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?

Heat lost by water cooling from 30 °C to 0 °C = m × 1000 × 4.2 × 30 J (using specific heat 4.2 J/g°C and m in kg means mass in g is 1000m). Heat gained by ice = (i) warming ice from –20 °C to 0 °C: 5 × 2.1 × 20 = 210 J, plus (ii) melting 5 g of ice: 5 × 336 = 1680 J. Total heat needed = 1890 J. Setting equal: m × 1000 × 4.2 × 30 = 1890, giving m = 1890 / 126000 = 0.015 kg.