$A$ thermally insulated vessel contains $150\, g$ of water at $0\, ^oC$. Then the air from the vessel is pumped out adiabatically. $A$ fraction of water turns into ice and the rest evaporates at $0\, ^oC$ itself. The mass of evaporated water will be closest to ....... $g$ (Latent heat of vaporization of water $= 2.10 \times 10^6\, J/kg$ and Latent heat of fusion of water $= 3.36 \times 10^5\, J/kg$).

$A$ thermocouple produces $40 \, \mu V/K$. The temperatures of the cold and hot junctions are $40 \, ^\circ C$ and $20 \, ^\circ C$ respectively. If $150$ such thermocouples are connected in series,what is the total thermo-emf produced in $mV$?

Consider a rectangular sheet of solid material of length $l=9 \ cm$ and width $d=4 \ cm$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \ K^{-1}$ at room temperature and one atmospheric pressure. The mass of the sheet is $m=0.1 \ kg$ and the specific heat capacity is $C_v=900 \ J \ kg^{-1} K^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \ J$,then the change in area of the rectangular sheet is:

$A$ child running a temperature of $101\,^{\circ} F$ is given an antipyrin (i.e. a medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to $98\,^{\circ} F$ in $20$ minutes,what is the average rate of extra evaporation caused by the drug (in $g/min$)? Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is $30\; kg$. The specific heat of the human body is approximately the same as that of water,and the latent heat of evaporation of water at that temperature is about $580\; cal \;g^{-1}$.

Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of $0.1 \,g/s$. It melts completely in $100 \,s$. The rate of rise of temperature of the resulting water thereafter will be ............ $^{\circ}C/s$.

$A$ 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).