The molar heat capacity of a substance is the amount of energy needed to increase the temperature of one mole of that substance by one kelvin (equivalently, one degree Celsius). It quantifies how much heat a given amount of material must absorb to raise its temperature and is an intrinsic property that depends on the material and its thermodynamic conditions.

In SI units the molar heat capacity is often expressed by the relation

where denotes the molar heat capacity, is the heat supplied and is the observed temperature change. The SI unit for molar heat capacity is joules per mole per kelvin (J·mol⁻¹·K⁻¹).

Molar heat capacity differs from specific heat capacity, which is the heat required per unit mass (J·kg⁻¹·K⁻¹). For gases the heat capacity is commonly reported at constant pressure (C

p

) or at constant volume (C

v

); for an ideal gas these satisfy C

p

− C

v

= R, where R is the gas constant (approximately 8.314 J·mol⁻¹·K⁻¹).

How it is measured

Direct experimental determination of molar heat capacity relies on delivering a known amount of heat to a known amount of substance and recording the resulting temperature change while accounting for heat losses and the heat capacity of the apparatus. Common approaches include:

  • Simple laboratory method: an immersion heater with a calibrated energy display is placed in a measured mass of sample (for liquids, for example). The heater’s energy reading gives Q, the sample mass and its molar mass give the number of moles, and temperature is recorded at intervals while stirring to ensure uniform temperature.
  • Calorimetry with a calorimeter or bomb calorimeter: a well-insulated calorimeter reduces heat exchange with the environment and often has a known heat capacity that must be included in calculations. A bomb calorimeter is typically used for measuring energy released by combustion; for molar heat capacities of substances in other phases, specially designed calorimeters (adiabatic or isoperibol) are used to keep experimental conditions controlled.
  • Corrections and calibration: to improve accuracy, experimenters correct for heat lost to the surroundings, heat absorbed by the container and stirrer, and non-ideal behaviour; repeated runs and calibration with substances of known heat capacity are standard practice.

Typical values and temperature dependence

Molar heat capacity varies with material, phase (solid, liquid, gas), and temperature. Many simple solids have molar heat capacities near 3R (about 25 J·mol⁻¹·K⁻¹) at room temperature, a result summarized by the Dulong–Petit law, but values for solids fall below this at low temperatures due to quantum effects. Liquid water has a relatively large molar heat capacity — about 75 J·mol⁻¹·K⁻¹ near 25 °C — which is why water moderates temperature changes effectively.

Because molar heat capacity is a function of temperature and pressure, published values are usually given with the conditions under which they were measured (for example, "at constant pressure, 25 °C").