= Specific heat capacity
{title2=$c=C/m$}
{wiki}
Specific heat capacity is <heat capacity> per unit <mass>:
$$
c=\frac Cm,\qquad c_V=\frac{C_V}{m},\qquad c_p=\frac{C_p}{m}.
$$
Its units are $\mathrm{J\,kg^{-1}\,K^{-1}}$, and the constraint remains part of the definition. In particular, <specific heat capacity at constant volume> and <specific heat capacity at constant pressure> are different responses. For homogeneous material, doubling the <mass> doubles its <heat capacity> while leaving its <specific heat capacity> unchanged. https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry[OpenStax, Specific heat and heating calculations]{ref}
As an illustrative material model, give a fixed-<volume (thermodynamics)> body <mass> $m=2\,\mathrm{kg}$ and constant <specific heat capacity at constant volume> $c_V=400\,\mathrm{J\,kg^{-1}\,K^{-1}}$. With no <phase transition> and no other <work>, increasing its uniform <temperature> by $10\,\mathrm K$ requires
$$
C_V=mc_V=800\,\mathrm{J\,K^{-1}},\qquad
Q=mc_V\Delta T=8000\,\mathrm J=\Delta U.
$$
These stipulated values describe no measured substance. The right panel of the diagram in <heat capacity> shows the straight line $Q=mc_V\Delta T$: a <temperature> increase of $5\,\mathrm K$ takes $4000\,\mathrm J$ of <heat>. If the <specific heat capacity at constant volume> depends on <temperature>, use $Q=m\int_{T_1}^{T_2}c_V(T)\,dT$ instead. The corresponding fixed-<pressure> calculation uses <specific heat capacity at constant pressure> and gives $Q=\Delta H$ under the assumptions in <heat capacity>.
Choosing between <specific heat capacity>, <molar heat capacity> and <volumetric heat capacity> is choosing whether to compare equal <mass>, equal <amount of substance> or equal <volume (thermodynamics)>. A small sample with large <specific heat capacity> can still have less total <heat capacity> than a much larger sample.
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