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 $3.4\times {10}^{5}J/kgandg=10N/kg$]

Moderate

Solution

Gravitational potential energy of a piece of ice at a height $\left(h\right)=mgh$

Heat absorbed by the ice to melt completely

$\Delta Q=\frac{1}{4}mgh.......\left(1\right)$

$\text{Also,}\Delta Q=mL.......\left(2\right)$

$\text{From eqns. (1) and (2),}mL=\frac{1}{4}mgh\text{or,}h=\frac{4L}{g}$

$\begin{array}{l}\text{Here}L=3.4\times {10}^{5}\mathrm{J}{\mathrm{kg}}^{-1},g=10\mathrm{N}{\mathrm{kg}}^{-1}\\ \therefore h=\frac{4\times 3.4\times {10}^{5}}{10}=4\times 34\times {10}^{3}=136\mathrm{km}\end{array}$

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