Specific heat capacity - Revision history

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2026-11-02T17:12:44Z

Add Intermediate SVG figures with Fire Safety Academy watermark at planned locations; preserve article text

← Older revision		Revision as of 18:12, 2 November 2026
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	For heat flow through a material, the heat capacity per unit volume is often more relevant than the value per kilogram. This product of density and specific heat is called the volume specific heat.<ref name="KH-1-161" /> With the densities in the same book, steel stores about 3.6 MJ per cubic metre per kelvin and concrete about 2.0 MJ. Polyurethane foam stores only about 0.03 MJ, because of its very low density.<ref name="VR-5.5">Van Rossum (2027), §5.5.</ref> A light foam can therefore heat up very quickly at its surface even though its specific heat per kilogram is high.<ref name="VR-5.2" />		For heat flow through a material, the heat capacity per unit volume is often more relevant than the value per kilogram. This product of density and specific heat is called the volume specific heat.<ref name="KH-1-161" /> With the densities in the same book, steel stores about 3.6 MJ per cubic metre per kelvin and concrete about 2.0 MJ. Polyurethane foam stores only about 0.03 MJ, because of its very low density.<ref name="VR-5.5">Van Rossum (2027), §5.5.</ref> A light foam can therefore heat up very quickly at its surface even though its specific heat per kilogram is high.<ref name="VR-5.2" />

			[[File:fse-specific-heat-capacity-v1.svg\|thumb\|upright=1.5\|alt=Two bar charts side by side for steel, concrete, gypsum plaster, spruce, PUR foam and water: per kilogram foam is high, per cubic metre foam is almost zero.\|Specific heat capacity per kilogram (left) and heat capacity per cubic metre (right) of common materials at 20 °C. Based on Van Rossum (2027), §3.4 and §5.5.]]

	== Change with temperature ==		== Change with temperature ==
	Like density, specific heat depends on temperature, although much less strongly.<ref name="VR-3.4" /> For structural steel, the NIST investigation of the World Trade Center fitted a polynomial to measured data for iron between 0 °C and 650 °C, with an uncertainty of 2 %.<ref name="BA-104">Banovic et al. (2005), p. 104.</ref> This fit gives about 430 J/(kg·K) at 20 °C, about 600 J/(kg·K) at 400 °C and about 730 J/(kg·K) at 600 °C. At the phase transformation of carbon steel, above about 720 °C, the heat capacity becomes effectively infinite. All added energy then goes into changing the crystal structure rather than raising the temperature.<ref name="BA-104" />		Like density, specific heat depends on temperature, although much less strongly.<ref name="VR-3.4" /> For structural steel, the NIST investigation of the World Trade Center fitted a polynomial to measured data for iron between 0 °C and 650 °C, with an uncertainty of 2 %.<ref name="BA-104">Banovic et al. (2005), p. 104.</ref> This fit gives about 430 J/(kg·K) at 20 °C, about 600 J/(kg·K) at 400 °C and about 730 J/(kg·K) at 600 °C. At the phase transformation of carbon steel, above about 720 °C, the heat capacity becomes effectively infinite. All added energy then goes into changing the crystal structure rather than raising the temperature.<ref name="BA-104" />

			[[File:fse-specific-heat-capacity-v2.svg\|thumb\|upright=1.5\|alt=Rising curve of steel specific heat from about 430 J/(kg·K) at 20 °C to about 730 at 600 °C and 790 at 650 °C.\|Specific heat capacity of structural steel (iron) between 20 °C and 650 °C, from the NIST fit to measured data. Based on Banovic et al. (2005), p. 104.]]

