A beaker contains $200\, gm$ of water. The heat capacity of the beaker is equal to that of $20\, gm$ of water. The initial temperature of water in the beaker is $20°C.$ If $440\, gm$ of hot water at $92°C$ is poured in it, the final temperature (neglecting radiation loss) will be nearest to........ $^oC$

A lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it, the initial speed of bullet is ............ $ms ^{-1}$

(Given, initial temperature of the bullet $=127^{\circ} C$,

Melting point of the bullet $=327^{\circ} C$,

Latent heat of fusion of lead $=2.5 \times 10^{4} \,J Kg ^{-1}$,

Specific heat capacity of lead $=125 \,J / kg K$ )

The temperature of equal masses of three different liquids $A, B$ and $C$ are $12°C, 19°C$ and $28°C$ respectively. The temperature when $A$ and $B$ are mixed is $16°C$ and when $B$ and $C$ are mixed is $23°C$. The temperature when $A$ and $C$ are mixed is........ $^oC$

Due to cold weather a $1\, {m}$ water pipe of cross-sectional area $1\, {cm}^{2}$ is filled with ice at $-10^{\circ} {C}$. Resistive heating is used to melt the ice. Current of $0.5\, {A}$ is passed through $4\, {k} \Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In ${s}$)

(Given latent heat of fusion for water/ice $=3.33 \times 10^{5}\, {J} {kg}^{-1}$, specific heat of ice $=2 \times 10^{3}\, {J}$ ${kg}^{-1}$ and density of ice $=10^{3}\, {kg} / {m}^{3}$

$100 \,gm$ of ice at $0°C$ is mixed with $100\, g$ of water at $100°C.$ What will be the final temperature of the mixture .......... $^oC$

Find the amount of heat supplied to decrease the volume of an ice water mixture by $1 \,\,cm^3$ without any change in temperature. $(\rho_ {ice} = 0.9 \rho_{water}, L_{ice} = 80 \,\,cal/gm).$ ......... $cal$