A bullet moving with velocity $v$ collides against a wall. Consequently, half of its kinetic energy is converted into heat. If the whole heat is acquired by the bullet, the rise in temperature will be,

$2 \mathrm{kg}$ ice at $-20°\mathrm{C}$ is mixed with $5 \mathrm{kg}$ water at $20°\mathrm{C}$. Then final amount of water in the mixture would be;

(Given specific heat of ice $=0.5\mathrm{cal}/\mathrm{g}°\mathrm{C}$, specific heat of water $=1\mathrm{cal}/\mathrm{g}°\mathrm{C}$ and latent heat of fusion of ice $=80\mathrm{cal}/\mathrm{g}$)

A block of mass $2.5 \mathrm{kg}$ is heated to a temperature of $500°\mathrm{C}$ and placed on a large ice block. What is the maximum amount of ice that can melt (approximately)?

(specific heat for the body$=0.1 \mathrm{cal} {\mathrm{g}}^{-1} °{\mathrm{C}}^{-1}$)

$1 \mathrm{kg}$ of ice at $–10°\mathrm{C}$ is mixed with $4.4 \mathrm{kg}$ of water at $30°\mathrm{C}$. The final temperature of mixture is,

(specific heat of ice$=2100 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{k}}^{-1}$, specific heat of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{k}}^{-1}$, Latent heat of ice $=3.36\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$ )

The amount of heat required to convert $1 \mathrm{g}$ of ice at $0°\mathrm{C}$ into steam at $100°\mathrm{C}$ is,

Specific heat of water $=1 \mathrm{cal} {\mathrm{g}}^{-1} °{\mathrm{C}}^{-1}$, Latent heat of vaporisation $=540 \mathrm{cal} {\mathrm{g}}^{-1}$