If a metallic sphere cools from $62^{\circ}C$ to $50^{\circ}C$ in $10 \; \text{minutes}$ and in the next $10 \; \text{minutes}$ cools to $42^{\circ}C$,then the temperature of the surroundings is ......... $^{\circ}C$.

$A$ bowl filled with very hot soup cools from $98^{\circ}C$ to $86^{\circ}C$ in $2$ minutes when the room temperature is $22^{\circ}C$. How many minutes will it take to cool from $75^{\circ}C$ to $69^{\circ}C$?

$A$ container with $1 \ kg$ of water is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received from sunlight is $700 \ W \ m^{-2}$ 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 the effect of the container, and take the constant for Newton's law of cooling $k = 0.001 \ s^{-1}$, Heat capacity of water $s = 4200 \ J \ kg^{-1} \ K^{-1}$)

$A$ solid sphere and a hollow sphere of the same material and same radius are heated to the same temperature. They are placed in an environment of the same temperature. If the temperature difference between both and the surroundings is $T$,then .......

$A$ 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 $P(\theta = \theta_2)$ and $Q(\theta = \theta_1)$. These tangents meet the time axis at angles of $\varphi_2$ and $\varphi_1$,as shown in the figure.

$A$ bowl filled with very hot water cools from $98^\circ C$ to $86^\circ C$ in $2$ minutes when the room temperature is $22^\circ C$. How long will it take to cool from $75^\circ C$ to $69^\circ C$?