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61-530: The SEER rating of a unit is the cooling output during a typical cooling-season divided by the total electric energy input during the same period. The higher the unit's SEER rating the more energy efficient it is. In the U.S., the SEER is the ratio of cooling in British thermal units (BTUs) to the energy consumed in watt-hours. For example, consider a 5000 BTU/h (1465-watt cooling capacity) air-conditioning unit, with

122-604: A 30.5 SEER rating mini split in 2015 as well. Carrier launched a 42 SEER ductless air conditioner during 2018 Consumer electronic Show (CES), held in Las Vegas. Traditional AC systems with ducts have maximum SEER ratings slightly below these levels. Also, practically, central systems will have an achieved energy efficiency ratio 10–20% lower than the nameplate rating due to the duct-related losses. Additionally, there are ground-source residential AC units with SEER ratings up to 75. However, ground-source heat pump effective efficiency

183-446: A SEER of 10 BTU/(W·h), operating for a total of 1000 hours during an annual cooling season (e.g., 8 hours per day for 125 days). The annual total cooling output would be: With a SEER of 10 BTU/(W·h), the annual electrical energy usage would be about: The average power usage may also be calculated more simply by: If your electricity cost is $ 0.20/(kW·h), then your cost per operating hour is: The energy efficiency ratio (EER) of

244-403: A SEER rating of 10, operates 1000 hours per year at an electric energy cost of $ 0.12 per kilowatt-hour (kW·h). What is the annual cost of the electric energy it uses? Example 2. A residence near Chicago has an air conditioner with a cooling capacity of 4 tons and an SEER rating of 10. The unit is operated 120 days each year for 8 hours per day (960 hours per year), and the electric energy cost

305-488: A dollar today is worth more than a dollar in the future. The time value of money is among the factors considered when weighing the opportunity costs of spending rather than saving or investing money. As such, it is among the reasons why interest is paid or earned: interest, whether it is on a bank deposit or debt , compensates the depositor or lender for the loss of their use of their money. Investors are willing to forgo spending their money now only if they expect

366-453: A favorable net return on their investment in the future, such that the increased value to be available later is sufficiently high to offset both the preference to spending money now and inflation (if present); see required rate of return . The Talmud (~500 CE) recognizes the time value of money. In Tractate Makkos page 3a the Talmud discusses a case where witnesses falsely claimed that

427-487: A given problem. For example, one may know that: the interest is 0.5% per period (per month, say); the number of periods is 60 (months); the initial balance (of the debt, in this case) is 25,000 units; and the final balance is 0 units. The unknown variable may be the monthly payment that the borrower must pay. For example, £100 invested for one year, earning 5% interest, will be worth £105 after one year; therefore, £100 paid now and £105 paid exactly one year later both have

488-779: A growing annuity (FVA) formula has five variables, each of which can be solved for by numerical methods: Where i ≠ g : Where i = g : The following table summarizes the different formulas commonly used in calculating the time value of money. These values are often displayed in tables where the interest rate and time are specified. Increasing percentage (g) F = D ⋅ n ( 1 + i ) n 1 + g {\displaystyle F=D\cdot {\frac {n(1+i)^{n}}{1+g}}}   (for i = g) Increasing percentage (g) P = D ⋅ n 1 + g {\displaystyle P=D\cdot {\frac {n}{1+g}}}   (for i = g) Notes: The formula for

549-413: A heat pump to move heat from outdoors into a warmer house. A heat pump with a higher SEER rating for cooling mode would also usually be more efficient in heating mode, rated using HSPF . When operated in heating mode, a heat pump is typically more efficient than an electrical resistance heater. This is because a space heater can convert only the input electrical energy directly to output heat energy, while

610-399: A heat pump transfers heat from outdoors. In heating mode, the coefficient of performance is the ratio of heat provided to the energy used by the unit. An ideal resistance heater converting 100% of its input electricity to output heat would have COP = 1, equivalent to a 3.4 EER. The heat pump becomes less efficient as the outside temperature decreases, and its performance may become comparable to

671-406: A lump-sum "present value" of the entire income stream; all of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, "discounted" to the present by an amount equal to the time value of money. For example, the future value sum F V {\displaystyle FV} to be received in one year is discounted at

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732-486: A particular cooling device is the ratio of output cooling energy (in BTUs) to input electrical energy (in watt-hours) at a given operating point. EER is generally calculated using a 95 °F (35 °C) outside temperature and an inside (actually return-air) temperature of 80 °F (27 °C) and 50% relative humidity. The EER is related to the coefficient of performance ( COP ) commonly used in thermodynamics , with

