How many ice cubes did she add to the pool to get the temperature to 16 C?

Question

I don't know where to start from? Pls help if you know
Thanks!
Here is the problem:

Trying to beat the heat of the last summer, a physics student went to the local toy store and purchased a plastic child's swimming pool. Upon returning home, she filled it with 200 liters of water at 25oC. Realizing that the water would probably not be cool enough, she threw ice cubes from her refrigerator, each of mass 30g, into the pool. (The ice cubes were originally at 0oC.) She continued to add ice cubes, until the temperature stabilized to 16oC. She then got in the pool.
The density of water is 1000 kg/m3, the specific heat of water is 1.0 cal/g C, the specific heat of ice is 0.5 cal/g C, and the latent heat of fusion of water is 80 cal/g.


How many ice cubes did she add to the pool to get the temperature to 16 C? (Consider the pool and ice cubes an isolated system.)

Answer 1

This is a heat transfer problem. The heat lost by the water in the pool is equal to the heat gained by the ice.

Heat lost by water when temperature drops from 25 to 16 degrees, in calories:

( 200 liters ) ( 1000 gram / liter ) ( 80 cal / gram - degree C ) ( -9 degrees C )

Heat gained by ONE ice cube: melt it, then raise the temperature from zero to 16 degrees, in calories:

( 50 grams ) ( 80 cal / gram ) + ( 50 grams ) ( 80 cal / gram - degree C ) ( +16 degrees C )

Divide the former into the latter to get the number of ice cubes required. Since she isn't adding fractions of ice cubes, any fractional remainder means one more cube.