A body takes $10\, minutes$ to cool from $60\,^oC$ to $50\,^oC$. The temperature of surroundings is constant at $25\,^oC$. Then, the temperature of the body after next $10\, minutes$ will be approximately ……. $^oC$

A liquid cools from $50^oC$ to $45^oC$ in 5 minutes and from $45 ^o C$ to $41.5 ^o C$ in the next $5$ minutes. The temperature of the surrounding is …… $^oC$

Instantaneous temperature difference between cooling body and the surroundings obeying Newton's law of cooling is $\theta$. Which of the following represents the variation of $\ln \theta$ with time $t$ ?

The 'Kangri' is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the 'Kangri' is spherical and of surface area $7 \times 10^{-2} \,m ^{2}$. It contains $300 g$ of a mixture of coal, wood and leaves with calorific value of $30 \,kJ / g$ (and provides heat with $10 \%$ efficiency). The surface temperature of the 'Kangri' is $60^{\circ} C$ and the room temperature is $0^{\circ} C$. Then, a reasonable estimate for the duration $t$ (in h) that the 'Kangri' heat will last is (take the 'Kangri' to be a black body)

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.