793-423: A periodic rate of interest, the number of periods, and a series of cash flows. (In the case of a debt, cash flows are payments against principal and interest; in the case of a financial asset, these are contributions to or withdrawals from the balance.) More generally, the cash flows may not be periodic but may be specified individually. Any of these variables may be the independent variable (the sought-for answer) in

854-610: A resistance heater. For a heat pump with the minimum 13 SEER cooling efficiency, this is typically below −10 °F (−23 °C). Lower temperatures may cause a heat pump to operate below the efficiency of a resistance heater, so conventional heat pumps often include heater coils or auxiliary heating from LP or natural gas to prevent low efficiency operation of the refrigeration cycle. "Cold climate" heat pumps are designed to optimize efficiency below 0 °F (−18 °C). As of 2023 heat pumps are marketed that will extract heat from outdoor temperatures as low as −40 °F (−40 °C). In

915-413: Is $ 0.10 per kilowatt-hour. What is its annual cost of operation in terms of electric energy? First, we convert tons of cooling to BTU/h: The annual cost of the electric energy is: Today there are mini-split (ductless) air conditioner units available with SEER ratings up to 42. During the 2014 AHR Expo, Mitsubishi unveiled a new mini-split ductless AC unit with a SEER rating of 30.5. GREE also released

976-615: Is a measure of heat , which is a form of energy . It was originally defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit . It is also part of the United States customary units . The SI unit for energy is the joule (J) ; one Btu equals about 1,055 J (varying within the range of 1,054–1,060 J depending on the specific definition of BTU; see below). While units of heat are often supplanted by energy units in scientific work, they are still used in some fields. For example, in

1037-589: Is also the COP (or EER) expressed in BTU/watt-hour, but instead of being evaluated at a single operating condition, it represents the expected overall performance for a typical year's weather in a given location. The SEER is thus calculated with the same indoor temperature, but over a range of outside temperatures from 65 °F (18 °C) to 104 °F (40 °C), with a certain specified percentage of time in each of 8 bins spanning 5 °F (2.8 °C). There

1098-571: Is approximately equivalent to an EER of 11, and a COP of 3.2, which means that 3.2 units of heat are removed from indoors per unit of energy used to run the air conditioner. The SEER and EER of an air conditioner are limited by the laws of thermodynamics . The refrigeration process with the maximum possible efficiency is the Carnot cycle . The COP of an air conditioner using the Carnot cycle is: where T C {\displaystyle T_{C}}

1159-419: Is composed of two types of payments: a stream of coupon payments similar to an annuity, and a lump-sum return of capital at the end of the bond's maturity —that is, a future payment. The two formulas can be combined to determine the present value of the bond. An important note is that the interest rate i is the interest rate for the relevant period. For an annuity that makes one payment per year, i will be

1220-438: Is designed to better reflect current field conditions. DOE increases systems' external static pressure from current SEER (0.1 in. of water) to SEER2 (0.5 in. of water). These pressure conditions were devised to consider ducted systems that would be seen in the field. With this change, new nomenclature will be used to denote M1 ratings (including EER2 and HSPF2). Electric power is usually measured in kilowatts (kW). Electric energy

1281-463: Is equal to 1.8 Btu or 1,899 joules. In 1974, this unit was "still sometimes used" in the United Kingdom as an alternative to Btu. Another legacy unit for energy in the metric system is the calorie , which is defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius . Time value of money The time value of money refers to

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1342-453: Is no allowance for different climates in this rating, which is intended to give an indication of how the EER is affected by a range of outside temperatures over the course of a cooling season. Typical EER for residential central cooling units = 0.875 × SEER. SEER is a higher value than EER for the same equipment. A more detailed method for converting SEER to EER uses this formula: A SEER of 13

1403-600: Is rare to see systems rated below SEER 9 in the United States because aging, existing units are being replaced with new, higher efficiency units. Beginning in January 2006 a minimum SEER 13 was required. The United States requires that residential systems manufactured after 2005 have a minimum SEER rating of 13. ENERGY STAR qualified Central Air Conditioners must have a SEER of at least 14.5. Window units are exempt from this law so their SEERs are still around 10. In 2011

1464-454: Is reliant on the temperature of the ground or water source used. Hot climates have a much higher ground or surface water temperature than cold climates and therefore will not be able to achieve such efficiencies. Moreover, the ARI rating scheme for ground-source heat pumps allows them to largely ignore required pump power in their ratings, making the achievable SEER values often practically lower than

