A 5\text{ g} piece of ice at -20^\circ\text{C} is put into m\text{ kg} of water at 30^\circ\text{C} temperature. The heat is exchanged only between the ice and the water. The final temperature of the mixture is 0^\circ\text{C} in liquid phase. What is the value of m in kg?

  1. A. 0.050
  2. B. 0.010
  3. C. 0.015
  4. D. 0.150

Correct Answer: C. 0.015

Explanation

Heat gained by ice to reach 0^\circ\text{C} and melt = (5 \times 0.5 \times 20) + (5 \times 80) = 450\text{ cal}. Heat lost by water = m \times 1000 \times 1 \times 30 = 30000m\text{ cal}. Equating them gives m = 0.015\text{ kg}.

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