What is the specific heat of a gas in an isothermal process and an adiabatic process?

(A) For an isothermal process,the temperature change $\Delta T = 0$. Since the specific heat is defined as $C = \frac{\Delta Q}{m \Delta T}$,as $\Delta T \to 0$,the specific heat $C$ becomes infinite.
For an adiabatic process,there is no heat exchange with the surroundings,so $\Delta Q = 0$. Substituting this into the formula $C = \frac{\Delta Q}{m \Delta T}$,we get $C = 0$.