{{Short description|Temperature reached by a flame under ideal conditions}} thumb|upright|Ethanol burning with its spectrum depicted In the study of combustion, the '''adiabatic flame temperature''' is the temperature reached by a flame under ideal conditions. It is an upper bound of the temperature that is reached in actual processes.
There are two types of adiabatic flame temperature: ''constant volume'' and ''constant pressure'', depending on how the process is completed. The constant volume adiabatic flame temperature is the temperature that results from a complete combustion process that occurs without any work, heat transfer or changes in kinetic or potential energy. Its temperature is higher than in the ''constant pressure'' process because no energy is utilized to change the volume of the system (i.e., generate work).
==Common flames== [[Image:Propan Lewis.svg|thumb|Propane]] [[File:Alkane IUPAC1.svg|thumb|Iso-Octane (2,2,4-Trimethylpentane)]] In daily life, the vast majority of flames one encounters are those caused by rapid oxidation of hydrocarbons in materials such as wood, wax, fat, plastics, propane, and gasoline. The constant-pressure adiabatic flame temperature of such substances in air is in a relatively narrow range around {{cvt|1950|C|K F|abbr=on}}.{{cn|date=June 2024}} This is mostly because the heat of combustion of these compounds is roughly proportional to the amount of oxygen consumed, which proportionally increases the amount of air that has to be heated, so the effect of a larger heat of combustion on the flame temperature is offset. Incomplete reaction at higher temperature further curtails the effect of a larger heat of combustion.{{cn|date=June 2024}}
Because most combustion processes that happen naturally occur in the open air, there is nothing that confines the gas to a particular volume like the cylinder in an engine. As a result, these substances will burn at a constant pressure, which allows the gas to expand during the process.
== Common flame temperatures == Assuming initial atmospheric conditions (1{{nbsp}}bar and 20 °C), the following table<ref name=":0">See under "Tables" in the external references below.</ref> lists the flame temperature for various fuels under constant pressure conditions. The temperatures mentioned here are for a stoichiometric fuel-oxidizer mixture (i.e. equivalence ratio ''φ'' = 1).
These are theoretical, not actual, flame temperatures produced by a flame that loses no heat. The closest will be the hottest part of a flame, where the combustion reaction is most efficient. This also assumes complete combustion (e.g. perfectly balanced, non-smoky, usually bluish flame). Several values in the table significantly disagree with the literature<ref name=":0" /> or predictions by online calculators.
{|class="wikitable sortable" style="text-align:center" |+ Adiabatic flame temperature (constant pressure) of common fuels <!-- The temperatures reported for Methane and Propane in air, at 1950 °C, around 1950 °C, and 1980 °C, are consistent with an entry in http://www.engineeringtoolbox.com/adiabatic-flame-temperature-d_996.html, while that same reference gives a value for hydrogen that's 99 degrees lower. The Engineering Toolbox reference reports results for CONSTANT PRESSURE, NOT CONSTANT VOLUME. Editorial comments above on this page indicate constant pressure combustion temperatures for all hydrocarbons at around 1950 °C. Constant volume results would be hundreds of degrees higher, much larger than errors in reported experimental data. Thus, it seems clear that the table below shows CONSTANT PRESSURE results. Propane–oxygen value should be higher since almost all other reference sources suggest a value of around 2800 Celsius --> |- ! rowspan=2 | Fuel ! rowspan=2 | Oxidizer<br/>1 bar<br/>20 °C ! colspan=2 | <math>T_\text{ad}</math> |- ! (°C) ! (°F) |- | rowspan=2 | Acetylene ({{chem2|C2H2}}) | Air || 2,500 || 4,532 |- | Oxygen || 3,480 || 6,296 |- | Butane ({{chem2|C4H10}}) || Air || 2,231|| 4,074<ref name="als">{{cite news |last1=Libal |first1=Angela |title=What Temperatures Do Lighters Burn At? |url=https://sciencing.com/temperatures-do-lighters-burn-8475271.html |agency=Sciencing |publisher=Leaf