	Many building materials undergo physical or chemical changes when heated. Kodur and Harmathy therefore use an apparent specific heat that includes both the sensible heat and the latent heat of these changes.<ref name="KH-1-161" /> In a temperature range where an endothermic reaction takes place, the apparent specific heat shows a peak.<ref name="KH-1-161" /> For concrete, the type of aggregate and the moisture content strongly affect the specific heat.<ref name="KH-1-170">Kodur and Harmathy (2002), p. 1-170.</ref> For type X gypsum board, the dehydration of the gypsum produces two peaks, around 100 °C and 650 °C.<ref name="KH-1-178">Kodur and Harmathy (2002), p. 1-178.</ref>		Many building materials undergo physical or chemical changes when heated. Kodur and Harmathy therefore use an apparent specific heat that includes both the sensible heat and the latent heat of these changes.<ref name="KH-1-161" /> In a temperature range where an endothermic reaction takes place, the apparent specific heat shows a peak.<ref name="KH-1-161" /> For concrete, the type of aggregate and the moisture content strongly affect the specific heat.<ref name="KH-1-170">Kodur and Harmathy (2002), p. 1-170.</ref> For type X gypsum board, the dehydration of the gypsum produces two peaks, around 100 °C and 650 °C.<ref name="KH-1-178">Kodur and Harmathy (2002), p. 1-178.</ref>
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	The same principle underlies several [[extinguishing mechanisms]]. Water is the most common extinguishing agent, mainly because it is widely available and inexpensive. It also has a high specific heat and a high latent heat of vaporisation.<ref name="FL-4-72" /> Tewarson calculates the heat needed to evaporate water starting at 298 K. Heating the liquid to 373 K takes 0.32 kJ/g, and evaporation takes another 2.26 kJ/g, so the total is about 2.58 kJ/g.<ref name="TE-3-100">Tewarson (2002), p. 3-100.</ref> The heating of the liquid thus accounts for only about 12 % of the heat that water can absorb.		The same principle underlies several [[extinguishing mechanisms]]. Water is the most common extinguishing agent, mainly because it is widely available and inexpensive. It also has a high specific heat and a high latent heat of vaporisation.<ref name="FL-4-72" /> Tewarson calculates the heat needed to evaporate water starting at 298 K. Heating the liquid to 373 K takes 0.32 kJ/g, and evaporation takes another 2.26 kJ/g, so the total is about 2.58 kJ/g.<ref name="TE-3-100">Tewarson (2002), p. 3-100.</ref> The heating of the liquid thus accounts for only about 12 % of the heat that water can absorb.

			[[File:fse-specific-heat-capacity-v3.svg\|thumb\|upright=1.5\|alt=Stacked bar of 2.58 kJ per gram for water: 0.32 for heating from 25 to 100 °C and 2.26 for evaporation.\|Heat absorbed by one gram of water heated from 25 °C and evaporated at 100 °C: sensible heat 0.32 kJ and latent heat 2.26 kJ. Based on Tewarson (2002), p. 3-100.]]

	Gaseous agents also act through heat capacity. Halon replacement agents remove heat from the flame zone through their heat of vaporisation, their heat capacity and the energy absorbed in their decomposition.<ref name="DI-4-174">DiNenno (2002), p. 4-174.</ref> Inert gases reduce the oxygen concentration and raise the heat capacity of the atmosphere around the flame. The concentration of inert gas needed to extinguish a fire therefore depends on its heat capacity, which is why the minimum extinguishing concentration differs between inert gases.<ref name="DI-4-174" />		Gaseous agents also act through heat capacity. Halon replacement agents remove heat from the flame zone through their heat of vaporisation, their heat capacity and the energy absorbed in their decomposition.<ref name="DI-4-174">DiNenno (2002), p. 4-174.</ref> Inert gases reduce the oxygen concentration and raise the heat capacity of the atmosphere around the flame. The concentration of inert gas needed to extinguish a fire therefore depends on its heat capacity, which is why the minimum extinguishing concentration differs between inert gases.<ref name="DI-4-174" />

Daan: New FSE wiki article: Specific heat capacity (written by Claude Opus 5.5)

2026-11-01T22:44:50Z

New FSE wiki article: Specific heat capacity (written by Claude Opus 5.5)

New page

'''Specific heat capacity''', often shortened to specific heat, is the amount of heat needed to raise the temperature of one unit of mass of a substance by one degree.<ref name="VR-3.4">Van Rossum (2027), §3.4.</ref><ref name="DR-1-91">Drysdale (2002), p. 1-91.</ref> Its SI unit is the joule per kilogram per kelvin, J/(kg·K). One kilogram of steel needs about 460 J to warm by one kelvin, one kilogram of air about 1005 J and one kilogram of water about 4186 J.<ref name="VR-3.4" /> The value is usually determined by experiment.<ref name="VR-3.4" />

