Question

A 2 kg iron block is taken from a furnace where its temperature was 650 centigrade and placed on a large block of ice at 0 centigrade.Assuming that all the heat given up by the iron is used to melt the ice , how much ice is melted.

Answer 1

A 2 kg iron block is taken from a furnace where its temperature was 650 centigrade and placed on a large block of ice at 0 centigrade. Assuming that all the heat given up by the iron is used to melt the ice, how much ice is melted.

**Solution.**

$$m_{1} = 2kg, C = 450\frac{J}{kg \cdot {}{}^{\circ}\mathrm{C}}, L = 334 \cdot 10^{3}\frac{J}{kg}, t_{1} = 650{}^{\circ}\mathrm{C}, t_{2} = 0{}^{\circ}\mathrm{C};$$ $$m_{2} - ?$$

Heat balance equation:

$$Q_{1} = Q_{2};$$ $$Q_{1} = m_{1}C|t_{2} - t_{1}|;$$ $$Q_{2} = Lm_{2};$$ $$m_{1}C|t_{2} - t_{1}| = Lm_{2};$$ $$m_{2} = \frac{m_{1}C|t_{2} - t_{1}|}{L}.$$ $$m_{2} = \frac{2 \cdot 450 \cdot |0 - 650|}{334 \cdot 10^{3}} = 1.75(kg).$$

**Answer:** $m_{2} = 1.75kg$.