Given: a House is losing heat at an average rate of $50,000$ kJ$/$h $,$ but is being maintained at $22$C$.50$ containers of water provide some of the heat for a $10$ hour perios one winter night. they are heated during the day by solar energy, and begin the night at $80$C$,$ and end at $25$C$.$ Each container holds $20$L of water. A $15$ kW backup electric resistance heater provides the balance of the energy needed to maintain the house temperature. Find: a$)$ how long do the electric heaters run during the $10$ hour period? b$)$ how much entropy was generated during the night by the electric heater?