At temperatures close to $0\ K$ , the heat capacity $C$ of a certain solid is related to its temperature $T$ by the equation $C = aT^3$ , where a is a constant characteristic of the solid. Heat is supplied to the solid at a steady rate. Which graph best represents the variation of its temperature $T$ with time $t$ ?

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 spectfic heat of human body is approximately the same as that of water, and latent heat of evaporation of water at that temperature is about $580\; cal \;g^{-1}$.

Heat is supplied to a certain homogenous sample of matter, at a uniform rate. Its temperature is plotted against time, as shown. Which of the following conclusions can be drawn

When $M_1$ gram of ice at $-10\,^oC$ (specific heat $= 0.5\, cal\, g^{-1}\,^oC^{-1}$) is added to $M_2$ gram of water at $50\,^oC$, finally no ice is left and the water is at $0\,^oC$. The value of latent heat of ice, in $cal\, g^{-1}$ is

A stationary object at $4°C$ and weighing $3.5\, kg$ falls from a height of $2000\, m$ on a snow mountain at  $0°C$. If the temperature of the object just before hitting the snow is $0°C$ and the object comes to rest immediately $(g = 10\,m/{s^2})$ and (latent heat of ice$ = 3.5 \times {10^5}\,joule/\sec $), then the object will melt