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 ........

On what does the proportionality constant depends given in Newton's law of cooling.

A body cools in a surrounding which is at a constant temperature of ${\theta _0}$. Assume that it obeys Newton's law of cooling. Its temperature $\theta $ is plotted against time $t$ . Tangents are drawn to the curve at the points $P(\theta = {\theta _1})$ and $Q(\theta = {\theta _2})$. These tangents meet the time axis at angles of ${\varphi _2}$and ${\varphi _1}$, as shown

Newton’s law of cooling, holds good only if the temperature difference between the body and the surroundings is

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.

A solid cube and a solid sphere of identical material and equal masses are heated to the same temperature and left to cool in the same surroundings. Then,