$A$ cup of coffee cools from $150^{\circ} F$ to $144^{\circ} F$ in $1 \ min$ in a room at a temperature of $72^{\circ} F$. How much time will the coffee take to cool from $110^{\circ} F$ to $104^{\circ} F$ in the same room (in $min$)?

For a small temperature difference between the body and the surroundings,the relation between the rate of loss of heat $R$ and the temperature of the body $\theta$ is depicted by:

$A$ 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.

$A$ body takes $5 \ min$ to cool from $90^{\circ}C$ to $60^{\circ}C$. If the temperature of the surroundings is $20^{\circ}C$,how much time (in $min$) will it take to cool from $60^{\circ}C$ to $30^{\circ}C$?

$A$ body initially at $80^\circ C$ cools to $64^\circ C$ in $5$ minutes and to $52^\circ C$ in $10$ minutes. The temperature of the body after $15$ minutes will be ...... $^\circ C$.

Consider two hot bodies $B_1$ and $B_2$ which have temperatures $100^oC$ and $80^oC$ respectively at $t = 0$. The temperature of the surroundings is $40^oC$. The ratio of the respective rates of cooling $R_1$ and $R_2$ of these two bodies at $t = 0$ will be