Specific heat capacity

Template:Material properties (thermodynamics) Specific heat capacity, also known simply as specific heat (Symbol: C or c) is the measure of the heat energy required to raise the temperature of a specific quantity of a substance (thus, the name “specific” heat) by certain amount, usually one kelvin. A kelvin is a unit increment of thermodynamic temperature and is precisely equal to an increment of one degree Celsius. Virtually any substance may have its specific heat capacity measured, including pure chemical elements, compounds, alloys, solutions, and composites.

Symbols and standards

When measuring specific heat capacity, the specified quantity of the substance can be in terms of either mass or moles (which is a certain number of atoms or molecules). When mass is the unit quantity, the symbol for specific heat capacity is lowercase c. When the mole is the unit quantity, the symbol is uppercase C (and it is also known as molar heat capacity). Alternatively—especially in chemistry as opposed to engineering—the uppercase version for specific heat, C, may be used in combination with the symbol for enthalpy (H or h) as a suffix. When the mole is the unit quantity, the enthalpy symbol is uppercase H and when mass is the unit quantity, the symbol is lowercase h.

The modern SI units for measuring specific heat capacity are either the joule per gram per kelvin (J g^–1 K^–1) or the joule per mole per kelvin (J mol^–1 K^–1). The various SI prefixes can create variations of these units (such as kJ kg^–1 K^–1 and kJ mol^–1 K^–1).  Other units of measure are often employed in the measure of specific heat capacity. These include calories and BTUs for energy, pounds-mass for quantity, and degree Fahrenheit (°F) for the increment of temperature.

There are two distinctly different experimental conditions under which specific heat capacity is measured and these are denoted with a subscripted suffix modifying the symbols C or c. The specific heat of substances are typically measured under constant pressure (Symbols: C_p or c_p). However, fluids (gases and liquids) are typically also measured at constant volume (Symbols: C_v or c_v).  Measurements under constant pressure produces greater values than those at constant volume because work must be performed in the former. This difference is particularly great in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume

Thus, the symbols for specific heat capacity are as follows:

	Under constant pressure	At constant volume
Unit quantity = mole	Cp or CpH	Cv or CvH
Unit quantity = mass	cp or Cph	cv or Cvh

The specific heat capacities of substances comprised of molecules (distinct from the monatomic gases) are not fixed constants and vary somewhat depending on temperature.  Accordingly, the temperature at which the measurement is made is usually also specified. Examples of two common ways to cite the specific heat of a substance are as follows:

Water (liquid): c_p = 4.1855 J g^–1 K^–1 (15 °C), and…
Water (liquid): C_vH = 74.539 J mol^–1 K^–1 (25 °C)

The pressure at which specific heat capacity is measured is especially important for gases and liquids. The standard pressure was once virtually always “one standard atmosphere” which is defined as the sea level–equivalent value of precisely 101.325 kPa (760 torr). In the case of water, 101.325 kPa is still typically used due to water’s unique role in temperature and physical standards. However, in 1985, the International Union of Pure and Applied Chemistry (IUPAC) recommended that for the purposes of specifying the physical properties of substances, “the standard pressure” should be defined as precisely 100 kPa (≅750.062 torr). Besides being a round number, this had a very practical effect: relatively few people live and work at precisely sea level; 100 kPa equates to the mean pressure at an altitude of about 112 meters (which is closer to the 194–meter world–wide median altitude of human habitation). Accordingly, the pressure at which specific heat capacity is measured should be specified since one can not assume its value. An example of how pressure is specified is as follows:

Water (gas): C_vH = 28.03 J mol^–1 K^–1 (100 °C, 101.325 kPa)

Note in the above specification that the experimental condition is at constant volume.  Still, the pressure within this fixed volume is controlled and specified.

Why different materials have different specific heat capacities

• When the specific heat capacity, c, of a material is measured (lowercase c means the unit quantity is in terms of mass), different values arise because different substances have different molar masses (essentially, the weight of the individual atoms or molecules). Heat energy arises, in part, due to the number of atoms or molecules that are vibrating. If a substance has a lighter molar mass, then each gram of it has more atoms or molecules available to store heat energy. This is why hydrogen—the lightest substance there is—has such a high specific heat capacity on a gram basis; one gram of it contains a relatively great many molecules.

