# British thermal unit

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The British thermal unit (Btu or BTU) is a traditional unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is part of the British Imperial system of units.[1] Its counterpart 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.[2] Heat is now known to be equivalent to energy, for which the metric unit is the joule; one BTU is about 1055 joules. While units of heat are often supplanted by energy units in scientific work, they are still important in many fields. As examples, in the United States the price of natural gas is quoted in dollars per million BTUs.[3][4] Chemical bond energies are often given in calories per mole of substance.[5]

## Definitions

A BTU was originally defined as the amount of heat required to raise the temperature of 1 avoirdupois pound of liquid water by 1 degree Fahrenheit at a constant pressure of one atmosphere.[6] There are several different definitions of the BTU that are now known to 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%. In the table, thermochemical and steam table (IT) values, which are now defined in terms of exact values in joules, have been rounded to four decimal places.

Nominal temperature Btu equivalent in joules Notes
Thermochemical ≡ 1054.3503 Originally, the thermochemical BTU was defined as the heat required to raise the temperature of one pound of water from its freezing point to its boiling point, divided by the temperature difference (180 F). The similar, "thermochemical calorie" was defined as the heat required to raise the temperature of one gram of water from freezing to boiling divided by the temperature difference in Celsius (100 C). The International Standards Organization now redefines the thermochemical calorie as exactly 4.184 J.[6] The thermochemical BTU is then defined using the conversions from grams to pounds and from Celsius to Fahrenheit.[7]
59 °F (15.0 °C) ≈ 1054.80[8] Used for U.S. natural gas pricing.[4]
60 °F (15.6 °C) ≈ 1054.68[9] Chiefly Canadian.[citation needed]
39 °F (3.9 °C) ≈ 1059.67[9] Uses the calorie value of water at its maximum density (4 °C or 39.2 °F).[citation needed]
IT ≡ 1055.0559 An early effort to define heat units directly in terms of energy units, and hence to remove the direct association with the properties of water, was taken by the International Steam Table Conferences. These conferences originally adopted the simplified definition that 860 "IT" calories corresponded exactly to one watt-hour; the watt hour is an energy unit. This definition ultimately became the statement that 1 IT calorie is exactly 4.1868 J.[6][10] The BTU is then calculated from the calorie as is done for the thermochemical definitions of the BTU and the calorie.[7]
ISO ≡ 1055.06 International standard ISO 31-4 on Quantities and units—Part 4: Heat.[11] This value uses the IT calorie and is rounded to a realistic accuracy.

### Prefixes

Units 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 is metric system units for 1,000.

The units MBtu and MMBtu are used in the natural gas and other industries to indicate 1,000 and 1,000,000 BTUs, respectively.[12][13] This is presumably from the Roman numeral system, where "M" stands for one thousand (1,000). However, Roman Numeral MM represents two thousand, adding confusion if the Roman system is cited as the source for MM.

There is an ambiguity in that the metric system uses the prefix "M" to indicate one million (1,000,000), and "MBtu" is also used to indicate one million BTUs.[14] Because of this ambiguity, some authors have deprecated the use of the unit Btu.[13]

Energy analysts acustomed to the metric K 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 is used to represent 100,000 (or 105) BTUs.[12] A decatherm is 10 therms or one MBtu. The unit quad is commonly used to represent one quadrillion (1015) BTUs.[14]

## Conversions

One Btu is approximately:

• 1.054 to 1.060 kJ (kilojoules)
• 0.293071 W·h (watt hours)
• 252 to 253 cal (calories, or "little calories")
• 0.25 kcal (kilocalories, "large calories", or "food calories")
• 25,031 to 25,160 ft·pdl (foot-poundal)
• 778 to 782 ft·lbf (foot-pounds-force)
• 5.40395 (lbf/in2)·ft3

A Btu can be approximated as the heat produced by burning a single wooden kitchen match[15] or as the amount of energy it takes to lift a one-pound (0.45 kg) weight 778 feet (237 m).[16]

### For natural gas

• In natural gas pricing, the Canadian definition is that 1 MMBtu (1 million Btu) = 1.054615 GJ.[17]
• The energy content (high or low heating value) of a volume of natural gas varies with the composition of the natural gas, which means there is no universal conversion factor for the number of Btu to volume. 1 standard cubic foot of average natural gas yields ≈ 1030 Btu (between 1010 Btu and 1070 Btu, depending on quality, when burned)
• As a coarse approximation, 1000 ft3 of natural gas yields ≈ 1 MMBtu ≈ 1 GJ
• For natural gas price conversion 1000 m3 ≈ 36.906 MMBtu and 1 MMBtu ≈ 27.096 m3

### As a unit of power

When used as a unit of power for heating and cooling systems, Btu per hour (Btu/h) is the correct unit, though this is often abbreviated to just "Btu".[18]

• 1 watt is approximately 3.41214 Btu/h[19]
• 1000 Btu/h is approximately 293.071 W
• 1 horsepower is approximately 2544 Btu/h

## Associated units

• 1 ton of cooling, a common unit in North American refrigeration and air conditioning applications, is 12,000 Btu/h (3.52 kW). It is the rate of heat transfer needed to freeze 1 short ton (907 kg) of water into ice in 24 hours.
• In the US, the R-value that describes the performance of thermal insulation is typically quoted in ft2·°F·hr/BTU. For one square foot of the insulation, one BTU per hour of heat flows across the insulator for each degree of temperature difference across it.
• 1 therm is defined in the United States and European Union as 100,000 Btu—but the U.S. uses the Btu59 °F while the EU uses the BtuIT. The therm is used in natural gas pricing in the United Kingdom.[20]
• 1 quad (short for quadrillion Btu) is 1015 Btu, which is about one exajoule (1.055×1018 J). Quads are used in the United States for representing the annual energy consumption of large economies: for example, the U.S. economy used 99.75 quads in 2005.[21] One quad/year is about 33.43 gigawatts.

