The specific heat of substances is influenced by their molecular structure and degrees of freedom. Water has a higher specific heat than metals due to its ability to store energy through various modes, including kinetic motion and bond vibrations. Polyatomic gases, such as nitrogen (N2), exhibit higher specific heat than monoatomic gases because they can store energy in rotational and vibrational modes. The specific heat of nitrogen at constant volume is 20.6 J/K/mol at 15 °C, which is significantly greater than that of a hypothetical monoatomic gas with the same molecular mass.
PREREQUISITESChemists, physicists, and students studying thermodynamics, particularly those interested in the thermal properties of materials and their molecular behavior.
Polyatomic gases[edit]
On the other hand, a polyatomic gas molecule (consisting of two or more atoms bound together) can store heat energy in other forms besides its kinetic energy. These forms include rotation of the molecule, and vibration of the atoms relative to its center of mass.
These extra degrees of freedom or "modes" contribute to the specific heat of the substance. Namely, when heat energy is injected into a gas with polyatomic molecules, only part of it will go into increasing their kinetic energy, and hence the temperature; the rest will go to into those other degrees of freedom. In order to achieve the same increase in temperature, more heat energy will have to be provided to a mol of that substance than to a mol of a monoatomic gas. Therefore, the specific heat of a polyatomic gas depends not only on its molecular mass, but also on the number of degrees of freedom that the molecules have.[15][16] [17]
Quantum mechanics further says that each rotational or vibrational mode can only take or lose energy in certain discrete amount (quanta). Depending on the temperature, the average heat energy per molecule may be too small compared to the quanta needed to activate some of those degrees of freedom. Those modes are said to be "frozen out". In that case, the specific heat of the substance is going to increase with temperature, sometimes in a step-like fashion, as more modes become unfrozen and start absorbing part of the input heat energy.
For example, the molar heat capacity of nitrogen N
2 at constant volume is {\displaystyle c_{V,\mathrm {m} }={}}20.6 J/K/mol (at 15 °C, 1 atm), which is 2.49{\displaystyle R}
.[18] That is the value expected from theory if each molecule had 5 degrees of freedom. These turn out to be three degrees of the molecule's velocity vector, plus two degrees from its rotation about an axis through the center of mass and perpendicular to the line of the two atoms. Because of those two extra degrees of freedom, the specific heat {\displaystyle c_{V}}
of N
2 (736 J/K/kg) is greater than that of an hypothetical monoatomic gas with the same molecular mass 28 (445 J/K/kg), by a factor of 5/3.
This value for the specific heat of nitrogen is practically constant from below −150 °C to about 300 °C. In that temperature range, the two additional degrees of freedom that correspond to vibrations of the atoms, stretching and compressing the bond, are still "frozen out". At about that temperature, those modes begin to "un-freeze", and as a result {\displaystyle c_{V}}starts to increase rapidly at first, then slower as it tends to another constant value. It is 35.5 J/K/mol at 1500 °C, 36.9 at 2500 °C, and 37.5 at 3500 °C.[19] The last value corresponds almost exactly to the predicted value for 7 degrees of freedom per molecule.