$50 \,g$ ice at $0^{\circ} C$ is dropped into a calorimeter containing $100 \,g$ water at $30^{\circ} C$. If thermal capacity of calorimeter is zero then amount of ice left in the mixture at equilibrium is .......... $g$

A mass of material exists in its solid format its melting temperature $0\,^o  C$. The following processes then occur to the material

Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.

Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$

........ $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.

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 $=125 \,J / kg K$ )

A mass of $50\,g$ of water in a closed vessel, with surroundings at a constant temperature takes $2\, minutes$ to cool from $30\,^oC$ to $25\,^oC$. A mass of $100\,g$ of another liquid in an identical vessel with identical surroundings takes the same time to cool from $30\,^oC$ to $25\,^o C$. The specific heat of the liquid is .......... $kcal/kg$ (The water equivalent of the vessel is $30\,g$.)

$10\, gm$ of ice at $0°C$ is mixed with $100 \,gm $ of water at $50°C.$ What is the resultant temperature of mixture........ $^oC$

Boiling water is changing into steam. Under this condition, the specific heat of water is