$3\mathrm{.}42$ If the two$-$phase mixture in Example $3\mathrm{.}2$ requires $50$ minutes to undergo process $1-2,$ determine the rate at which the hot plate transfers energy, in kW $,$ to the mixture. If the rate of energy transfer remains the same, determine the time, in min $,$ required to bring the mixture from state $2$ to state $3.$