Question
A 5\, g piece of ice at -20^ C is put into m kg of water at 30^ C temperature. The heat is exchanged only between the ice and the water. The final temperature of the mixture is 0^ C in liquid phase. What is the value of m in kg?
NDA
General Ability
General Science
2026
NDA 2026 (Phase 1)
NDA General Ability Question (2026) — Solution
Options
- A. 0.050
- B. 0.010
- C. 0.015
- D. 0.150
Answer
C. 0.015
Step-by-step solution
Heat gained by ice to reach 0^ C in the liquid phase consists of the heat required to raise its temperature to 0^ C and the latent heat of fusion to melt it. Using the specific heat of ice s_ ice = 0.5 cal/g ^ C and latent heat of fusion L = 80 cal/g , the total heat gained is: Q_ gained = m_ ice s_ ice T + m_ ice L Q_ gained = 5 0.5 20 + 5 80 Q_ gained = 50 + 400 = 450 cal Heat lost by water to cool from 30^ C to 0^ C is: Q_ lost = m_ water s_ water T Since the mass of water is m kg = 1000m g and s_ water = 1 cal/g ^ C : Q_ lost = (1000m) 1 30 = 30000m cal By the principle of calorimetry, heat gained equals heat lost: 30000m = 450 m = 450 30000 = 0.015 kg Answer: 0.015
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