Question

A cup contains 50 g of boiling water (100°C), into which a 5 g ice cube (0°

C) is dropped. Which of the following is true about the final temperature of the water in the cup after the ice cube melts and the temperature reaches equilibrium? Assume the temperature immediately drops below 100°
C so that none of the water boils away into the air: all 55 g of liquid remain in the end of the cup after the experiment. Also, assume that we can ignore heat lost to the environment and imagine the cup is perfectly insulated. The final temperature must be warmer than 90.9° C.

Answer 1

To verify if the final temperature is above 90.9°C after adding an ice cube to boiling water, calculations involving heat transfer, phase change, and thermal equilibrium are necessary. However, initial intuition suggests that the significant cooling due to the ice cube melting may prevent the final temperature from being above 90.9°C.

Step-by-step explanation:

To determine if the final temperature must be warmer than 90.9°C after a 5 g ice cube at 0°C is dropped into 50 g of boiling water at 100°C, the heat transfer between the ice cube and the water needs to be calculated. We must consider the heat required for the ice to change phase from solid to liquid and the amount of heat the water will release while reaching thermal equilibrium with the melted ice.

Let's consider the specific heat of ice, the enthalpy of fusion of ice, and the temperature change of the water. However, without a detailed calculation, it is not possible to confirm whether the final temperature is indeed above 90.9°C, but the question seems to have a misleading premise, as the addition of the ice cube will likely have a significant cooling effect on the boiling water.