$10\,gm$ of ice at $0\,^oC$ is mixed with $'m'\,gm$ of water at $50\,^oC$ . ........ $gm$ is minimum value of $m$ so that ice melts completely. ( $L_f = 80\,cal/gm$ and $S_W = 1\,cal/gm-\,^oC$ )

sphere of $0.047 \;kg$ aluminium is placed for sufficient time in a vessel containing boiling water, so that the sphere is at $100\,^{\circ} C .$ It is then immediately transfered to $0.14 \;kg$ copper calorimeter containing $0.25\; kg$ water at $20\,^{\circ} C$. The temperature of water rises and attains a steady state at $23\,^{\circ} C$. Calculate the specific heat capacity of aluminium in $kJ\;kg^{-1} K^{-1}$ 

Calculate the heat required to convert $3\; kg$ of ice at $-12\,^{\circ} C$ kept in a calorimeter to steam at $100\,^{\circ} C$ at atmospheric pressure. Given specific heat capacity of $ice =2100\; J \,kg ^{-1} K ^{-1}$. specific heat capacity of water $=4186\; J kg ^{-1} K ^{-1}$, latent heat of fusion of ice $=3.35 \times 10^{5} \;J \,kg ^{-1}$ and latent heat of steam $=2.256 \times 10^{6}\; J \,kg ^{-1}$

A steam engine intakes $50\, g$ of steam at $100^{\circ} C$ per minute and cools it down to $20^{\circ} C$. If 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.$

The water equivalent of $20 \,g$ of aluminium (specific heat $0.2 \,cal ^{-1}{ }^{\circ} C ^{-1}$ ), is ......... $g$

Calorie is defined as the amount of heat required to raise temperature of $1g$ of water by $1°C$ and it is defined under which of the following conditions