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Specific heat capacity
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==Units== ===International system=== The SI unit for specific heat capacity is joule per kelvin per kilogram {{sfrac|J|kg⋅K}}, J⋅K<sup>−1</sup>⋅kg<sup>−1</sup>. Since an increment of temperature of one [[Celsius scale|degree Celsius]] is the same as an increment of one kelvin, that is the same as joule per degree Celsius per kilogram: J/(kg⋅°C). Sometimes the [[gram]] is used instead of kilogram for the unit of mass: 1 J⋅g<sup>−1</sup>⋅K<sup>−1</sup> = 1000 J⋅kg<sup>−1</sup>⋅K<sup>−1</sup>. The specific heat capacity of a substance (per unit of mass) has [[dimensional analysis|dimension]] L<sup>2</sup>⋅Θ<sup>−1</sup>⋅T<sup>−2</sup>, or (L/T)<sup>2</sup>/Θ. Therefore, the SI unit J⋅kg<sup>−1</sup>⋅K<sup>−1</sup> is equivalent to [[metre]] squared per [[second]] squared per [[kelvin]] (m<sup>2</sup>⋅K<sup>−1</sup>⋅s<sup>−2</sup>). ===Imperial engineering units=== Professionals in [[construction]], [[civil engineering]], [[chemical engineering]], and other technical disciplines, especially in the [[United States]], may use [[English Engineering Units|English Engineering units]] including the [[pound (mass)|pound]] (lb = 0.45359237 kg) as the unit of mass, the [[Fahrenheit|degree Fahrenheit]] or [[Rankine scale|Rankine]] (°R = {{sfrac|5|9}} K, about 0.555556 K) as the unit of temperature increment, and the [[British thermal unit]] (BTU ≈ 1055.056 J),<ref name=Koch> {{cite book |title=VDI Steam Tables |publisher=Springer |edition=4 |date=2013 |last=Koch |first=Werner |page=8 |url=https://books.google.com/books?id=bJ_wBgAAQBAJ&pg=PA8|isbn=9783642529412 }} Published under the auspices of the ''Verein Deutscher Ingenieure'' (VDI). </ref><ref> {{cite book |title=Scientific Unit Conversion: A Practical Guide to Metrication |first=Francois |last=Cardarelli |others=M.J. Shields (translation) |edition=2 |publisher=Springer |date=2012 |page=19 |url=https://books.google.com/books?id=-ZveBwAAQBAJ&pg=PA19-IA35 |isbn=9781447108054 }}</ref> as the unit of heat. In those contexts, the unit of specific heat capacity is BTU/lb⋅°R, or 1 {{sfrac|BTU|lb⋅°R}} = 4186.68{{sfrac|J|kg⋅K}}.<ref>From direct values: 1{{sfrac|BTU|lb⋅°R}} × 1055.06{{sfrac|J|BTU}} × ({{sfrac|1|0.45359237}}){{sfrac|lb|kg}} x {{sfrac|9|5}}{{sfrac|°R|K}} = 4186.82{{sfrac|J|kg⋅K}}</ref> The BTU was originally defined so that the average specific heat capacity of water would be 1 BTU/lb⋅°F.<ref>°F=°R</ref> Note the value's similarity to that of the calorie - 4187 J/kg⋅°C ≈ 4184 J/kg⋅°C (~.07%) - as they are essentially measuring the same energy, using water as a basis reference, scaled to their systems' respective lbs and °F, or kg and °C. ===Calories=== In chemistry, heat amounts were often measured in [[calorie]]s. Confusingly, there are two common units with that name, respectively denoted ''cal'' and ''Cal'': * the ''small calorie'' (''gram-calorie, cal'') is 4.184 J exactly. It was originally defined so that the specific heat capacity of liquid water would be 1 cal/(°C⋅g). *The ''grand calorie'' (''kilocalorie, kilogram-calorie, food calorie, kcal, Cal'') is 1000 small calories, 4184 J exactly. It was defined so that the specific heat capacity of water would be 1 Cal/(°C⋅kg). While these units are still used in some contexts (such as kilogram calorie in [[nutrition]]), their use is now deprecated in technical and scientific fields. When heat is measured in these units, the unit of specific heat capacity is usually: {{block indent|1=1 {{sfrac|cal|°C⋅g}} = 1 {{sfrac|Cal|°C⋅kg}} = 1 {{sfrac|kcal|°C⋅kg}} = 4184 {{sfrac|J|kg⋅K}}<ref>°C=K</ref> = 4.184 {{sfrac|kJ|kg⋅K}}.}} Note that while cal is '''{{frac|1|1000}}''' of a Cal or kcal, it is also per ''gram'' instead of '''kilo'''''gram'': ergo, in either unit, the specific heat capacity of water is approximately 1.
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