### Re: Which elements trigger the highest specific heat capacities in materials?

Date: Tue Aug 29 15:41:22 2000
Posted By: David Ellis, Researcher, NASA Lewis Research Center
Area of science: Chemistry
ID: 966726462.Ch
Message:

## Heat Capacity

Heat capacity is defined as "The quantity of heat required to increase the temperature of a system or substance one degree of temperature." [1]. The value is either expressed as being at constant volume or constant pressure. The Specific heat capacity is the ratio of the heat capacity to that of water at 15 degrees centigrade.

In 1819, Dulong and Petit offered the empirical relationship that the molar heat capacity of all elements was 3R or 24.9 joules/K*mole (R = gas constant = 8.319 joules/K*mole) [2]. While this is true for many elements around room temperature, the actual values approach 0 at 0 K and can exceed 3R at elevated temperatures.

Theoretical calculation of heat capacity as a function of temperature was one of the first great triumphs of quantum physics. Einstein was the first to offer a model that was in good agreement with the experimental data by assuming all atoms in a material were vibrating at the same frequency. His calculations explain the high temperature heat capacity very well, but the heat capacity approaches 0 at 0 K too quickly.

Debye modified Einstein's work by assuming a range of frequencies for the atoms in a material. This is closer to reality. The result was an equation that agrees very well with the experimental data.

To calculate the heat capacity of an alloy, compound, molecule, mixture, etc., the individual heat capacities of each atom can be combined to determine the total heat capacity. [3] So for an individual water atom, the heat capacity at any temperature is equal to the heat capacity of two hydrogen atoms plus one oxygen atom at that temperature. Normally the heat capacities are referred to in terms of molar heat capacities or the heat capacities per molecular weight of a substance. In the case of water, that would be the heat in joules needed to raise approximately 18 grams of water 1 K. Even complex substances like metallic alloys have been shown to obey this behavior. [4]

The heat capacity at sufficiently high temperatures is nearly identical for all elements and is close to 3R. Some elements such as iron and oxygen can exhibit higher than average heat capacities while others such as carbon can be much lower than average. The largest differences are generally observed at and below room temperature. In that temperature regime the heat capacities can differ tremendously. For example, lead has a heat capacity near 25 J/K*mole at 100 K while aluminum is only about 12.5 J/K*mole. Carbon's heat capacity has decreased to less than 1 J/K*mole at 100 K.

What you referred to as the heat capacity in your question might be the heat of formation. That is the amount of energy given off or absorbed when a chemical compound is created. The chemical reaction of hydrogen and oxygen is very energetic. Indeed, rocket engines such as those for the space shuttle main engine (SSME) use hydrogen and oxygen to propel the spacecraft for that very reason.

## Practical Applications For Space

Thermal storage and control are two prime areas of potential usage. A substance that can store a large amount of heat per unit mass can be used to provide energy to a space station. An example would be a simple turbine driving a generator similar in design to electric power plants here on Earth. The heat stored in the material could be released to create steam or an equivalent to drive the turbine that in turn drives the generator that supplies electrical power to the space station.

As a spacecraft orbits the Earth, it goes from about +100 degrees centigrade in the sun to -100 degrees centigrade in the shade. Heat can be stored while a spacecraft orbiting the Earth is in the sunlight to cool the spacecraft. When it goes into shade behind the Earth the stored energy can be released to heat the spacecraft.

## References

1. CRC Handbook of Chemistry and Physics, R.C. Weast, Ed., CRC Press, Boca Raton, FL, (1984), p. F-84
2. Introduction to Metallurgical Thermodynamics, David R. Gaskell, McGraw-Hill Book Company, New York, NY, (1981), pp. 114-125
3. Selected Values of Thermodynamic Properties of the Elements, R.R. Hultgree, ASM International, Metals Park, OH (1973)
4. Thermophysical Properties of GRCop-84, D.L. Ellis and D.J. Keller, NASA Glenn Research Center, Cleveland, OH (June 2000)

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