We can calculate the total amount of heat energy required to freeze the water using the heat of fusion of ice. The heat of fusion of ice is 80 cal/g.
So, the total heat energy required = 800g * 80 cal/g = 64000 cal.
Since heat is being removed at a rate of 15 cal/sec, the time taken to freeze all the water can be calculated using:
Time = Total heat energy required / Heat removal rate
Time = 64000 cal / 15 cal/sec
Time = 4266.67 sec
Converting seconds to minutes:
Time = 4266.67 sec * (1 min / 60 sec)
Time ≈ 71.11 minutes
Therefore, it will take approximately 71.11 minutes for all of the water to freeze in the aluminum ice cube tray.