$A$ 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 $L = 3.4 \times 10^{5} \text{ J/kg}$ and $g = 10 \text{ N/kg}$) (in $\text{ km}$)

$A$ boy is able to chew $20 \, g$ of ice cream in $5 \, minutes$. Calculate the power of the boy in horse power $(HP)$. (Assume the latent heat of fusion of ice is $80 \, cal/g$ and $1 \, cal = 4.2 \, J$).

The thermo $e.m.f.$ of a thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700\,^{\circ}C$. If the cold junction is kept at $0\,^{\circ}C$,then the neutral temperature is:

$10 \, g$ of ice at $0^{\circ} C$ is kept in a calorimeter of water equivalent $10 \, g$. How much heat (in $cal$) should be supplied to the apparatus to evaporate the water thus formed? (Neglect loss of heat)

$A$ glass flask of volume $1$ litre is fully filled with mercury at $0\,^{\circ}C$. Both the flask and mercury are now heated to $100\,^{\circ}C$. If the coefficient of volume expansion of mercury is $1.82 \times 10^{-4}/^{\circ}C$ and the coefficient of linear expansion of glass is $10 \times 10^{-6}/^{\circ}C$,the amount of mercury which is spilled out is ............ $ml$. (in $.2$)

Why is cooking faster in a pressure cooker?