In fire safety engineering, specific heat capacity determines how much energy a material or a gas absorbs as it warms up. It is used to calculate how walls, floors and load-bearing structures heat up during a fire.<ref name="VR-3.4" /> It also links the energy carried into a smoke layer to the temperature of that layer.<ref name="VR-3.4" /> Together with density and [[thermal conductivity]], it sets the [[thermal inertia]] and the [[thermal diffusivity]] of a material. These two properties describe how fast a surface heats up and how deep heat penetrates.<ref name="VR-5.2">Van Rossum (2027), §5.2.</ref>

The specific heat capacity of the combustion products limits the [[adiabatic flame temperature]] of a fuel.<ref name="DR-1-96">Drysdale (2002), p. 1-96.</ref> Water, the most commonly used extinguishing agent, combines a high specific heat with a high latent heat of vaporisation.<ref name="FL-4-72">Fleming (2002), p. 4-72.</ref> The solid materials in the book's table range from 380 to 2850 J/(kg·K), but the value can change strongly with temperature where moisture evaporates or the material decomposes.<ref name="VR-3.4" /><ref name="KH-1-161">Kodur and Harmathy (2002), p. 1-161.</ref>

== Definition ==
''Introduction to Fire Safety Engineering'' defines specific heat as a measure of the heat needed to raise the temperature of a unit of mass by a given amount. In practice it is the energy in joules needed to warm one kilogram of a substance by one degree.<ref name="VR-3.4" /> The SFPE Handbook uses the same definition and notes that, for thermochemical problems, values per mole, in J/(mol·K), are often more convenient.<ref name="DR-1-91" /> A difference of one kelvin equals a difference of one degree Celsius, so the unit can also be written as J/(kg·°C).<ref name="VR-5.2" />

The specific heat can be determined at constant volume or at constant pressure.<ref name="VR-3.4" /> The two values are written as <math>c_v</math> and <math>c_p</math>.<ref name="KA-1-2">Kandola (2002), p. 1-2.</ref> For solids the difference is small in practice, but for gases it is substantial. For air and smoke, <math>c_p</math> is about 40 % larger than <math>c_v</math>, a ratio of about 1.4.<ref name="VR-3.4" /> For an ideal gas, the difference between the two equals the gas constant.<ref name="DR-1-92">Drysdale (2002), p. 1-92.</ref> Because a fire is usually an open system in which the gases can expand, fire calculations normally use <math>c_p</math>, for instance to find the temperature of a smoke layer in a zone model.<ref name="VR-3.4" />

The concept is mostly associated with solids and liquids, but it applies equally to gases. Specific heats of gases are needed, for example, to calculate flame temperatures.<ref name="DR-1-91" /> Drysdale treats "heat capacity" as a synonym of specific heat.<ref name="DR-1-91" /> He uses "thermal capacity" for the heat needed to warm a whole mixture of gases by one kelvin, in J/K.<ref name="DR-1-96" />

== Calculating absorbed heat ==
The definition leads directly to the most common calculation with specific heat capacity. ''Introduction to Fire Safety Engineering'' uses it both for building elements and for smoke layers.<ref name="VR-3.4" /> If the mass, the specific heat capacity and the temperature rise are known, the energy absorbed by a material follows from a simple relation:<ref name="VR-3.4" />

<math display="block">E = m \cdot c_p \cdot \Delta T</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>E</math> || energy absorbed by the material || J
|-
| <math>m</math> || mass || kg
|-
| <math>c_p</math> || specific heat capacity at constant pressure || J/(kg·K)
|-
| <math>\Delta T</math> || temperature rise || K or °C
|}

The relation is valid when the specific heat capacity is roughly constant over the temperature range considered. At large temperature differences the specific heat can change. A phase change, such as the evaporation of water, needs additional energy that the relation does not include.<ref name="VR-3.4" /> Melting and evaporation take energy from the surroundings, while condensation and solidification release it.<ref name="VR-3.5">Van Rossum (2027), §3.5.</ref>

