Constant Volume Specific Heat

Constant-volume specific heat $c_v$ is a type of specific heat, signifying the energy required to raise the temperature of a unit mass of a substance by one degree at constant volume.

Since the volume is constant, all of the energy transfer goes into changing the temperature, such that we have

$$q=\Delta u$$

Thus, is is given by:

$$\begin{array}{rl}\int du& =\int c_v(T)dT\\ du& =c_v(T)dT\\ u_2-u_1& =\overline{c_v}(T_2-T_1)\end{array}$$

The variation of specific heats with temperature is smooth and may be approximated as linear over small temperature intervals, so our equation above using ${\bar{c}}_v$ is valid if $\Delta T$ is small (a few hundred degrees).

• The flat (constant temperature) parts of the graph are parts where the added energy is going toward breaking toward breaking intermolecular bonds (latent energy), not temperature change (sensible energy).