Enthalpies

[eduardomorales5]

If an ice cube is dropped into a hot coffee cup at 300K, how would we be able to determine how much ice would be needed to drop the temperature to 250K?

[Ryan Yee 1J]

You would make 2 q=(mass)(specific heat)(change in temperature) and then set them equal to each other (since the heat lost by the coffee is gained by the ice). So now you have (mass of ice)(specific heat of ice)(change in temperature) = (mass of coffee [which should just be mass of cup of water because its a solution and I feel its ok to approximate])(specific heat of water)(change in temperature), but since you have a phase change of the ice to water, you need to include q=(mass)(enthalpy change) on the side of ice in the equation.