When $100\,g$ of a liquid $A$ at $100\,^oC$ is added to $50\,g$ of a liquid $B$ at temperature $75\,^oC$, the temperature of the mixture becomes $90\,^oC$. The temperature of the mixture, if $100\,g$ of liquid $A$ at $100\,^oC$ is added to $50\,g$ of liquid $B$ at $50\,^oC$, will be ........$^oC$

Water of volume $2\, L$ in a closed container is heated with a coil of $1\,kW$. While water is heated, the container loses energy at a rate of $160\, J/s$ . In how much time will the temperature of water rise from $27\,^oC$ to $77\,^oC$ ? (Specific heat of water is $4.2\, kJ/kg$ and that of the container is negligible)

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 $30\,g$.)

An aluminium container of mass $100\,\, gm$ contains $200 \,\,gm$ of ice at $-20^o\,\, C$. Heat is added to the system at the rate of $100 \,\,cal/s$. The temperature of the system after $4$ minutes will be ....... $^oC$ (specific heat of ice $= 0.5$ and $L = 80 \,\,cal/gm$, specific heat of $Al= 0.2\,\, cal/gm/^o C$)

A piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $h$ is

[Latent heat of ice is $3.4 \times 10^{5}\; J / k g$ and $g=10\; N / kg ]$

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 $=125 \,J / kg K$ )