A2 Daily A Level Physics question
Two 0.20 kg samples are heated in identical insulated beakers by the same 100 W immersion heater. Sample X is ice at −10°C that is heated until it becomes liquid water at +10°C. Sample Y is liquid water at 0°C heated to +20°C. Take c_ice ≈ 2100 J kg−1 K−1, c_water ≈ 4200 J kg−1 K−1, and the latent heat of fusion of ice ≈ 334 kJ kg−1. Ignore energy losses. Which statement must be true about the times taken?
Answer
The correct answer is A.
Correct: A — The ice-to-water heating takes about five times longer, because most energy goes into melting at constant temperature. A is correct because the total energy for X ≈ 0.20×(2100×10 + 334000 + 4200×10) J ≈ 79 kJ, while for Y ≈ 0.20×(4200×20) J ≈ 17 kJ, giving a time ratio ≈ 79/17 ≈ 4.7, dominated by the latent heat plateau. B is wrong because focusing on the 10°C colder start ignores the large extra energy needed for the phase change, which is far more than a modest temperature difference. C is wrong because equal overall temperature rises do not imply equal energy when a phase change (with no temperature rise) adds a large extra energy requirement. D is wrong because comparing specific heats alone neglects the latent heat; despite ice’s smaller c, melting requires substantial additional energy, so it is not quicker.