# What is Specific Heat Capacity?

Heat capacity is an extensive property defined as the amount of energy that must be subtracted from or added to a substance to lower or raise its temperature [1]. It is the ratio of the added heat to the temperature increment of the system. Heat capacity is denoted by the symbol C with the S.I. unit of J/K (Joule/Kelvin) [2].

When the heat capacity of a substance is divided by its mass, the resultant is the value of the substance’s specific heat capacity, an intensive property that is not dependent on sample size or mass [2].

• what specific heat capacity is
• how it is calculated and what affects it
• what applications it is involved in as a key factor

## Specific heat capacity

Specific heat capacity, or simply specific heat, refers to the heat capacity per unit mass of a pure substance. In other words, it is defined as the amount of heat needed to increase the temperature of 1kg of a material by 1K and is expressed in terms of J/kg·K or equivalently J/kg·°C. As an intensive property, specific heat capacity changes with the change in the material’s type or phase and can be considered for objects of arbitrary size.

As a life-sustaining factor on Earth, water has one of the largest specific heat capacity values among all materials, which is ten fold the specific heat of iron and five times that of glass. This means it requires 10 times the amount of heat to raise water’s temperature the same amount as compared to iron and 5 times the heat as compared to glass [3].

Listed in the table below are specific heat capacities of some compounds, elements and substances [4], [5]:

 Substances Specific Heat Capacity (J/kg·K) Specific Heat Capacity (kcal/kg·°C) Water (Liquid) 4184 1 Ethylene glycol (antifreeze) 2390 0.57 Water (ice) 2060 0.492 Wood 1800 0.43 Aluminium (Al) 897 0.214 Glass 800 0.191 Iron (Fe) 449 0.107 Copper (Cu) 385 0.09 Chromium (Cr) 442 - 487 0.105 - 0.116 Boron (B) 1285 - 1620 0.307 - 0.387 Nickel (Ni) 453 - 473 0.108 - 0.113 Cobalt (Co) 414 - 452 0.099 - 0.108 Sodium (Na) 1222 - 1234 0.292 - 0.295 Magnesium (Mg) 1060 0.253 Cast bronze 376 - 440 0.09 - 0.105 High strength structural steel 486 0.116

## Specific heat capacity at constant pressure or volume

Specific heat at constant volume is when the volume remains constant while heated through a short range of temperature, and is denoted by the symbol cv.

Specific heat at constant pressure, on the other hand, is when the pressure remains constant while heated through a short range of temperature, and is denoted by the symbol cp.

The specific heat at constant pressure (cp) is the most common expression of a substance’s heat capacity, and can be derived from the material’s enthalpy, which is the overall energy in a system, comprising both the internal energy and the energy required to displace its environment, as shown in the following equation [1]:

`c_p=(frac{delta H}{delta T})_p`

where H is the enthalpy, T is the temperature, and the subscript p indicates constant pressure. For a short span of temperature, specific heat may be taken as a constant value; yet, since the relationship between specific heat and temperature is non-linear, it may be better conveyed in a polynomial form for particular temperature ranges [1].

Specific heat has infinite values – a fact most notable in the case of gases, the pressure and volume of which change significantly with temperature. It is not possible to derive a specific heat of gas without supplying a constant amount of heat. Thus, it is essential to derive the specific heat of gases by subjecting them to constant pressure or constant volume [6].

## Applications of the specific heat capacity

The interrelation involving mass, energy, and specific heat capacity has abundant applicability. Liquid water’s specific heat capacity, which is the highest apart from liquid ammonia, allows large bodies of water to play a significant role in the Earth’s climate and weather. A lake, for instance, warms up more slowly than the air above it during the spring season, while in autumn the energy given off by the lake during cooling slows the drop in air temperature [4].

In commercial applications, cooking pots employ polished bottoms with materials such as copper or aluminium. Due to their low specific heat, the bottom can be warmed up quickly. The pot handles, however, are made with high-specific-heat material to resist heat increase and guarantee safety. Heat insulators invariably utilise materials with high specific heat [5].

The relevance of specific heat capacity can also be seen when fast-food restaurants notify customers of an apple pie filling being hotter than the paper wrapper or pie crust. Despite subjecting  the wrapper, pie crust, and filling to the same temperature, the amount of energy transferred to the fingers (or tongue) from the filling exceeds the amount of energy transferred from the wrapper and crust. This is because of the varying specific heat capacity of each substance [4].

## Sources

[1] S.K. McGuire, M.G. Jenkins, “Ceramic Testing”, In M. Kutz (ed.), Handbook of Materials Selection, NY: John Wiley & Sons, 2002.

[2] P.F. Hansen, “Chapter 2: Thermodynamic Concepts”, In O.M. Jensen (ed.), The Science of Construction Materials, Berlin: Springer Science & Business Media, 2009.

[3] “Specific Heat”, n.d. [Online]. Available: https://courses.lumenlearning.com/boundless-physics/chapter/specific-heat/

[4] J. Kotz, P. Treichel, J. Townsend, “Chapter 5: Principles of Chemical Reactivity: Energy and Chemical Reactions”, Chemistry and Chemical Reactivity, Cengage Learning, 2008.

[5] Fran Cverna, ASM Ready Reference: Thermal Properties of Metals, ASM International, 2002.

[6] “Specific Heat Capacity”, n.d. [Online]. Available: https://www.toppr.com/guides/physics/thermal-properties-of-matter/specific-heat-capacity/