A 5 g piece of ice at -20 °℃ is put into m kg of water at 30 ℃ temperature. The heat is exchanged only between the ice and the water. The final temperature of the mixture is 0 ℃ in liquid phase. What is the value of m in kg ?

To find the value of m, we apply the principle of calorimetry, which states that Heat Gained = Heat Lost.

1. Heat gained by ice:
   • To raise temperature from -20 °C to 0 °C: Q1 = mice × sice × ΔT = 5 g × 0.5 cal/g°C × 20 °C = 50 cal.
   • To melt ice at 0 °C: Q2 = mice × Lf = 5 g × 80 cal/g = 400 cal.
   • Total heat gained = 50 + 400 = 450 cal.
2. Heat lost by water:
   • Qloss = mwater × swater × ΔT = (m × 1000 g) × 1 cal/g°C × 30 °C = 30000m cal.
3. Equating the two:

   30000m = 450

   m = 450 / 30000 = 0.015 kg

Therefore, the value of m is 0.015 kg, which corresponds to option C.