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Effect of High Latent Heat of Fusion of Ice

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Question

From what height a piece of ice $(0^{o} C)$ fall so that melts completely? Only one-quarter of the energy produced is absorbed by the ice as heat.(Latent heat of ice $= 3.4 \times 10^{5} J {k g}^{- 1}, g = 10 {m / s}^{2}$ )

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Solution

As per conservation of energy, energy gained by ice during its fall from height $h$ is $E = m g h$
Given, only one-quarter of its energy is absorbed by the ice.
So, $\frac{m g h}{4} = m L_{f}$
$\Rightarrow h = \frac{4 L_{f}}{g} = \frac{3.4 \times 10^{5} \times 4}{10} = 136000$ m $= 136$ km

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