$A$ 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 $L = 3.4 \times 10^{5} \text{ J/kg}$ and $g = 10 \text{ N/kg}$) (in $\text{ km}$)

$A$ solid cube of mass $m$ at a temperature $\theta_0$ is heated at a constant rate. It becomes liquid at temperature $\theta_1$ and vapour at temperature $\theta_2$. Let $s_1$ and $s_2$ be specific heats in its solid and liquid states respectively. If $L_f$ and $L_v$ are latent heats of fusion and vaporisation respectively,then the minimum heat energy supplied to the cube until it vaporises is

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

Which of the following graphs shows the variation of thermoelectric power of a thermocouple with the temperature difference between the hot and cold junctions?

If liquefied oxygen at $1$ atmospheric pressure is heated from $50\, K$ to $300\, K$ by supplying heat at a constant rate,the graph of temperature vs. time will be:

$A$ hunter fired a metallic bullet of mass $m \ kg$ from a gun towards an obstacle and it just melts when it is stopped by the obstacle. The initial temperature of the bullet is $300 \ K$. If $\frac{1}{4}$ th of the heat is absorbed by the obstacle,then the minimum velocity of the bullet is (Melting point of bullet $= 600 \ K$,Specific heat of bullet $= 0.03 \ cal \ g^{-1} {}^{\circ} C^{-1}$,Latent heat of fusion of bullet $= 6 \ cal \ g^{-1}$) (in $ms^{-1}$)