The instantaneous temperature difference between a cooling body and its surroundings,which obeys Newton's law of cooling,is $\theta$. Which of the following graphs represents the variation of $\ln \theta$ with time $t$?

The circuit below is used to heat water kept in a bucket. Assuming heat loss only by Newton's law of cooling, the variation in the temperature of the water in the bucket as a function of time is depicted by

$A$ black body calorimeter filled with hot water cools from $60^{\circ}C$ to $50^{\circ}C$ in $4 \text{ min}$ and from $40^{\circ}C$ to $30^{\circ}C$ in $8 \text{ min}$. The approximate temperature of the surrounding is ........ $^{\circ}C$.

$A$ bucket full of hot water is kept in a room. If it cools from $75^{\circ} C$ to $70^{\circ} C$ in $t_1$ minutes,from $70^{\circ} C$ to $65^{\circ} C$ in $t_2$ minutes and $65^{\circ} C$ to $60^{\circ} C$ in $t_3$ minutes,then

Two metal spheres,one solid and one hollow,are heated to $300^{\circ}C$ and allowed to cool in the same environment. The rate of heat loss will be:

In an experiment to verify Newton's law of cooling,a graph is plotted between the temperature difference $(\Delta T)$ of the water and surroundings and time as shown in the figure. The initial temperature of water is taken as $80^{\circ}C$. The value of $t_{2}$ as mentioned in the graph will be...........