An insulated copper calorimeter contains 0.20 kg of water at 25°C. A piece of hot iron of mass 0.10 kg at 100°C is placed into the water. Assuming no heat loss to surroundings and neglecting calorimeter heat capacity, calculate the final equilibrium temperature. (Specific heat capacity of water = 4200 J/(kg·K), iron = 450 J/(kg·K))
Answer and explanation
Correct answer: C. 28.8°C
- Step 1: Heat lost by iron = Heat gained by water. Step 2. (0.10)(450)(100 - θ) = (0.20)(4200)(θ - 25) => 45(100 - θ) = 840(θ - 25). Step 3. 4500 - 45θ = 840θ - 21000 => 885θ = 25500 => θ ≈ 28.81°C. Answer: 28.8°C. Why not the others: 32.5°C assumes equal heat capacities; 26.2°C and 35.0°C result from incorrect ratio calculation.
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