Specific heat

The specific heat (capacity) cc of a substance is the amount of heat QQ that needs to be absorbed by a unit amount of matter to incur a unit change in temperature TT. The amount of matter can be determined by several variables, namely the amount of particles NN, the mass MM or the volume VV. It is defined starting from the heat capacity CC:

cN=CN =1Nlim⁡T→0ΔQΔTcM=CM=1Mlim⁡T→0ΔQΔTcV=CV  =1Vlim⁡T→0ΔQΔT\begin{align} c_{N}&=\frac{C}{N}\,=\frac{1}{N}\lim_{ T \to 0 } \frac{\Delta Q}{\Delta T} \\ c_{M}&=\frac{C}{M}=\frac{1}{M}\lim_{ T \to 0 } \frac{\Delta Q}{\Delta T} \\ c_{V}&=\frac{C}{V}\;=\frac{1}{V}\lim_{ T \to 0 } \frac{\Delta Q}{\Delta T} \end{align}