25 POINTS ------------------ (usatestprep)

Two iron balls of different mass are heated to 100°C and dropped in water. If the same amount of heat is lost by the two balls to water, what can be said about the final temperatures of the two balls? (Heat lost = mCpΔT, where m = mass of the object, Cp = specific heat capacity of the material, and ΔT = change in temperature).

A) Both balls will have the same temperature as the heat lost by both balls is the same.

B) Both balls will have the same temperature as the specific heat capacities of both balls are the same.

C) The lighter ball will have a higher temperature because the change of temperature is directly proportional to mass.

D) The heavier ball will have a higher temperature because the change of temperature is inversely proportional to mass.

In this problem, we are said that the amount of heat released by the two balls, Q, is the same. Cp is also the same: this means that the product [tex]m\Delta T[/tex] must be the same for the two balls. So, the mass and the change in temperature are inversely proportional: therefore, the heavier ball will have a smaller change in temperature. And since both balls starts from the same temperature, 100 C, this means that the heavier ball will reach a higher temperature than the lighter ball.