A glass of ice water was made by adding six 25 g ice cubes to one liter of water. If the water was initially 25C and the ice cubes were initially at -15C, what is the final temperature of the ice water?

To find the final temperature of the ice water, we can use the principle of conservation of energy. The heat gained by the ice cubes will be equal to the heat lost by the water.

First, let's calculate the heat gained by the ice cubes. The specific heat capacity of ice is approximately 2.09 J/g°C.

The heat gained by the ice:
Q_ice = mass_ice * specific_heat_capacity_ice * change_in_temperature_ice

For each ice cube:
mass_ice = 25 g
change_in_temperature_ice = final_temperature - initial_temperature = final_temperature - (-15°C) = final_temperature + 15°C

So, the total heat gained by the ice cubes:
Q_ice = 6 * (25 g) * (2.09 J/g°C) * (final_temperature + 15°C)

Second, let's calculate the heat lost by the water. The specific heat capacity of water is approximately 4.18 J/g°C.

The heat lost by the water:
Q_water = mass_water * specific_heat_capacity_water * change_in_temperature_water

mass_water = 1 liter of water = 1000 g
initial_temperature_water = 25°C
final_temperature_water = final_temperature

So, the total heat lost by the water:
Q_water = (1000 g) * (4.18 J/g°C) * (final_temperature - 25°C)

Since the heat gained by the ice is equal to the heat lost by the water, we can set up an equation:

6 * (25 g) * (2.09 J/g°C) * (final_temperature + 15°C) = (1000 g) * (4.18 J/g°C) * (final_temperature - 25°C)

Now we can solve this equation to find the final temperature of the ice water.