A piece of ice (heat capacity $=$ $2100$ $J kg^{-1}$ $^o C^{-1}$ and latent heat $=$ $3.36$ $×$ $10^5$ $J kg^{-1}$) of mass $m$ grams is at $-5^o C$ at atmospheric pressure. It is given $420$ $J$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1$ $gm$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is ...... $gm$

A heater supplying constant power $P$ watts is switched $ON$ at time $t=0 \,min$ to raise the temperature of a liquid kept in a calorimeter of negligible heat capacity. A student records the temperature of the liquid $T(t)$ at equal time intervals. A graph is plotted with $T(t)$ on the $Y$-axis versus $t$ on the $X$-axis. Assume that there is no heat loss to the surroundings during heating. Then,

Pure water super cooled to $-15^o C$ is contained in a thermally insulated flask. Small amount of ice is thrown into the flask. The fraction of water frozen into ice is :

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

Water is used to cool radiators of engines in car because

An earthen pitcher used in summer cools water in it essentially by evaporation of water from its porous surface. If a pitcher carries $4 \,kg$ of water and the rate of evaporation is $20$ g per hour, temperature of water in it decreases by $\Delta T$ in two hours. The value of $\Delta T$ is close to ........... $^{\circ} C$ (ratio of latent of evaporation to specific heat of water is $540^{\circ} C$