Heat capacity

Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature.

In architecture and civil engineering, the heat capacity of a building is often referred to as its thermal mass.

is the amount of heat that must be added to the object (of mass M) in order to raise its temperature by

The value of this parameter usually varies considerably depending on the starting temperature

The variation can be ignored in contexts when working with objects in narrow ranges of temperature and pressure.

For example, the heat capacity of a block of iron weighing one pound is about 204 J/K when measured from a starting temperature T = 25 °C and P = 1 atm of pressure.

One can trust that the same heat input of 204 J will raise the temperature of the block from 15 °C to 16 °C, or from 34 °C to 35 °C, with negligible error.

At constant pressure, heat supplied to the system contributes to both the work done and the change in internal energy, according to the first law of thermodynamics.

where the final equality follows from the appropriate Maxwell relations, and is commonly used as the definition of the isobaric heat capacity.

A system undergoing a process at constant volume implies that no expansion work is done, so the heat supplied contributes only to the change in internal energy.

Following from the equipartition of energy, it is deduced that an ideal gas has the isochoric heat capacity

This means that a monoatomic ideal gas (with zero internal degrees of freedom) will have isochoric heat capacity

No change in internal energy (as the temperature of the system is constant throughout the process) leads to only work done by the total supplied heat, and thus an 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.

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.

However, this computation is valid only when all parts of the object are at the same external pressure before and after the measurement.

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.

Then the change in temperature will depend on the particular path that the system followed through its phase space between the initial and final states.

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.

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).

The heat capacity of an object is an amount of energy divided by a temperature change, which has the dimension L2⋅M⋅T−2⋅Θ−1.

[5] The BTU was in fact defined so that the average heat capacity of one pound of water would be 1 BTU/°F.

Examples include a reversibly and nearly adiabatically expanding ideal gas, which cools,

Others are inhomogeneous systems that do not meet the strict definition of thermodynamic equilibrium.

They include gravitating objects such as stars and galaxies, and also some nano-scale clusters of a few tens of atoms close to a phase transition.

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

If a temperature is defined by the average kinetic energy, then the system therefore can be said to have a negative heat capacity.

According to black-hole thermodynamics, the more mass and energy a black hole absorbs, the colder it becomes.

According to the second law of thermodynamics, when two systems with different temperatures interact via a purely thermal connection, heat will flow from the hotter system to the cooler one (this can also be understood from a statistical point of view).

In contrast, for systems with negative heat capacities, the temperature of the hotter system will further increase as it loses heat, and that of the colder will further decrease, so that they will move farther from equilibrium.