1525-454: Is similar and uses the same variables. The present value formula is the core formula for the time value of money; each of the other formulas is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations. The present value ( PV ) formula has four variables, each of which can be solved for by numerical methods : The cumulative present value of future cash flows can be calculated by summing

1586-536: Is the watt . Btu per hour (Btu/h) is sometimes used in North America and the United Kingdom - the latter for air conditioning mainly, though "Btu/h" is sometimes abbreviated to just "Btu". MBH —thousands of Btu per hour—is also common. The Btu should not be confused with the Board of Trade Unit (BTU), an obsolete UK synonym for kilowatt hour (1 kW⋅h or 3,412 Btu). The Btu is often used to express

1647-448: Is the indoor temperature and T H {\displaystyle T_{H}} is the outdoor temperature. Both temperatures must be measured using a thermodynamic temperature scale based at absolute zero such as Kelvin or Rankine . The EER is calculated by multiplying the COP by 3.412 BTU/W⋅h as described above: Assuming an outdoor temperature of 95 °F (35 °C) and an indoor temperature of 80 °F (27 °C),

1708-554: Is used in natural gas and other industries to indicate 1,000 Btu. However, there is an ambiguity in that the metric system (SI) uses the prefix "M" to indicate ' Mega- ', one million (1,000,000). Even so, "MMbtu" is often used to indicate one million Btu particularly in the oil and gas industry. Energy analysts accustomed to the metric "k" (' kilo- ') for 1,000 are more likely to use MBtu to represent one million, especially in documents where M represents one million in other energy or cost units, such as MW, MWh and $ . The unit ' therm '

1769-432: Is used to represent 100,000 Btu. A decatherm is 10 therms or one million Btu. The unit quad is commonly used to represent one quadrillion (10 ) Btu. One Btu is approximately: A Btu can be approximated as the heat produced by burning a single wooden kitchen match or as the amount of energy it takes to lift a one-pound (0.45 kg) weight 778 feet (237 m). The SI unit of power for heating and cooling systems

1830-408: Is usually measured in kilowatt-hours (kW·h). For example, if an electric load that draws 1.5 kW of electric power is operated for 8 hours, it uses 12 kW·h of electric energy. In the United States, a residential electric customer is charged based on the amount of electric energy used. On the customer bill, the electric utility states the amount of electric energy, in kilowatt-hours (kW·h), that

1891-612: The Btu that differ slightly. This reflects the fact that the temperature change of a mass of water due to the addition of a specific amount of heat (calculated in energy units, usually joules) depends slightly upon the water's initial temperature. As seen in the table below, definitions of the Btu based on different water temperatures vary by up to 0.5%. Units of kBtu are used in building energy use tracking and heating system sizing. Energy Use Index (EUI) represents kBtu per square foot of conditioned floor area. "k" stands for 1,000. The unit Mbtu

Seasonal energy efficiency ratio - Misplaced Pages Continue

1952-494: The PV of a growing annuity due , multiply the above equation by (1 + i ). A perpetuity is payments of a set amount of money that occur on a routine basis and continue forever. When n → ∞, the PV of a perpetuity (a perpetual annuity) formula becomes a simple division. When the perpetual annuity payment grows at a fixed rate ( g , with g < i ) the value is determined according to

2013-479: The PV of an annuity due , multiply the above equation by (1 + i ). In this case each cash flow grows by a factor of (1+ g ). Similar to the formula for an annuity, the present value of a growing annuity (PVGA) uses the same variables with the addition of g as the rate of growth of the annuity (A is the annuity payment in the first period). This is a calculation that is rarely provided for on financial calculators. Where i ≠ g : Where i = g : To get

2074-741: The Southeastern Region of the United States of America must be at least 14 SEER. The Southeastern Region includes Alabama, Arkansas, Delaware, Florida, Georgia, Hawaii, Kentucky, Louisiana, Maryland, Mississippi, North Carolina, Oklahoma, South Carolina, Tennessee, Texas, and Virginia. Similarly, split-system central air conditioners installed in the Southwestern Region must be a minimum 14 SEER and 12.2 EER beginning on January 1, 2015. The Southwestern Region consists of Arizona, California, Nevada, and New Mexico. Split-system central air conditioners installed in all other states outside

2135-619: The Southeastern and Southwestern regions must continue to be a minimum of 13 SEER, which is the current national requirement. There have been many new advances in efficient technology over the past 10 years which have enabled manufacturers to increase their SEER ratings dramatically in order to stay above the required minimums set by the United States department of energy. Effective January 1, 2023, cooling products will be subject to regional minimum efficiencies, according to Seasonal Energy Efficiency Ratio 2 (SEER2) . New M1 testing procedure