Group Ltd. / Leaf Group Media |date=27 April 2018}}</ref> |- | Cyanogen ({{chem2|C2N2}}) || Oxygen || 4,525 || 8,177 |- | Dicyanoacetylene ({{chem2|C4N2}}) || Oxygen || 4,990 || 9,010 |- | Ethane ({{chem2|C2H6}}) || Air || 1,955 || 3,551 |- | Ethanol ({{chem2|C2H5OH}}) || Air || 2,082 || 3,779<ref name="che.msstate.edu">[http://www.che.msstate.edu/pdfs/fuel_cell_curriculum/me_mods/ME_Combustion_And_Air_Pollution_Module_1.doc Flame Temperature Analysis and NOx Emissions for Different Fuels]</ref> |- | Gasoline || Air || 2,138 || 3,880<ref name="che.msstate.edu"/> |- | Hydrogen ({{chem2|H2}}) || Air || 2,254 || 4,089<ref name="che.msstate.edu"/> |- | Magnesium (Mg) || Air || 1,982 || 3,600<ref>{{Cite web |url=https://www.reference.com/science/hot-magnesium-burn-b65985ed030138e7 |title=How hot does magnesium burn? {{pipe}} Reference.com |access-date=2017-09-17 |archive-url=https://web.archive.org/web/20170917172054/https://www.reference.com/science/hot-magnesium-burn-b65985ed030138e7 |archive-date=2017-09-17 |url-status=dead }}</ref> |- | Methane ({{chem2|CH4}}) || Air || 1,963 || 3,565<ref name="Physics p. 15-51">CRC Handbook of Chemistry and Physics, 96th Edition, p. 15-51</ref> |- | Methanol ({{chem2|CH3OH}}) || Air || 1,949 || 3,540<ref name="Physics p. 15-51"/> |- | Natural gas || Air || 1,960 || 3,562<ref>{{Cite web |url=http://www.uniongas.com/aboutus/aboutng/composition.asp |title=North American Combustion Handbook, Volume 1, 3rd edition, North American Mfg Co., 1986. |access-date=2009-12-09 |archive-date=2011-07-16 |archive-url=https://web.archive.org/web/20110716024101/http://www.uniongas.com/aboutus/aboutng/composition.asp |url-status=dead }}</ref> |- | Pentane ({{chem2|C5H12}}) || Air || 1,977 || 3,591<ref name="Physics p. 15-51"/> |- | Propane ({{chem2|C3H8}}) || Air || 1,980 || 3,596<ref>{{Cite web |url=http://www.rpgroup.caltech.edu/courses/me96/flame2003.pdf |title=Archived copy |access-date=2013-05-19 |archive-url=https://web.archive.org/web/20150924092312/http://www.rpgroup.caltech.edu/courses/me96/flame2003.pdf |archive-date=2015-09-24 |url-status=dead }}</ref> |- | rowspan=2 | Methylacetylene <br/>({{chem2|CH3CCH}}) | Air || 2,010 || 3,650 |- | Oxygen || 2,927 || 5,301 |- | Toluene ({{chem2|C7H8}}) || Air || 2,071 || 3,760<ref name="Physics p. 15-51"/> |- | Wood || Air || 1,980 || 3,596 |- | Kerosene || Air || 2,093<ref name="Chu">[http://myweb.ncku.edu.tw/~chuhsin/ppt/combustion%20principles%20and%20control/04-Flame%20Temperature.ppt Power Point Presentation: Flame Temperature] {{Webarchive|url=https://web.archive.org/web/20110717210941/http://myweb.ncku.edu.tw/~chuhsin/ppt/combustion%20principles%20and%20control/04-Flame%20Temperature.ppt |date=2011-07-17 }}, ''Hsin Chu, Department of Environmental Engineering, National Cheng Kung University, Taiwan''</ref> || 3,801 |- | Light fuel oil || Air || 2,104<ref name="Chu"/> || 3,820 |- | Medium fuel oil || Air || 2,101<ref name="Chu"/> || 3,815 |- | Heavy fuel oil || Air || 2,102<ref name="Chu"/> || 3,817 |- | Bituminous coal || Air || 2,172<ref name="Chu"/> || 3,943 |- | rowspan=2 | Anthracite | Air || 2,180<ref name="Chu"/> || 3,957 |- | Oxygen || data-sort-value="3,500" | ≈3,500<ref>[https://web.archive.org/web/20111112154713/http://web.mit.edu/mitei/docs/reports/hong-analysis.pdf Analysis of oxy-fuel combustion power cycle utilizing a pressurized coal combustor] by Jongsup Hong ''et al.'', MIT, which cites {{cite book |title=IPCC Special Report on Carbon Dioxide Capture and Storage |date=2005 |publisher=Intergovernmental Panel on Climate Change |page=122 |url=https://www.ipcc.ch/site/assets/uploads/2018/03/srccs_wholereport-1.pdf }}. But the IPCC report actually gives a much less precise statement: "The direct combustion of fuel and oxygen has been practised for many years in the metallurgical and glass industries where burners operate at near stoichiometric conditions with flame temperatures of up to 3500 °C." The temperature may depend on pressure, because at lower pressure there will be more dissociation of the combustion products, implying a lower adiabatic temperature.</ref> | data-sort-value="6332" | ≈6,332 |- | Aluminium || Oxygen || 3,732 || 6,750<ref name="Physics p. 15-51"/> |- | Lithium || Oxygen || 2,438 || 4,420<ref name="Physics p. 15-51"/> |- | Phosphorus (white) || Oxygen || 2,969 || 5,376<ref name="Physics p. 15-51"/> |- | Zirconium || Oxygen || 4,005 || 7,241<ref name="Physics p. 15-51"/> |}
