A $100 \,g$ of iron nail is hit by a $1.5\, kg$ hammer striking at a velocity of $60\, ms ^{-1}$. $............^{\circ}C$ will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail .

[Specific heat capacity of iron  $=0.42\, Jg ^{-1}{ }\,^{\circ}C ^{-1}$ ]

$80\, gm$ of water at $30°C$ are poured on a large block of ice at $0°C.$ The mass of ice that melts is ........ $gm$

$20\, gm$ of boiling water is poured into an ice-cold brass vessel (specific heat $0.1\, cal/gm-\,^oC$) of mass $100\, gm$. The resulting temperature is ........ $^oC$

$2\, kg$ of ice at $-20°C$ is mixed with $5\, kg$ of water at $20°C$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $1\, kcal/kg\, per °C$ and $0.5\, kcal/kg/°C$ while the latent heat of fusion of ice is $80\, k\,cal/kg$ ........ $kg$

If $1\; g$ of steam is mixed with $1\; g$ of ice, then the resultant temperature of the mixture is ........ $^oC$

The heat required to change $1 \,kg$ of ice at $-8^{\circ} C$ into water at $20^{\circ} C$. at $1 \,atm$ of pressure, is closest to .............$\,kJ$ (Assume that ice has a specific heat capacity $2.1 \,kJ / kg / K$. water has a specific heat capacity $4.2 \,kJ / kg / K$, and latent heat of fusion of ice is $333 \,kJ / kg$ )