2196-601: The US Department of Energy (DOE) revised energy conservation rules to impose elevated minimum standards and regional standards for residential HVAC systems. The regional approach recognizes the differences in cost-optimization resulting from regional climate differences. For example, there is little cost benefit in having a very high SEER air conditioning unit in Maine, a state in the northeast US. Starting January 1, 2015, split-system central air conditioners installed in

2257-404: The United States the price of natural gas is quoted in dollars per the amount of natural gas that would give 1 million Btu (1 "MMBtu") of heat energy if burned. A Btu was originally defined as the amount of heat required to raise the temperature of one pound of liquid water by one degree Fahrenheit at a constant pressure of one atmospheric unit . There are several different definitions of

2318-465: The above equation gives (when temperatures are converted to the Kelvin or Rankine scales) a COP of 36, or an EER of 120. This is about 10 times more efficient than a typical home air conditioner available today. The maximum EER decreases as the difference between the inside and outside air temperature increases, and vice versa. In a desert climate where the outdoor temperature is 120 °F (49 °C),

2379-426: The annual interest rate. For an income or payment stream with a different payment schedule, the interest rate must be converted into the relevant periodic interest rate. For example, a monthly rate for a mortgage with monthly payments requires that the interest rate be divided by 12 (see the example below). See compound interest for details on converting between different periodic interest rates. The rate of return in

2440-456: The borrower lose; therefore, it is the sum that they must pay." The notion was later described by Martín de Azpilcueta (1491–1586) of the School of Salamanca . Time value of money problems involve the net value of cash flows at different points in time. In a typical case, the variables might be: a balance (the real or nominal value of a debt or a financial asset in terms of monetary units),

2501-428: The calculations can be either the variable solved for, or a predefined variable that measures a discount rate, interest, inflation, rate of return, cost of equity, cost of debt or any number of other analogous concepts. The choice of the appropriate rate is critical to the exercise, and the use of an incorrect discount rate will make the results meaningless. For calculations involving annuities, it must be decided whether

Seasonal energy efficiency ratio - Misplaced Pages Continue

2562-437: The case of cold climates, water or ground-source heat pumps are often the most efficient solution. They use the relatively constant temperature of ground water or of water in a large buried loop to moderate the temperature differences in summer and winter and improve performance year round. The heat pump cycle is reversed in the summer to act as an air conditioner. British thermal unit The British thermal unit ( Btu )

2623-453: The contributions of FV t , the value of cash flow at time t : Note that this series can be summed for a given value of n , or when n is ∞. This is a very general formula, which leads to several important special cases given below. In this case the cash flow values remain the same throughout the n periods. The present value of an annuity (PVA) formula has four variables, each of which can be solved for by numerical methods: To get

2684-436: The conversion-efficiency of heat into electrical energy in power plants. Figures are quoted in terms of the quantity of heat in Btu required to generate 1 kW⋅h of electrical energy. A typical coal-fired power plant works at 10,500 Btu/kWh (3.1 kWh/kWh), an efficiency of 32–33%. The centigrade heat unit (CHU) is the amount of heat required to raise the temperature of one pound of water by one Celsius degree. It

2745-539: The customer used since the last bill, and the cost of the energy per kilowatt-hour (kW·h). Air-conditioner sizes are often given as "tons" of cooling , where 1 ton of cooling equals 12,000 BTU/h (3.5 kW). 1 ton of cooling equals the amount of power that needs to be applied continuously over a 24-hour period to melt 1 ton of ice. The annual cost of electric energy consumed by an air conditioner may be calculated as follows: Example 1: An air-conditioning unit rated at 72,000 BTU/h (21 kW) (6 tons), with

2806-488: The equations below, the formula may also be rearranged to determine one of the other unknowns. In the case of the standard annuity formula, there is no closed-form algebraic solution for the interest rate (although financial calculators and spreadsheet programs can readily determine solutions through rapid trial and error algorithms). These equations are frequently combined for particular uses. For example, bonds can be readily priced using these equations. A typical coupon bond

2867-425: The fact that there is normally a greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference . The time value of money refers to the observation that it is better to receive money sooner than later. Money you have today can be invested to earn a positive rate of return, producing more money tomorrow. Therefore,

2928-443: The following formula, obtained by setting n to infinity in the earlier formula for a growing perpetuity: In practice, there are few securities with precise characteristics, and the application of this valuation approach is subject to various qualifications and modifications. Most importantly, it is rare to find a growing perpetual annuity with fixed rates of growth and true perpetual cash flow generation. Despite these qualifications,

