Heat capacity

Heat capacity is the ratio of heat transferred to a system to the resulting change in its temperature for a stated process. For a small temperature change, it is written C = δQ/dT, where δQ denotes heat transferred and dT the temperature change. The heat capacity of an object depends on the amount of material as well as its composition and physical state. Specific heat capacity, often called specific heat, is heat capacity per unit mass; molar heat capacity is heat capacity per mole. Their SI units are respectively joules per kilogram per kelvin (J kg⁻¹ K⁻¹) and joules per mole per kelvin (J mol⁻¹ K⁻¹), while heat capacity itself is measured in joules per kelvin (J K⁻¹). A temperature interval has the same numerical size in kelvins and degrees Celsius.

When a substance remains in one phase and its heat capacity is approximately constant over the temperature range, heat transfer is commonly estimated with Q = mcΔT, where m is mass and c is specific heat capacity. Equivalently, for a body with heat capacity C, Q ≈ CΔT. This approximation must be adjusted when heat capacity varies significantly with temperature or when a phase change occurs; during melting or boiling, energy can be transferred without a temperature change. Calorimetry uses measured heat transfers and temperature changes to determine thermal properties or the energy exchanged between systems. In an insulated exchange, heat lost by one part is approximately gained by another, subject to any energy stored in the apparatus and other losses.

Different substances require different amounts of heat for the same mass and temperature change, and heat capacity can also vary with temperature and phase. In gases, the specified constraint matters: the heat capacity at constant pressure, Cp, is generally different from that at constant volume, Cv. At constant pressure, an expanding gas can do work on its surroundings, so more heat may be required for the same temperature increase than in a constant-volume process. For an ideal gas, the molar capacities satisfy Cp − Cv = R, where R is the molar gas constant. More generally, heat capacity refers to a response along a stated thermodynamic process rather than a single universal value independent of conditions.

Water has a relatively high specific heat capacity compared with many common materials. As a result, a substantial amount of heat is needed to change the temperature of a given mass of water, contributing to the moderating influence of oceans and lakes on nearby temperature patterns. Engineers use heat-capacity data when designing cooling systems, engines, buildings and thermal storage. In basic laboratory measurements, a calorimeter is used to estimate heat capacity by relating known or measured heat transfer to a temperature change.