A very thin metallic shell of radius $r$ is heated to temperature $T$ and then allowed to cool. The rate of cooling of shell is proportional to ……..

A container with $1 kg$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 Wm ^{-2}$ and it is absorbed by the water over an effective area of $0.05 m ^2$. Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${ }^{\circ} C$ ) in the temperature of water and the surroundings after a long time will be. . . . . . . . (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 s ^{-1}$, Heat capacity of water $\left.=4200 J kg ^{-1} K ^{-1}\right)$

In Newton's experiment of cooling, the water equivalent of two similar calorimeters is $10 $ gm each. They are filled with $350 gm$ of water and $300 gm$ of a liquid (equal volumes) separately. The time taken by water and liquid to cool from ${70^o}C$ to ${60^o}C$ is $3$ min and $95$ sec respectively. The specific heat of the liquid will be …… $Cal/gm\,^oC$

A body cools in $7$ minutes from ${60^o}C$ to ${40^o}C$ What time (in minutes) does it take to cool from ${40^o}C$ to ${28^o}C$ if the surrounding temperature is ${10^o}C$? Assume Newton’s Law of cooling holds

One day in the morning, Ramesh filled up $\frac {1}{3}$ bucket of hot water from geyser, to take bath. Remaining $\frac {2}{3}$ was to be filled by cold water (at room temperature) to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend to something which would take some times, say $5-10$ $\min$ before he could take bath. Now he had two options: $(1)$ fill the remaining bucket completely by cold water and then attend to the work, $(2)$ first  attend tothe work and fill the remaining bucket just before taking bath. Which option do you think would have kept water warmer ? Explain.