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Specific heat capacity

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Contents
  1. 1Definition
  2. 2Calculating absorbed heat
  3. 3Typical values
  4. 4Change with temperature
  5. 5Role in heating of structures and materials
  6. 6Flames and extinguishment
  7. 7Limits and common misconceptions
  8. 8See also
  9. 9Notes
  10. 10References

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.[1][2] 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.[1] The value is usually determined by experiment.[1]

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.[1] It also links the energy carried into a smoke layer to the temperature of that layer.[1] 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.[3]

The specific heat capacity of the combustion products limits the adiabatic flame temperature of a fuel.[4] Water, the most commonly used extinguishing agent, combines a high specific heat with a high latent heat of vaporisation.[5] 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.[1][6]

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.[1] The SFPE Handbook uses the same definition and notes that, for thermochemical problems, values per mole, in J/(mol·K), are often more convenient.[2] A difference of one kelvin equals a difference of one degree Celsius, so the unit can also be written as J/(kg·°C).[3]

The specific heat can be determined at constant volume or at constant pressure.[1] The two values are written as cv and cp.[7] For solids the difference is small in practice, but for gases it is substantial. For air and smoke, cp is about 40 % larger than cv, a ratio of about 1.4.[1] For an ideal gas, the difference between the two equals the gas constant.[8] Because a fire is usually an open system in which the gases can expand, fire calculations normally use cp, for instance to find the temperature of a smoke layer in a zone model.[1]

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.[2] Drysdale treats "heat capacity" as a synonym of specific heat.[2] He uses "thermal capacity" for the heat needed to warm a whole mixture of gases by one kelvin, in J/K.[4]

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.[1] If the mass, the specific heat capacity and the temperature rise are known, the energy absorbed by a material follows from a simple relation:[1]

E=m⋅cp⋅ΔT

Symbol Description Unit
E energy absorbed by the material J
m mass kg
cp specific heat capacity at constant pressure J/(kg·K)
ΔT 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.[1] Melting and evaporation take energy from the surroundings, while condensation and solidification release it.[9]

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.[1] 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).[10] The zone model CFAST uses a constant value of 1012 J/(kg·K) for the gas, regardless of its composition.[11]

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.[12] 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.[12] 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.[13]

Typical values

Introduction to Fire Safety Engineering lists the specific heat capacity of common materials at room temperature, 20 °C.[1] 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.[1] 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.[1] Air has 1005 J/(kg·K), and water has the highest value in the table at 4186 J/(kg·K).[1]

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.[14] 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.[14] 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.[4]

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.[6] 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.[15] A light foam can therefore heat up very quickly at its surface even though its specific heat per kilogram is high.[3]

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

Like density, specific heat depends on temperature, although much less strongly.[1] 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 %.[16] 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.[16]

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.[6] In a temperature range where an endothermic reaction takes place, the apparent specific heat shows a peak.[6] For concrete, the type of aggregate and the moisture content strongly affect the specific heat.[17] For type X gypsum board, the dehydration of the gypsum produces two peaks, around 100 °C and 650 °C.[18]

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.[3] Gypsum-board walls derive part of their fire resistance from the evaporation of chemically bound water.[3] Because conductivity and specific heat change with temperature, calculations with fixed properties are only approximations.[3]

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.[1] 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.[3] The thermal diffusivity, the conductivity divided by the product of density and specific heat, governs how fast heat penetrates into the material.[3]

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.[3]

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.[3] The concrete surface heats more slowly, but the temperature change penetrates deeper, about 0.054 m against 0.024 m for timber.[3] Thin steel parts, in contrast, warm almost uniformly through their thickness.[3]

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.[19]

Flames and extinguishment

The heat released by combustion is first absorbed by the reaction products, unreacted fuel or oxygen and any diluent gases.[4] 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.[4] 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.[4]

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.[5] 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.[20] The heating of the liquid thus accounts for only about 12 % of the heat that water can absorb.

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.[21] 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.[21]

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.[1][15] Its surface heats quickly in a fire.[3] 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.[22] 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.[22] For gases, using cv instead of cp in an open fire compartment would underestimate the energy needed to heat the smoke by about 30 %.[1]

See also

Notes

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 Van Rossum (2027), §3.4.
  2. ↑ 2.0 2.1 2.2 2.3 Drysdale (2002), p. 1-91.
  3. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 Van Rossum (2027), §5.2.
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 Drysdale (2002), p. 1-96.
  5. ↑ 5.0 5.1 Fleming (2002), p. 4-72.
  6. ↑ 6.0 6.1 6.2 6.3 Kodur and Harmathy (2002), p. 1-161.
  7. ↑ Kandola (2002), p. 1-2.
  8. ↑ Drysdale (2002), p. 1-92.
  9. ↑ Van Rossum (2027), §3.5.
  10. ↑ Van Rossum (2027), §9.3 (How a zone model works).
  11. ↑ Peacock et al. (2026), p. 7.
  12. ↑ 12.0 12.1 Van Rossum (2027), §5.3.
  13. ↑ Milke (2002b), p. 4-303.
  14. ↑ 14.0 14.1 White (2002), p. 4-270.
  15. ↑ 15.0 15.1 Van Rossum (2027), §5.5.
  16. ↑ 16.0 16.1 Banovic et al. (2005), p. 104.
  17. ↑ Kodur and Harmathy (2002), p. 1-170.
  18. ↑ Kodur and Harmathy (2002), p. 1-178.
  19. ↑ Milke (2002a), p. 4-222.
  20. ↑ Tewarson (2002), p. 3-100.
  21. ↑ 21.0 21.1 DiNenno (2002), p. 4-174.
  22. ↑ 22.0 22.1 Kodur and Harmathy (2002), p. 1-162.

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.
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