In an isothermal process, the temperature of the gas remains constant, which means the change in temperature ($\Delta T$) is zero. The specific heat capacity ($c$) is defined as the amount of heat ($q$) required to raise the temperature of unit mass ($m$) of a substance by one unit, given by the formula $c = \frac{q}{m \Delta T}$. Since $\Delta T = 0$, the specific heat capacity $c$ approaches infinity ($c = \frac{q}{0} = \infty$).