The specific heat of a gas:

(1) has two values $C_p$ and $C_v$ (2) can have any value between 0 and infinity (3) has a value proportional to the square root of its absolute temperature (4) Both (2) and (3)

Specific heat capacity ($S = \large\frac{\Delta Q}{m\Delta T}$) can have any value from zero to infinity depending on the type of process the gas undergoes.