$A$ hollow copper sphere $S$ and a hollow copper cube $C$,both with negligible thin walls of the same surface area,are filled with water at $90^{\circ}C$ and allowed to cool in the same environment. The graph that correctly represents their cooling is:

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 ......... $^{\circ}C$.

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

$A$ liquid cools down from $70^{\circ}C$ to $60^{\circ}C$ in $5$ minutes. The time taken to cool it from $60^{\circ}C$ to $50^{\circ}C$ will be

$A$ system $S$ receives heat continuously from an electrical heater of power $10 \ W$. The temperature of $S$ becomes constant at $50^{\circ}C$ when the surrounding temperature is $20^{\circ}C$. After the heater is switched off, $S$ cools from $35.1^{\circ}C$ to $34.9^{\circ}C$ in $1 \ minute$. The heat capacity of $S$ is........ $J/^{\circ}C$.

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