It is possible for a substance to coexist in all three phases in equilibrium,when the substance is at

$A$ metal ball immersed in alcohol weighs $W_1$ at $0^{\circ}C$ and $W_2$ at $50^{\circ}C$. The coefficient of cubical expansion of the metal $(\gamma)_m$ is less than that of alcohol $(\gamma)_{Al}$. Assuming that the density of the metal is large compared to that of alcohol,it can be shown that:

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:

$A$ sphere of ice at $0^{\circ}C$ having initial radius $R$ is placed in an environment having ambient temperature $> 0^{\circ}C$. The ice melts uniformly,such that the shape remains spherical. After a time $t$,the radius of the sphere has reduced to $r$. Assuming the rate of heat absorption is proportional to the surface area of the sphere at any moment,which graph best depicts $r(t)$?

$A$ lead bullet at $27\ ^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle,the velocity of the bullet at the time of striking is ....... $m/s$. (Melting point of lead $= 327\ ^oC$,specific heat of lead $= 0.03\ cal/g\ ^oC$,latent heat of fusion of lead $= 6\ cal/g$,and $J = 4.2\ J/cal$)

$A$ geyser heats water flowing at the rate of $3.0 \, L/min$ from $27 \, ^{\circ}C$ to $77 \, ^{\circ}C$. If the geyser operates on a gas burner,what is the rate of consumption (in $g/min$) of the fuel if its heat of combustion is $4.0 \times 10^{4} \, J/g$?