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A piece of ice at $$-10^\circ\text{C}$$ is heated to $$-1^\circ\text{C}$$ using a certain quantity of energy. Then another 20 times as much energy is necessary to finally obtain water. Using that the specific heat of ice is half of the specific heat of $$4.2\text{ kJ}/(\text{kg}\,^\circ\text{C})$$ of water, determine the heat of fusion of ice (in kJ/kg) from the above measurement data.
Correct Answer: 375.9
Per kg, heating ice from $$-10^\circ\text{C}$$ to $$-1^\circ\text{C}$$ takes $$2.1 \times 9 = 18.9\text{ kJ}$$. The next stage takes $$20 \times 18.9 = 378\text{ kJ}$$, which warms the ice from $$-1^\circ\text{C}$$ to $$0^\circ\text{C}$$ (2.1 kJ) and then melts it. So the heat of fusion is $$378 - 2.1 = 375.9\text{ kJ/kg}$$.
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