In the worked example of ''Introduction to Fire Safety Engineering'', 100 kg of steel with a specific heat of 460 J/(kg·K) is heated by 100 K. The steel absorbs 100 × 460 × 100 J, which is 4.6 MJ.<ref name="VR-3.4" /> The same relation, read the other way, gives the temperature rise caused by a known amount of energy. With 100 kJ, one kilogram of steel would warm by about 217 K, but one kilogram of water by only about 24 K.

The book uses this relation to find the temperature of a smoke layer. In a zone model, the new layer temperature equals the ambient temperature plus the energy in the layer divided by the product of the layer mass and the specific heat. For air the specific heat is taken as 1005 J/(kg·K).<ref name="VR-9.3a">Van Rossum (2027), §9.3 (How a zone model works).</ref> The zone model CFAST uses a constant value of 1012 J/(kg·K) for the gas, regardless of its composition.<ref name="CF-7">Peacock et al. (2026), p. 7.</ref>

For a flow of gas, the energy is carried per second instead of stored. The heat carried by a smoke flow equals the density times the specific heat times the volume flow times the temperature rise above the incoming air.<ref name="VR-5.3">Van Rossum (2027), §5.3.</ref> In the book's example, a smoke and heat exhaust system removes 100 m³/s of smoke at 463 °C, with a density of 0.48 kg/m³. With an outdoor temperature of 20 °C, it carries away about 21 MW.<ref name="VR-5.3" /> Milke applies the same balance to an atrium. A 5000 kW fire with a convective fraction of 0.7 heats a smoke flow of 410 kg/s with a specific heat of 1.0 kJ/(kg·K) by only 8.5 °C.<ref name="MI-4-303">Milke (2002b), p. 4-303.</ref>

== Typical values ==
''Introduction to Fire Safety Engineering'' lists the specific heat capacity of common materials at room temperature, 20 °C.<ref name="VR-3.4" /> Metals have low values: 380 J/(kg·K) for copper and 460 J/(kg·K) for steel. Mineral building materials lie in the middle, at 840 J/(kg·K) for masonry, float glass and gypsum plaster and 880 J/(kg·K) for concrete.<ref name="VR-3.4" /> Organic materials have higher values. The table gives 1420 J/(kg·K) for PMMA, 1400 J/(kg·K) for polyurethane foam, 2380 J/(kg·K) for oak and 2850 J/(kg·K) for spruce.<ref name="VR-3.4" /> Air has 1005 J/(kg·K), and water has the highest value in the table at 4186 J/(kg·K).<ref name="VR-3.4" />

Other sources give somewhat different values for wood. White gives a relation for dry wood in which the heat capacity rises linearly with the absolute temperature.<ref name="WH-4-270">White (2002), p. 4-270.</ref> It yields about 1.24 kJ/(kg·K) at 20 °C and about 1.55 kJ/(kg·K) at 100 °C. For moist wood, the heat capacity of the water and a correction for the bond between wood and water are added.<ref name="WH-4-270" /> For combustion gases, Drysdale tabulates molar heat capacities at 1000 K of 54.3 J/(mol·K) for carbon dioxide, 41.2 J/(mol·K) for water vapour and 32.7 J/(mol·K) for nitrogen.<ref name="DR-1-96" />

For heat flow through a material, the heat capacity per unit volume is often more relevant than the value per kilogram. This product of density and specific heat is called the volume specific heat.<ref name="KH-1-161" /> With the densities in the same book, steel stores about 3.6 MJ per cubic metre per kelvin and concrete about 2.0 MJ. Polyurethane foam stores only about 0.03 MJ, because of its very low density.<ref name="VR-5.5">Van Rossum (2027), §5.5.</ref> A light foam can therefore heat up very quickly at its surface even though its specific heat per kilogram is high.<ref name="VR-5.2" />

