Heat required to convert $5\ kg$ of ice at $0\ ^oC$ into water at $100\ ^oC$ is:

$A$ piece of ice (heat capacity = $2100 \text{ J kg}^{-1} \text{ }^\circ\text{C}^{-1}$ and latent heat = $3.36 \times 10^5 \ J kg^{-1}$) of mass $m$ grams is at $-5^oC$ 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 ...... $gm$.

Which of the following graphs shows the variation of thermoelectric power with temperature difference $\theta$ between the hot and cold junctions in thermocouples?

$A$ glass flask of volume $200 \, cm^3$ is just filled with mercury at $20^{\circ} C$. The amount of mercury that will overflow when the temperature of the system is raised to $100^{\circ} C$ is ........ $cm^3$ $(\gamma_{\text{glass}} = 1.2 \times 10^{-5} /^{\circ}C, \gamma_{\text{mercury}} = 1.8 \times 10^{-4} /^{\circ}C)$

$A$ lead bullet moving with velocity $V$ strikes a wall and stops. If $75 \%$ of its energy is converted into heat,then the increase in temperature is ($s=$ specific heat of lead,$J=$ mechanical equivalent of heat).

$A$ beaker is filled with water at $4\,^{\circ}C$. At one time the temperature is increased by a few degrees above $4\,^{\circ}C$ and at another time it is decreased by a few degrees below $4\,^{\circ}C$. One shall observe that: