Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature.
Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume.
Heat capacities for a homogeneous system undergoing different thermodynamic processes
At constant pressure (Isobaric process)
At constant volume (Isochoric process)
Calculating and for an ideal gas
Using the above two relations, the specific heats can be deduced as follows:
At constant temperature (Isothermal process)
No change in internal energy (as the temperature of the system is constant throughout the process) leads to only work done of the total supplied heat, and thus infinite amount of heat is required to increase the temperature of the system by a unit temperature, leading to infinite or undefined heat capacity of the system.
At the time of phase change (Phase transition)
Heat capacity of a system undergoing phase transition is infinite, because the heat is utilized in changing the state of the material rather than raising the overall temperature.
The heat capacity may be well-defined even for heterogeneous objects, with separate parts made of different materials; such as an electric motor, a crucible with some metal, or a whole building. In many cases, the (isobaric) heat capacity of such objects can be computed by simply adding together the (isobaric) heat capacities of the individual parts.
For complex thermodynamic systems with several interacting parts and state variables, or for measurement conditions that are neither constant pressure nor constant volume, or for situations where the temperature is significantly non-uniform, the simple definitions of heat capacity above are not useful or even meaningful. The heat energy that is supplied may end up as kinetic energy (energy of motion) and potential energy (energy stored in force fields), both at macroscopic and atomic scales. Then the change in temperature will depends on the particular path that the system followed through its phase space between the initial and final states. Namely, one must somehow specify how the positions, velocities, pressures, volumes, etc. changed between the initial and final states; and use the general tools of thermodynamics to predict the system's reaction to a small energy input. The "constant volume" and "constant pressure" heating modes are just two among infinitely many paths that a simple homogeneous system can follow.
The heat capacity can usually be measured by the method implied by its definition: start with the object at a known uniform temperature, add a known amount of heat energy to it, wait for its temperature to become uniform, and measure the change in its temperature. This method can give moderately accurate values for many solids; however, it cannot provide very precise measurements, especially for gases.
The SI unit for heat capacity of an object is joule per kelvin (J/K, or J K−1). Since an increment of temperature of one degree Celsius is the same as an increment of one kelvin, that is the same unit as J/°C.
English (Imperial) engineering units
Professionals in construction, civil engineering, chemical engineering, and other technical disciplines, especially in the United States, may use the so-called English Engineering units, that include the Imperial pound (lb = 0.45459237 kg) as the unit of mass, the degree Fahrenheit or Rankine (5/9 K, about 0.55556 K) as the unit of temperature increment, and the British thermal unit (BTU ≈ 1055.06 J), as the unit of heat. In those contexts, the unit of heat capacity is BTU/°F ≈ 1900 J. The BTU was in fact defined so that the average heat capacity of one pound of water would be 1 BTU/°F.
In chemistry, heat amounts are often measured in calories. Confusingly, two units with that name, denoted "cal" or "Cal", have been commonly used to measure amounts of heat:
the "small calorie" (or "gram-calorie", "cal") is 4.184 J, exactly. It was originally defined so that the heat capacity of 1 gram of liquid water would be 1 cal/°C.
The "grand calorie" (also "kilocalorie", "kilogram-calorie", or "food calorie"; "kcal" or "Cal") is 1000 small calories, that is, 4184 J, exactly. It was originally defined so that the heat capacity of 1 kg of water would be 1 kcal/°C.
With these units of heat energy, the units of heat capacity are
- 1 cal/°C ("small calorie") = 4.184 J/K
- 1 kcal/°C ("large calorie") = 4184 J/K
Negative heat capacity
Most physical systems exhibit a positive heat capacity. However, even though it can seem paradoxical at first, there are some systems for which the heat capacity is negative. These are inhomogeneous systems that do not meet the strict definition of thermodynamic equilibrium. They include gravitating objects such as stars and galaxies, and also sometimes some nano-scale clusters of a few tens of atoms, close to a phase transition. A negative heat capacity can result in a negative temperature.
Stars and black holes
According to the virial theorem, for a self-gravitating body like a star or an interstellar gas cloud, the average potential energy Upot and the average kinetic energy Ukin are locked together in the relation
The total energy U (= Upot + Ukin) therefore obeys
If the system loses energy, for example, by radiating energy into space, the average kinetic energy actually increases. If a temperature is defined by the average kinetic energy, then the system therefore can be said to have a negative heat capacity.
A more extreme version of this occurs with black holes. According to black-hole thermodynamics, the more mass and energy a black hole absorbs, the colder it becomes. In contrast, if it is a net emitter of energy, through Hawking radiation, it will become hotter and hotter until it boils away.
Quantum statistical mechanics
Heat capacity ratio
Thermodynamic databases for pure substances
Heat transfer coefficient
Heat of mixing
Material properties (thermodynamics)
Joback method (Estimation of heat capacities)
Specific heat of melting (Enthalpy of fusion)
Specific heat of vaporization (Enthalpy of vaporization)
Volumetric heat capacity
Table of specific heat capacities