==Thermodynamics== thumb|right|300px|First law of thermodynamics for a closed reacting system From the first law of thermodynamics for a closed reacting system we have :<math>{}_RQ_P - {}_RW_P = U_P - U_R </math> where, <math>{}_RQ_P</math> and <math>{}_RW_P</math> are the heat and work transferred from the system to the surroundings during the process, respectively, and <math>U_R</math> and <math> U_P </math> are the internal energy of the reactants and products, respectively. In the constant volume adiabatic flame temperature case, the volume of the system is held constant and hence there is no work occurring: : <math> {}_RW_P = \int\limits_R^P {pdV} = 0</math> There is also no heat transfer because the process is defined to be adiabatic: <math> {}_RQ_P = 0 </math>. As a result, the internal energy of the products is equal to the internal energy of the reactants: <math> U_P = U_R </math>. Because this is a closed system, the mass of the products and reactants is constant and the first law can be written on a mass basis, : <math> U_P = U_R \Rightarrow m_P u_P = m_R u_R \Rightarrow u_P = u_R </math>.
[[Image:hrhp.jpg|thumb|right|200px|Enthalpy versus temperature diagram illustrating closed system calculation]]
In the case of the constant pressure adiabatic flame temperature, the pressure of the system is held constant, which results in the following equation for the work: : <math> {}_RW_P = \int\limits_R^P {pdV} = p\left( {V_P - V_R } \right) </math> Again there is no heat transfer occurring because the process is defined to be adiabatic: <math> {}_RQ_P = 0 </math>. From the first law, we find that, :<math> - p\left( {V_P - V_R } \right) = U_P - U_R \Rightarrow U_P + pV_P = U_R + pV_R </math> Recalling the definition of enthalpy we obtain <math> H_P = H_R </math>. Because this is a closed system, the mass of the products and reactants is the same and the first law can be written on a mass basis: : <math> H_P = H_R \Rightarrow m_P h_P = m_R h_R \Rightarrow h_P = h_R </math>.
We see that the adiabatic flame temperature of the constant pressure process is lower than that of the constant volume process. This is because some of the energy released during combustion goes, as work, into changing the volume of the control system.
[[File:Adiabatic flame temperatures and pressures as function of stoichiometry (chart).jpg|thumb|left|300px|Adiabatic flame temperatures and pressures as a function of ratio of air to iso-octane. A ratio of 1 corresponds to the stoichiometric ratio]] thumb|right|300px|Constant volume flame temperature of a number of fuels, with air
If we make the assumption that combustion goes to completion (i.e. forming only {{chem|C|O|2}} and {{chem|H|2|O}}), we can calculate the adiabatic flame temperature by hand either at stoichiometric conditions or lean of stoichiometry (excess air). This is because there are enough variables and molar equations to balance the left and right hand sides,
:<math>{\rm{C}}_\alpha {\rm{H}}_\beta {\rm{O}}_\gamma {\rm{N}}_\delta + \left( {a{\rm{O}}_{\rm{2}} + b{\rm{N}}_{\rm{2}} } \right) \to \nu _1 {\rm{CO}}_{\rm{2}} + \nu _2 {\rm{H}}_{\rm{2}} {\rm{O}} + \nu _3 {\rm{N}}_{\rm{2}} + \nu _4 {\rm{O}}_{\rm{2}} </math>
Rich of stoichiometry there are not enough variables because combustion cannot go to completion with at least {{chem|C|O}} and {{chem|H|2}} needed for the molar balance (these are the most common products of incomplete combustion),
:<math> {\rm{C}}_\alpha {\rm{H}}_\beta {\rm{O}}_\gamma {\rm{N}}_\delta + \left( {a{\rm{O}}_{\rm{2}} + b{\rm{N}}_{\rm{2}} } \right) \to \nu _1 {\rm{CO}}_{\rm{2}} + \nu _2 {\rm{H}}_{\rm{2}} {\rm{O}} + \nu _3 {\rm{N}}_{\rm{2}} + \nu _5 {\rm{CO}} + \nu _6 {\rm{H}}_{\rm{2}} </math>
However, if we include the water gas shift reaction, : <math> {\rm{CO}}_{\rm{2}} + H_2 \Leftrightarrow {\rm{CO}} + {\rm{H}}_{\rm{2}} {\rm{O}} </math> and use the equilibrium constant for this reaction, we will have enough variables to complete the calculation.
