# Heat capacity

The heat capacity of an object is the amount of energy (in Joules) it takes to increase its temperature by one Kelvin. Often the heat capacity is stated for some unit amount of the material and one must be careful to define what that unit is. There are 3 possibilities:

## 1. The specific heat capacity (sometimes just called the specific heat)

Specific means “per unit mass” so this is the heat capacity per unit mass (in J kg^{-1} K^{-1}).

The convention is to use a lowercase *c* and to specify with a subscript whether it is at constant pressure or constant volume (not that it makes much difference when describing solids). We will refer to the constant pressure version, so this is Cp.

## 2. The molar heat capacity

This is the heat capacity per mole (in J kg^{-1} K^{-1}).

The convention is to use an uppercase C and sometimes the suffix m may be added to indicate “per mole”, hence Cp,m.

Clearly this can be calculated by multiplying the specific heat capacity by the molar mass, M (in kg mol^{-1}):

Cp,m = Cp M

## 3. The volumetric heat capacity

This is the heat capacity per unit volume (in J m^{-3} K^{-1}).

The convention is to use an uppercase C and to add the suffix V to indicate “per unit volume”, hence Cp,V.

Clearly this can be calculated by multiplying the specific heat capacity by the density (in kg m^{-3}):

Cp,V = Cp ρ