Specific heat (specific heat capacity)

Definition and basic relation

For a mass m of material, the heat q added to produce a temperature change ΔT (with no phase change) is conventionally written q = m c ΔT, where c is the specific heat. The SI unit is joules per kilogram per kelvin (J·kg⁻¹·K⁻¹). Closely related are heat capacity (the extensive quantity dependent on sample size) and molar heat capacity (heat per mole per degree). For gases two common values are quoted: specific heat at constant pressure (c_p) and at constant volume (c_v); in gases c_p is larger because work is done on expansion at constant pressure. For ideal gases the molar quantities obey c_p − c_v = R, the universal gas constant.

Physical origin and temperature dependence

Specific heat reflects the microscopic ways a system can store energy: translational, rotational and vibrational motion of atoms and molecules, and in some materials electronic or magnetic excitations. Classical equipartition theory links heat capacity to the number of active degrees of freedom, but quantum mechanics shows that some modes become inaccessible at low temperature, reducing the specific heat. Empirical and theoretical models such as the Dulong–Petit rule for many solids at room temperature and the Debye model for low-temperature lattice behavior explain typical trends without requiring detailed microscopic calculations.

Variation with phase and temperature

Specific heat generally varies with temperature and differs markedly between phases. Solids, liquids and gases of the same substance usually have distinct specific heats. Near a phase transition, added energy may go into latent heat rather than raising temperature, so the simple q = m c ΔT relation no longer applies. In many practical calculations a material's specific heat is assumed approximately constant over a limited temperature interval, but accurate modeling of thermal processes often requires the temperature dependence to be included.

Measurement methods

Specific heat is determined experimentally by calorimetry. Classic calorimeters measure the temperature change of a sample when a known amount of heat is supplied or removed. Modern techniques include differential scanning calorimetry and adiabatic calorimetry, which improve precision and allow measurement over a wide temperature range. For gases, specific heats may be inferred from measurements of pressure, volume and temperature changes under controlled conditions. Results are tabulated for engineering and scientific use.

Applications and examples

• Climate and environment: Water has a relatively large specific heat compared with many solids and gases, so oceans store and transport heat and moderate climate.
• Engineering: Specific heat guides material choice for heat exchangers, thermal storage, and cooling systems; it is central to transient heat transfer design and thermal management of electronic devices.
• Everyday contexts: Cooking, heating systems and thermal comfort depend on how substances respond to applied heat.
• Scientific work: Thermodynamic calculations, calorimetry experiments and modeling of heat flow use specific heat values and their temperature dependence.

Important considerations

When using specific heat data be aware that values are property- and condition-dependent: they can vary with temperature, pressure, composition (mixtures or alloys) and phase. For porous or heterogeneous materials an effective specific heat may be used. The process of adding energy is a transfer of heat that changes the internal energy of a system; specific heat quantifies the resulting temperature response per unit mass. For context and broader theory see general treatments of thermodynamics.

Historically, measurements of specific heat contributed to the foundations of calorimetry and the development of statistical mechanics, linking macroscopic thermal properties to microscopic motion. Today specific heat remains a fundamental and practical material property across physics, chemistry, engineering and environmental science.