Molar heat capacity

The molar heat capacity of a substance is the energy needed to raise the temperature of one mole of it by one degree Celsius.

When using SI units, it can be calculated with the equation [math]\displaystyle{ c_n = \frac Q {\Delta T} }[/math] where [math]\displaystyle{ c_n }[/math] refers to the molar heat capcity (in joules per Kelvin), [math]\displaystyle{ Q }[/math] to the heat supplied (in joules) and [math]\displaystyle{ \Delta T }[/math] (in Kelvin) to the temperature change in the substance.

The molar heat capacity of a given substance can be found by heating the substance by releasing a known amount of energy into the substance and measuring the temperature change.

For example, a common school experiment to find the molar heat capacity of water involves heating a beaker of water with an immersion heater (that can display the heat released in joules on a display) and stirring the water, while checking the temperature at specific intervals.

For more accurate results, a bomb calorimeter can be used; these contain a chamber of fuel (in this case, a compound that will release heat when needed) inside a chamber of water, with the water chamber protected by heat-proof walls (to ensure minimal heat loss, which would affect the final heat capacity recorded).

Molar Heat Capacity Media

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  Vibration of atoms in the molecule and rotation of the molecule store some of the energy (transferred to the molecule as heat) that otherwise would contribute to the molecule's kinetic energy.

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  Constant-volume specific heat capacity of a diatomic gas (idealised). As temperature increases, heat capacity goes from 3/2R (translation contribution only), to 5/2R (translation plus rotation), finally to a maximum of 7/2R (translation + rotation + vibration)

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  Constant-volume specific heat capacity of diatomic gases (real gases) between about 200 K and 2000 K. This temperature range is not large enough to include both quantum transitions in all gases. Instead, at 200 K, all but hydrogen are fully rotationally excited, so all have at least 5/2R heat capacity. (Hydrogen is already below 5/2, but it will require cryogenic conditions for even H2 to fall to 3/2R).

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  The dimensionless heat capacity divided by three, as a function of temperature as predicted by the Debye model and by Einstein's earlier model. The horizontal axis is the temperature divided by the Debye temperature. Note that, as expected, the dimensionless heat capacity is zero at absolute zero, and rises to a value of three as the temperature becomes much larger than the Debye temperature. The red line corresponds to the classical limit of the Dulong–Petit law