The Btu should not be confused with the Board of Trade Unit (B.O.T.U.), which is a much larger quantity of energy (1 kW·h or 3,412 Btu).

The Btu is often used to express 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/kW·h, an efficiency of 32–33%.[22]

The centigrade heat unit (CHU) is the amount of heat required to raise the temperature of one pound of water by one degree Celsius. It is equal to 1.8 BTU or 1899 joules.[23] This unit was sometimes used in the United Kingdom as an alternative to BTU but is now obsolete.

## References

1. ^ In a short note, Woledge notes that the actual technical term "British thermal unit" apparently originated in the United States, and was subsequently adopted in Great Britain. See Woledge, G. (30 May 1942). "History of the British Thermal Unit". Nature. 149 (149): 613. Bibcode:1942Natur.149..613W. doi:10.1038/149613c0. (Subscription required (help)).
2. ^ Hargrove, James L. (2007). "Does the history of food energy units suggest a solution to 'Calorie confusion'?". Nutrition Journal. 6: 44. doi:10.1186/1475-2891-6-44.
3. ^ "Henry Hub Natural Gas Spot Price". U.S. Energy Information Administration.
4. ^ a b The Btu used in US natural gas pricing is "the amount of heat required to raise the temperature of one (1) pound of avoirdupois pure water from fifty-eight and five tenths degrees (58.5) Fahrenheit to fifty-nine and five tenths degrees (59.5) Fahrenheit at a constant pressure of 14.73 pounds per square inch absolute." See "Chapter 220: Henry Hub Natural Gas Futures" (PDF). NYMex Rulebook. New York Mercantile Exchange (NYMex). Retrieved 2017-01-06.
5. ^ Luo, Yu-Ran (2002). Handbook of Bond Dissociation Energies in Organic Compounds. CRC Press. ISBN 9781420039863.
6. ^ a b c Smith, J. M.; Van Ness, H. C.; Abbott, M. M. (2003). Introduction to Chemical Engineering Thermodynamics. B. I. Bhatt (adaptation) (6 ed.). Tata McGraw-Hill Education. p. 15. ISBN 0-07-049486-X.
7. ^ a b The pound is now defined as 453.59237 grams; see "Appendix C of NIST Handbook 44, Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices, General Tables of Units of Measurement" (PDF). United States National Bureau of Standards. p. C-12. Archived from the original (PDF) on 2006-11-26. One degree Fahrenheit is now defined as exactly 5/9 of a degree Celsius.
8. ^ Thompson, Ambler; Taylor, Barry N. "Guide for the Use of the International System of Units (SI) 2008 Edition" (PDF). National Institute of Standards and Technology (NIST). p. 58. NIST Special Publication 811.
9. ^ a b Sørensen, Bent (2008). Renewable Energy Focus e-Mega Handbook. Academic Press. p. 5. ISBN 9780123747068.
10. ^ Koch, Werner (2013). VDI Steam Tables (4 ed.). Springer. p. 8. Published under the auspices of the Verein Deutscher Ingenieure (VDI).
11. ^ Cardarelli, Francois (2012). Scientific Unit Conversion: A Practical Guide to Metrication. M.J. Shields (translation) (2 ed.). Springer. p. 19.
12. ^ a b "What are Mcf, Btu, and therms? How do I convert prices in Mcf to Btus and therms?". U.S. Energy Information Administration. April 6, 2016. Retrieved 2016-12-30.
13. ^ a b Price, Gary D. (2014). Power Systems and Renewable Energy: Design, Operation, and Systems Analysis. Momentum Press. p. 98.
14. ^ a b "Energy Units". American Physical Society. Retrieved 2016-12-26.
15. ^ Energy and the Environment. Ristinen, Robert A. c. 2006, pg 13
16. ^ Energy and the Environment. Ristinen, Robert A. c. 2006, pg 14
17. ^ "Energy Measurements". Government of Alberta Province. Retrieved 2017-01-07.
18. ^ Ken Matesz (2010). Masonry Heaters: Designing, Building, and Living with a Piece of the Sun. Chelsea Green Publishing. p. 148.
19. ^
20. ^ "The GB gas wholesale market". OFGEM. Retrieved Jan 13, 2013. The wholesale gas market in Britain has one price for gas irrespective of where the gas comes from. This is called the National Balancing Point (NBP) price of gas and is usually quoted in price per therm of gas.
21. ^ Husher, John Durbin (2009). Crises of the 21st Century: Start Drilling-The Year 2020 Is Coming Fast. iUniverse. p. 376. ISBN 9781440140549. OCLC 610004375..
22. ^ Bellman, David K., ed. (July 18, 2007). "Electric Generation Efficiency" (PDF). National Petroleum Council (NPC). Working Document of the NPC Global Oil & Gas Study.