$A$ steam engine intakes $50 \, g$ of steam at $100^{\circ} C$ per minute and cools it down to $20^{\circ} C$. If the latent heat of vaporization of steam is $540 \, cal \, g^{-1}$,then the heat rejected by the steam engine per minute is .........$\times 10^{3} \, cal$.

$A$ 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 $\text{ km}$)

$A$ hammer of mass $1 \, kg$ having a speed of $50 \, m/s$ hits an iron nail of mass $200 \, g$. If the specific heat of iron is $0.105 \, cal/g^{\circ}C$ and half of the kinetic energy is converted into heat,the rise in temperature of the nail is ........ $^{\circ}C$.

For a copper-iron $(Cu-Fe)$ couple,the thermo $e.m.f.$ (temperature of cold junction $= 0\,^{\circ}C$) is given by $E = (14\theta - 0.02\theta^2)\,\mu V$. The neutral temperature will be

$A$ 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 $1 \, cal = 4.2 \, J$).

$500\, g$ of water and $100\, g$ of ice at $0\,^{\circ}C$ are in a calorimeter whose water equivalent is $40\, g$. $10\, g$ of steam at $100\,^{\circ}C$ is added to it. Then the final amount of water in the calorimeter is ....... $g$ (Latent heat of ice $= 80\, cal/g$,Latent heat of steam $= 540\, cal/g$).