Coefficient of performance – wikipedia gas x ultra strength during pregnancy

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The coefficient of performance or COP (sometimes CP or CoP) of a heat pump, refrigerator or air conditioning system is a ratio of useful heating or cooling provided to work required. [1] [2] Higher COPs equate to lower operating costs. The COP usually exceeds 1, especially in heat pumps, because, instead of just converting work to heat (which, if 100% efficient, would be a COP_hp of 1), it pumps additional heat from a heat source to where the heat is required. For complete systems, COP calculations should include energy consumption of all power consuming 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. [3]

According to the first law of thermodynamics, in a reversible system we can show that Q H = Q C + W {\displaystyle Q_{H}=Q_{C}+W} and W = Q H − Q C {\displaystyle W=Q_{H}-Q_{C}} , where Q H {\displaystyle Q_{H}} is the heat transferred to the hot reservoir and Q C {\displaystyle Q_{C}} is the heat collected from the cold reservoir.

For a heat pump operating at maximum theoretical efficiency (i.e. Carnot efficiency), it can be shown that Q H T H = Q C T C {\displaystyle {\frac {Q_{H}}{T_{H}}}={\frac {Q_{C}}{T_{C}}}} and Q C = Q H T C T H {\displaystyle Q_{C}={\frac {Q_{H}T_{C}}{T_{H}}}}

C O P h e a t i n g {\displaystyle {\rm {COP}}_{\rm {heating}}} applies to heat pumps and C O P c o o l i n g {\displaystyle {\rm {COP}}_{\rm {cooling}}} applies to air conditioners or refrigerators. For heat engines, see 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 T H {\displaystyle {T_{H}}} and 0 °C (32 °F) for T C {\displaystyle {T_{C}}} . According to the above formula, the maximum achievable COP would be 8.8. 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. [4] Improving COP [ edit ]

As the formula shows, the COP of a heat pump system can be improved by reducing the temperature gap T h o t {\displaystyle T_{hot}} minus T c o l d {\displaystyle T_{cold}} at which the system works. For a heating system this would mean two things: 1) reducing the output temperature to around 30 °C (86 °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 [5] ). Accurately determining thermal conductivity will allow for much more precise ground loop [6] or borehole sizing, [7] resulting in higher return temperatures and a more efficient system. 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) by decreasing the speed of fluid which in turn lower the Re number and hence the turbulence (and noise) and the head loss (see hydraulic head). The heat pump itself can be improved by increasing the size of the internal heat exchangers which in turn increase the efficiency (and the price) relative to the power of the compressor, and also by reducing the system’s internal temperature gap over the compressor. Obviously, this latter measure makes such heat pumps unsuitable to produce high temperatures which means that a separate machine is needed for producing hot tap water. Example [ edit ]

A geothermal heat pump operating at a C O P h e a t i n g {\displaystyle {\rm {COP}}_{\rm {heating}}} of 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.

A heat pump with C O P h e a t i n g {\displaystyle {\rm {COP}}_{\rm {heating}}} of 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 (e.g. Connecticut or New York City).

A heat pump cooler operating at a C O P c o o l i n g {\displaystyle {\rm {COP}}_{\rm {cooling}}} of 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).

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.

For example, the 2009 US average price per therm (100,000 British thermal units (29 kWh)) of electricity was $3.38 while the average price per therm of natural gas was $1.16. [8] Using these prices, a heat pump with a COP of 3.5 in moderate climate would cost $0.97 [9] to provide one therm of heat, while a high efficiency gas furnace with 95% efficiency would cost $1.22 [10] to provide one therm of heat. With these average prices, the heat pump costs 20% less [11] 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. Conditions of use [ edit ]