC]]
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| ==Notes==
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| {{Reflist|2}}
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| == External links ==
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| {{Commons category|Coefficient of performance}}
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| *[http://www.icax.co.uk/gshp.html Discussion on changes to COP of a heat pump depending on input and output temperatures]
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| *[http://www-3.unipv.it/energy/web/Libro%20petrecca/pdf/capitolododicesimo.pdf See COP definition in Cap XII of the book Industrial Energy Management - Principles and Applications]
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| {{DEFAULTSORT:Coefficient Of Performance}}
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| [[Category:Heat pumps]]
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| [[Category:Heating, ventilating, and air conditioning]]
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| [[Category:Mechanical engineering]]
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| [[Category:Dimensionless numbers of thermodynamics]]
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All person who wrote some sort of article is called Leland but it's not this most masucline name presently. To go to karaoke is the thing she loves most of every bit. He works as a cashier. His wife and him live in Massachusetts and he is bound to have everything that he prefers there. He's not godd at design but you might want to check their website: http://prometeu.net
Here is my blog how to hack clash of clans (read page)