(a) A system, maintained at constant volume, is brought in contact with a thermal reservoir at temperature $T_f$. If the initial temperature of the system is $T_i$, then calculate the change in the total entropy ($\Delta S$). You may assume that the specific heat of the system is independent of temperature.
(b) Assume now that the change in system temperature is brought about through successive contacts with N reservoirs at temperature
$T_i + \Delta T, T_i + 2\Delta T, \dots, T_f - \Delta T, T_f$
where $N\Delta T = T_f - T_i$. What will the change in the total entropy in the limit $N \to \infty$ and $\Delta T \to 0$?
(c) Comment on the difference between (a) and (b) in the light of the second law of thermodynamics.