First slide

Change of state

Question

A piece of ice falls from a height h, so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is (Take, latent heat of ice is 3.4 X 10⁵ ]/kg and g = 10 N/kg)

Moderate

A

544 km
B

136 km
C

68 km
D

34 km

Solution

According to the conservation of energy, energy gained by the ice during its fall from height h is given by
E = mgh
As given, only one quarter of its energy is absorbed by the ice.
So, $\frac{m g h}{4} = m L_{f}$
$\Rightarrow h = \frac{m L_{f} \times 4}{m g} = \frac{L_{f} \times 4}{g} = \frac{3.4 \times 10^{5} \times 4}{10} = 13.6 \times 10^{4}$
= 136000 m = 136km

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