A copper block of mass 5.0 kg is heated to a temperature of 500°C and is 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 °C⁻¹ and latent heat of fusion of water : 335 J g⁻¹]

Solution

Physics sir · 4 steps

All the heat the copper gives up while cooling to 0 °C goes into melting ice, so equate the two.

1. Where copper stops. The ice block is large, so it stays at 0 °C. The copper cools from 500 °C to 0 °C, a drop of 500 °C. Melting the most ice means using all of the heat released in that drop.

   m_(Cu) s_(Cu) Δ T = m_(ice) L_f

2. Heat released. With the mass in grams to match the units of s: Q = 5000 × 0.39 × 500 = 975000 J.
3. Ice melted. m_(ice) = 975000/335 ≈ 2910 g.
4. So. About 2.9 kg of ice melts, which is option (c).

The idea to keep. For a hot body on a large ice block, the final temperature is 0 °C. The heat it releases, msΔ T, equals mL for the ice. Keep the mass in the same units as s and L.

Answer from the NTA final answer key. Solution by PrepWiser.