2989-471: The general approach may be used in valuations of real estate, equities, and other assets. This is the well known Gordon growth model used for stock valuation . The future value (after n periods) of an annuity (FVA) formula has four variables, each of which can be solved for by numerical methods: To get the FV of an annuity due, multiply the above equation by (1 + i). The future value (after n periods) of

3050-419: The highest efficiency air-source equipment—particularly for air cooling. There are a variety of technologies that will allow SEER and EER ratings to increase further in the near future. Some of these technologies include rotary compressors, inverters, DC brushless motors, variable-speed drives, and integrated systems such as those found in solar-powered air conditioning . A refrigeration cycle can be operated as

3111-424: The initial value being a = C , the multiplicative factor being 1 + i , with n terms. Applying the formula for geometric series, we get The present value of the annuity (PVA) is obtained by simply dividing by ( 1 + i ) n {\displaystyle (1+i)^{n}} : Another simple and intuitive way to derive the future value of an annuity is to consider an endowment, whose interest

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3172-501: The maximum COP drops to 13, or an EER of 46 (for an indoor temperature of 80 °F (27 °C)). The maximum SEER can be calculated by averaging the maximum EER over the range of expected temperatures for the season. ‹The template Manual is being considered for merging .›   SEER rating reflects overall system efficiency on a seasonal basis and EER reflects the system's energy efficiency at one specific operating condition. Both ratings are useful when choosing products, but

3233-408: The most cost effective. However, the efficiency of air conditioners can degrade significantly over time. But when either replacing equipment, or specifying new installations, a variety of SEERs are available. For most applications, the minimum or near-minimum SEER units are most cost effective, but the longer the cooling seasons, the higher the electricity costs, and the longer the purchasers will own

3294-502: The payments are made at the end of each period (known as an ordinary annuity), or at the beginning of each period (known as an annuity due). When using a financial calculator or a spreadsheet , it can usually be set for either calculation. The following formulas are for an ordinary annuity. For the answer for the present value of an annuity due, the PV of an ordinary annuity can be multiplied by (1 + i ). The following formula use these common variables: The future value ( FV ) formula

3355-419: The present value of a regular stream of future payments (an annuity) is derived from a sum of the formula for future value of a single future payment, as below, where C is the payment amount and n the period. A single payment C at future time m has the following future value at future time n : Summing over all payments from time 1 to time n, then reversing t Note that this is a geometric series , with

3416-405: The primary difference being that the COP of a cooling device is unit-less, because the numerator and denominator are expressed in the same units. The EER uses mixed units, so it does not have an immediate physical sense and is obtained by multiplying the COP by the conversion factor from BTUs to watt-hours: EER = 3.41214 × COP (see British thermal unit ). The seasonal energy efficiency ratio (SEER)

3477-550: The rate of interest r {\displaystyle r} to give the present value sum P V {\displaystyle PV} : Some standard calculations based on the time value of money are: There are several basic equations that represent the equalities listed above. The solutions may be found using (in most cases) the formulas, a financial calculator or a spreadsheet . The formulas are programmed into most financial calculators and several spreadsheet functions (such as PV, FV, RATE, NPER, and PMT). For any of

3538-416: The same rating must be used for comparisons. Substantial energy savings can be obtained from more efficient systems. For example, by upgrading from SEER 9 to SEER 13, the power consumption is reduced by 30% (equal to 1 − 9/13). With existing units that are still functional and well-maintained, when the time value of money is considered, retaining existing units rather than proactively replacing them may be

3599-417: The same value to a recipient who expects 5% interest assuming that inflation would be zero percent. That is, £100 invested for one year at 5% interest has a future value of £105 under the assumption that inflation would be zero percent. This principle allows for the valuation of a likely stream of income in the future, in such a way that annual incomes are discounted and then added together, thus providing

3660-399: The systems, the more that incrementally higher SEER units are justified. Residential split-system AC units of SEER 20 or more are now available. The higher SEER units typically have larger coils and multiple compressors, with some also having variable refrigerant flow and variable supply air flow. In 1987 legislation taking effect in 1992 was passed requiring a minimum SEER rating of 10. It

3721-409: The term of a loan was 30 days when it was actually 10 years. The false witnesses must pay the difference of the value of the loan "in a situation where he would be required to give the money back (within) thirty days..., and that same sum in a situation where he would be required to give the money back (within) 10 years...The difference is the sum that the testimony of the (false) witnesses sought to have

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