For a simple compressible substance, two useful specific heats are associated with changes in internal energy and enthalpy:

$$c_v=\left(\frac{\partial u}{\partial T}\right)_v,\qquad c_p=\left(\frac{\partial h}{\partial T}\right)_p.$$

For an ideal gas, internal energy and enthalpy depend only on temperature, so

$$du=c_v(T),dT,\qquad dh=c_p(T),dT.$$

If the specific heats are approximately constant over a temperature interval,

$$\Delta u\approx c_v\Delta T,\qquad \Delta h\approx c_p\Delta T.$$

For an ideal gas they also satisfy

$$c_p-c_v=R_s,$$

where $R_s$ is the gas's specific gas constant.

For example, with constant $c_p=1.005\ \mathrm{kJ/(kg,K)}$, heating an ideal gas from $300$ to $500\ \mathrm K$ gives

$$\Delta h\approx1.005(200)=201\ \mathrm{kJ/kg}.$$

The distinction between $c_p$ and $c_v$ is not that every process must literally occur at constant pressure or constant volume. They are thermodynamic derivatives that conveniently relate temperature to $h$ and $u$.