First slide

Questions on calorimetry without phase change

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 [latent heat of ice is $3.4 \times 10^{5} J / k g a n d g = 10 N / k g$ ]

Moderate

A

$136 k m$
B

$68 k m$
C

$34 k m$
D

$544 k m$

Solution

Gravitational potential energy of a piece of ice at a height $(h) = m g h$
Heat absorbed by the ice to melt completely
$Δ Q = \frac{1}{4} m g h . . . . . . . (1)$
$Also, Δ Q = m L . . . . . . . (2)$
$From eqns. (1) and (2), m L = \frac{1}{4} m g h or, h = \frac{4 L}{g}$
$\begin{array}{l} Here L = 3.4 \times 10^{5} J {kg}^{- 1}, g = 10 N {kg}^{- 1} \\ ∴ h = \frac{4 \times 3.4 \times 10^{5}}{10} = 4 \times 34 \times 10^{3} = 136 km \end{array}$

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