$(20\%)$ A sample of $50\mathrm{.}0$ kg of ice at $0\mathrm{.}0$C is mixed with $50\mathrm{.}0$ kg of water at $50\mathrm{.}0$C$.($a$)$ Explain the

corresponding reversible process you choose. $($b$)$ Estimate the net change in entropy of the whole system

$($ice $+$ water$).$