Different fuels with different levels of energy and molar constituents will have different adiabatic flame temperatures.
thumb|left|300px|Constant pressure flame temperature of a number of fuels, with air thumb|right|300px|Nitromethane versus isooctane flame temperature and pressure
We can see by the following figure why nitromethane (CH<sub>3</sub>NO<sub>2</sub>) is often used as a power boost for cars. Since each molecule of nitromethane contains an oxidant with relatively high-energy bonds between nitrogen and oxygen, it can burn much hotter than hydrocarbons or oxygen-containing methanol. This is analogous to adding pure oxygen, which also raises the adiabatic flame temperature. This in turn allows it to build up more pressure during a constant volume process. The higher the pressure, the more force upon the piston creating more work and more power in the engine. It stays relatively hot rich of stoichiometry because it contains its own oxidant. However, continual running of an engine on nitromethane will eventually melt the piston and/or cylinder because of this higher temperature.
thumb|right|300px|Effects of dissociation on adiabatic flame temperature
In real world applications, complete combustion does not typically occur. Chemistry dictates that dissociation and kinetics will change the composition of the products. There are a number of programs available that can calculate the adiabatic flame temperature taking into account dissociation through equilibrium constants (Stanjan, NASA CEA, AFTP). The following figure illustrates that the effects of dissociation tend to lower the adiabatic flame temperature. This result can be explained through Le Chatelier's principle.
==See also== *Flame speed
==References== <references/>
== External links ==
=== General information === * {{Cite web | last = Babrauskas | first = Vytenis | title = Temperatures in flames and fires | work = Fire Science and Technology Inc. | accessdate = 2008-01-27 | date = 2006-02-25 | url = http://www.doctorfire.com/flametmp.html | archiveurl = https://web.archive.org/web/20080112141325/http://www.doctorfire.com/flametmp.html | archivedate = 12 January 2008 | url-status = dead }} * [http://elearning.cerfacs.fr/combustion/n7masterCourses/adiabaticflametemperature/index.php Computation of adiabatic flame temperature] {{Webarchive|url=https://web.archive.org/web/20190227234417/http://elearning.cerfacs.fr/combustion/n7masterCourses/adiabaticflametemperature/index.php |date=2019-02-27 }} * [http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node111.html Adiabatic flame temperature]
=== Tables === * {{Cite web | title = Adiabatic Flame Temperature | work = The Engineering Toolbox | accessdate = 2008-01-27 | url = http://www.engineeringtoolbox.com/adiabatic-flame-temperature-d_996.html | archiveurl= https://web.archive.org/web/20080128053804/http://www.engineeringtoolbox.com/adiabatic-flame-temperature-d_996.html| archivedate= 28 January 2008 | url-status= live}} adiabatic flame temperature of hydrogen, methane, propane and octane with oxygen or air as oxidizers * {{Cite web | title = Flame Temperatures for some Common Gases | work = The Engineering Toolbox | accessdate = 2008-01-27 | url = http://www.engineeringtoolbox.com/flame-temperatures-gases-d_422.html | archiveurl= https://web.archive.org/web/20080107164751/http://www.engineeringtoolbox.com/flame-temperatures-gases-d_422.html| archivedate= 7 January 2008 | url-status= live}} * [http://hypertextbook.com/facts/1998/JamesDanyluk.shtml Temperature of a blue flame and common materials]
=== Calculators === * [http://elearning.cerfacs.fr/combustion/tools/adiabaticflametemperature/index.php Online adiabatic flame temperature calculator] {{Webarchive|url=https://web.archive.org/web/20121226004838/http://elearning.cerfacs.fr/combustion/tools/adiabaticflametemperature/index.php |date=2012-12-26 }} using Cantera * [https://web.archive.org/web/20101022164211/http://people.ku.edu/~depcik/aftp/aftp.htm Adiabatic flame temperature program] * [http://www.gaseq.co.uk Gaseq], program for performing chemical equilibrium calculations. * [https://web.archive.org/web/20150521041644/http://astronautics.usc.edu/utility/flame_temperature.php Flame Temperature Calculator] - Constant pressure bipropellant adiabatic combustion * [http://www.engr.colostate.edu/~allan/thermo/page12/adia_flame/Flamemain.html Adiabatic Flame Temperature calculator]
Category:Combustion Category:Temperature Category:Threshold temperatures