== Change with temperature ==
Like density, specific heat depends on temperature, although much less strongly.<ref name="VR-3.4" /> For structural steel, the NIST investigation of the World Trade Center fitted a polynomial to measured data for iron between 0 °C and 650 °C, with an uncertainty of 2 %.<ref name="BA-104">Banovic et al. (2005), p. 104.</ref> This fit gives about 430 J/(kg·K) at 20 °C, about 600 J/(kg·K) at 400 °C and about 730 J/(kg·K) at 600 °C. At the phase transformation of carbon steel, above about 720 °C, the heat capacity becomes effectively infinite. All added energy then goes into changing the crystal structure rather than raising the temperature.<ref name="BA-104" />

Many building materials undergo physical or chemical changes when heated. Kodur and Harmathy therefore use an apparent specific heat that includes both the sensible heat and the latent heat of these changes.<ref name="KH-1-161" /> In a temperature range where an endothermic reaction takes place, the apparent specific heat shows a peak.<ref name="KH-1-161" /> For concrete, the type of aggregate and the moisture content strongly affect the specific heat.<ref name="KH-1-170">Kodur and Harmathy (2002), p. 1-170.</ref> For type X gypsum board, the dehydration of the gypsum produces two peaks, around 100 °C and 650 °C.<ref name="KH-1-178">Kodur and Harmathy (2002), p. 1-178.</ref>

''Introduction to Fire Safety Engineering'' describes the same effect for moisture. Once the temperature inside a material passes 100 °C, all the water present must evaporate first, which takes much energy.<ref name="VR-5.2" /> Gypsum-board walls derive part of their fire resistance from the evaporation of chemically bound water.<ref name="VR-5.2" /> Because conductivity and specific heat change with temperature, calculations with fixed properties are only approximations.<ref name="VR-5.2" />

== Role in heating of structures and materials ==
Specific heat capacity alone does not determine how fast a building element heats up. The heat supply, the dimensions, the density and the thermal conductivity all play a part.<ref name="VR-3.4" /> Two combined properties are used. The thermal inertia, the square root of the product of conductivity, density and specific heat, governs how quickly the surface warms.<ref name="VR-5.2" /> The thermal diffusivity, the conductivity divided by the product of density and specific heat, governs how fast heat penetrates into the material.<ref name="VR-5.2" />

A material with a low thermal inertia, such as a light insulation material, can become hot at its surface very quickly. If it is combustible, this can contribute to rapid ignition. A material with a high thermal inertia, such as concrete, absorbs much heat and conducts it inwards, so its surface temperature usually rises more slowly.<ref name="VR-5.2" />

''Introduction to Fire Safety Engineering'' compares a thick timber wall with a thick concrete wall exposed to the same fire for one hour. The concrete has a lower specific heat than the timber but a much higher density and conductivity. Its thermal inertia is therefore about 1876 J/(m²·K·√s) against about 322 for timber.<ref name="VR-5.2" /> The concrete surface heats more slowly, but the temperature change penetrates deeper, about 0.054 m against 0.024 m for timber.<ref name="VR-5.2" /> Thin steel parts, in contrast, warm almost uniformly through their thickness.<ref name="VR-5.2" />

For unprotected steel members, the specific heat of steel appears directly in the hand calculation of the steel temperature. The temperature rise in each time step is proportional to the heat transferred to the section. It is inversely proportional to the steel specific heat and the ratio of steel weight to heated perimeter.<ref name="MI-4-222">Milke (2002a), p. 4-222.</ref>

== Flames and extinguishment ==
The heat released by combustion is first absorbed by the reaction products, unreacted fuel or oxygen and any diluent gases.<ref name="DR-1-96" /> Drysdale shows how this sets the adiabatic flame temperature. Burning one mole of propane in a stoichiometric mixture with air releases 2044 kJ. The products have a total heat capacity of 942.5 J/K, so the maximum temperature rise is about 2169 K, giving an adiabatic flame temperature of 2467 K.<ref name="DR-1-96" /> Nitrogen accounts for about two thirds of this heat capacity. Without it, in pure oxygen, the calculated rise would be 6238 K, although dissociation limits the real flame temperature to about 3500 K.<ref name="DR-1-96" />

