A piece of ice falls from a height 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 is [2016]

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Solution

Q.
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 $[Latent heat of ice is 3.4 \times 10^{5} J/kg and g = 10 N/kg]$ [2016]

1 136 km

2 68 km

3 34 km

4 544 km

Ans.
(1)

Gravitational potential energy of a piece of ice at a height $(h) = m g h$

Heat absorbed by the ice to melt completely

$Δ Q = \frac{1}{4} m g h$ ...(i)

Also, $Δ Q = m L$ ...(ii)

From eqns. (i) and (ii), $m L = \frac{1}{4} m g h or, h = \frac{4 L}{g}$

Here $L = 3.4 \times 10^{5} {J kg}^{- 1},$ $g = 10 {N kg}^{- 1}$

$∴$ $h = \frac{4 \times 3.4 \times 10^{5}}{10} = 4 \times 34 \times 10^{3} = 136$ $km$

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