• Molecules are quite different from the monatomic gases like helium and argon.  With monatomic gases, heat energy is comprised only of translational motions. Translational motions are ordinary, whole-body movements in 3D space whereby particles move about and exchange energy in collisions (like rubber balls in a vigorously shaken container). These simple movements in the three X, Y, and Z–axis dimensions of space means monatomic atoms have the three spatial degrees of freedom.  Molecules, however, have various internal vibrational and rotational degrees of freedom because they are complex objects; they are a population of atoms that can move about within a molecule in different ways. Heat energy is stored in these internal motions. Water for instance, can absorb a large amount of heat energy per mole with only a modest temperature change because it has six active degrees of freedom, the maximum available. Not surprisingly, water gas molecules (steam molecules) have twice the specific heat capacity per mole as do the monatomic gases which move only within the three degrees of freedom comprising translational motion.

• Sometimes the translational degrees of freedom are effectively unavailable. Take the case of diamond: its intermolecular bonds are extraordinarily strong and its molar mass is fairly low. Consequently, the intermolecular bonds’ vibrational frequencies are so high that the quantum spacings between the different vibrational energy levels are very large. At relatively low temperatures (and room temperature counts as “low” in this context), these large quantum energy spacings makes the translational degrees of freedom largely unavailable.  Kinetic (heat) energy is still perfectly-well absorbed in diamond, it’s simply that little is stored in the three degrees of freedom that comprise translational motion (which is what gives a substance its temperature). This effect underlies why the specific heat capacities of molecular-based substances are not fixed constants and increase with greater temperatures; increasingly more heat energy can make the quantum jumps from one energy level to the next in the translational degrees of freedom.

• Hydrogen-containing molecules like ethanol, ammonia, and water have powerful, intermolecular hydrogen bonds when in their liquid phase. These bonds provide yet another place where kinetic (heat) energy is stored.

Equations

• The equation relating heat energy to specific heat capacity, where the unit quantity is in terms of mass is:

Q = m c ΔT

where Q is the heat energy put into or taken out of the substance, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

• Where the unit quantity is in terms of moles, the equation relating heat energy to specific heat capacity (also known as molar heat capacity) is

Q = n C ΔT

where Q is the heat energy put into or taken out of the substance, n is the number moles, C is the specific heat capacity, and ΔT is the change in temperature.

Table of specific heat capacities

Substance	Phase	cp J g-1 K-1	Cp J mol-1 K-1
Air (Sea level, dry, 0 °C)	gas	1.0035	29.07
Air (typical room conditionsA)	gas	1.012	29.19
Aluminium	solid	0.897	24.2
Ammonia	liquid	4.700	80.08
Argon	gas	0.5203	20.7862
Beryllium	solid	1.82	16.4
Copper	solid	0.385	24.47
Diamond	solid	0.5091	6.115
Ethanol	liquid	2.44	112
Gold	solid	0.1291	25.42
Graphite	solid	0.710	8.53
Helium	gas	5.1932	20.7862
Hydrogen	gas	14.30	28.82
Iron	solid	0.450	25.1
Lithium	solid	3.58	24.8
Mercury	liquid	0.1395	27.98
Nitrogen	gas	1.040	29.12
Neon	gas	1.0301	20.7862
Oxygen	gas	0.918	29.38
Silica (fused)	solid	0.703	42.2
Uranium	solid	0.116	27.7
Water	gas (100 °C)	2.080	37.47
	liquid (25 °C)	4.1813	75.327
	solid (0 °C)	2.114	38.09
All measurements are at 25 °C unless otherwise noted. Notable minimums and maximums are shown in maroon text.

^A Assuming an altitude of 194 meters above mean sea level (the world–wide median altitude of human habitation), an indoor temperature of 23 °C, a dewpoint of 9 °C (40.85% relative humidity), and 760 mm–Hg sea level–corrected barometric pressure (molar water vapor content = 1.16%).

Specific heat of building materials

Usually of interest to builders and solar designers

Substance	Phase	cp J g-1 K-1
Asphalt	solid	0.92
Brick	solid	0.84
Concrete	solid	0.88
Glass, crown	solid	0.67
Glass, flint	solid	0.503
Glass, pyrex	solid	0.753
Granite	solid	0.790
Gypsum	solid	1.09
Marble, mica	solid	0.880
Sand	solid	0.835
Soil	solid	0.80
Wood	solid	0.42

See also

• Heat
• Heat capacity ratio
• Heat equation
• Heat transfer coefficient
• Latent heat
• Specific melting heat
• Specific heat of vaporization
• Temperature
• Volumetric heat capacity

References