❓ Question
If 10 kg of ice at −10°C is mixed with 100 kg of water at 25°C, find the equilibrium temperature.
✍️ Solution
Let the final equilibrium temperature be T°C.
Step 1: Heat lost by water
Water cools from 25°C to T°C.
Q = mcΔT
= 100 × 1 × (25 − T)
= (2500 − 100T) kcal
Step 2: Heat gained by ice
(i) Heating ice from −10°C to 0°C
Q₁ = 10 × 0.5 × 10 = 50 kcal
(ii) Melting the ice
Q₂ = 10 × 80 = 800 kcal
(iii) Heating melted ice from 0°C to T°C
Q₃ = 10 × T = 10T kcal
Total heat gained:
Q = 50 + 800 + 10T = (850 + 10T) kcal
Step 3: Apply Principle of Calorimetry
Heat Lost = Heat Gained
2500 − 100T = 850 + 10T
1650 = 110T
T = 15°C
✅ Final Answer
15°C