$A$ body cools from $75 \, ^\circ \text{C}$ to $65 \, ^\circ \text{C}$ in $2 \, \text{min}$ in a room at $30 \, ^\circ \text{C}$. How long will it take to cool from $55 \, ^\circ \text{C}$ to $45 \, ^\circ \text{C}$ in the same room?

$A$ body takes $5$ minutes for cooling from $50^oC$ to $40^oC$. Its temperature comes down to $33.33^oC$ in the next $5$ minutes. The temperature of the surroundings is ....... $^oC$.

$A$ pan filled with hot food cools from $94^{\circ}C$ to $86^{\circ}C$ in $2$ minutes. When the room temperature is $20^{\circ}C$, how long will it take to cool from $74^{\circ}C$ to $66^{\circ}C$?

$A$ solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is $T$,then

$A$ 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 $s = 4200 \ J \ kg^{-1} \ K^{-1}$)

The initial temperature of a body is $80^{\circ}C$. If its temperature falls to $64^{\circ}C$ in $5$ minutes and in $10$ minutes to $52^{\circ}C$,then the temperature of the surrounding will be ...... $^{\circ}C$.