Question 13 of 20intermediate🔧 ApplyNumerical3 marks

A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and then placed on a large ice block. What is the maximum amount of ice that can melt? (Specific heat of copper = 0.39 J g−1 K−10.39 \text{ J g}^{-1} \text{ K}^{-1}; heat of fusion of water = 335 J g−1335 \text{ J g}^{-1}).

Correct Answer

The maximum amount of ice that can melt is approximately 1.5 kg (or 1455 g).

Exercise: EXERCISES | Q: 10.13 | (Page 23)
For More Understanding

Explanation

This problem applies the principle of heat exchange. When the hot copper block is placed on ice, it releases heat as it cools down from 500°C to 0°C. This released heat is completely utilized to melt the ice at 0°C. The key assumption is that the final temperature of the copper block reaches 0°C (the temperature of melting ice), which gives the maximum possible heat transfer.

Solution Steps

  1. Step 1: Convert mass to grams Mass of copper block = 2.5 kg = 2500 g

  2. Step 2: Calculate heat released by copper block Heat released = m × s × ΔT Heat released = 2500 g × 0.39 J g⁻¹ K⁻¹ × (500 - 0)°C Heat released = 2500×0.392500 \times 0.39 × 500 = 487500 J

  3. Step 3: Apply heat balance principle Heat released by copper = Heat absorbed by ice to melt Let M = mass of ice melted Heat absorbed = M × L = M × 335 J g⁻¹

  4. Step 4: Solve for mass of ice melted 487500 J = M × 335 J g⁻¹ M = 487500 / 335 = 1455.22 g ≈\approx 1.5 kg

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