The same principle underlies several [[extinguishing mechanisms]]. Water is the most common extinguishing agent, mainly because it is widely available and inexpensive. It also has a high specific heat and a high latent heat of vaporisation.<ref name="FL-4-72" /> Tewarson calculates the heat needed to evaporate water starting at 298 K. Heating the liquid to 373 K takes 0.32 kJ/g, and evaporation takes another 2.26 kJ/g, so the total is about 2.58 kJ/g.<ref name="TE-3-100">Tewarson (2002), p. 3-100.</ref> The heating of the liquid thus accounts for only about 12 % of the heat that water can absorb.

Gaseous agents also act through heat capacity. Halon replacement agents remove heat from the flame zone through their heat of vaporisation, their heat capacity and the energy absorbed in their decomposition.<ref name="DI-4-174">DiNenno (2002), p. 4-174.</ref> Inert gases reduce the oxygen concentration and raise the heat capacity of the atmosphere around the flame. The concentration of inert gas needed to extinguish a fire therefore depends on its heat capacity, which is why the minimum extinguishing concentration differs between inert gases.<ref name="DI-4-174" />

== Limits and common misconceptions ==
A common misconception is that a high specific heat per kilogram always means slow heating. Polyurethane foam has a specific heat of 1400 J/(kg·K), higher than concrete, but its density is so low that it stores very little heat per unit volume.<ref name="VR-3.4" /><ref name="VR-5.5" /> Its surface heats quickly in a fire.<ref name="VR-5.2" /> Heat storage, thermal inertia and heat penetration always depend on the combination of specific heat with density and conductivity.

Values for building materials in fire conditions are also uncertain. Measurements of apparent specific heat by differential scanning calorimetry may have an error as large as 20 % in the sensible heat contribution.<ref name="KH-1-162">Kodur and Harmathy (2002), p. 1-162.</ref> The heating rate in such tests was usually 5 °C per minute, and at higher heating rates the peaks shift to higher temperatures and become sharper.<ref name="KH-1-162" /> For gases, using <math>c_v</math> instead of <math>c_p</math> in an open fire compartment would underestimate the energy needed to heat the smoke by about 30 %.<ref name="VR-3.4" />

== See also ==
* [[Conduction]]
* [[Ideal gas law]]
* [[Heat transfer]]

== Notes ==
<references />

== References ==
* Banovic, S. W., McCowan, C. N., & Luecke, W. E. (2005). ''Physical properties of structural steels'' (NIST NCSTAR 1-3E). National Institute of Standards and Technology.
* DiNenno, P. J. (2002). Halon replacement clean agent total flooding systems. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-173–4-200). National Fire Protection Association; Society of Fire Protection Engineers.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association; Society of Fire Protection Engineers.
* Fleming, R. P. (2002). Automatic sprinkler system calculations. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-72–4-87). National Fire Protection Association; Society of Fire Protection Engineers.
* Kandola, B. S. (2002). Introduction to mechanics of fluids. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-1–1-26). National Fire Protection Association; Society of Fire Protection Engineers.
* Kodur, V. K. R., & Harmathy, T. Z. (2002). Properties of building materials. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-155–1-181). National Fire Protection Association; Society of Fire Protection Engineers.
* Milke, J. A. (2002a). Analytical methods for determining fire resistance of steel members. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-209–4-238). National Fire Protection Association; Society of Fire Protection Engineers.
* Milke, J. A. (2002b). Smoke management in covered malls and atria. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-292–4-310). National Fire Protection Association; Society of Fire Protection Engineers.
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST – Consolidated Fire and Smoke Transport: Vol. 1. Technical reference guide'' (Version 7, NIST Technical Note 1889v1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1889v1
* Tewarson, A. (2002). Generation of heat and chemical compounds in fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-82–3-161). National Fire Protection Association; Society of Fire Protection Engineers.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.
* White, R. H. (2002). Analytical methods for determining fire resistance of timber members. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-257–4-273). National Fire Protection Association; Society of Fire Protection Engineers.

[[Category:Physics & Heat Transfer]]