$A$ pan filled with hot food cools from $50^{\circ} C$ to $49.9^{\circ} C$ in $5 \text{ sec}$. How long will it take to cool from $40^{\circ} C$ to $39.9^{\circ} C$, if the room temperature is $30^{\circ} C$ (in $\text{ sec}$)?

$A$ body cools from $70^{\circ} C$ to $40^{\circ} C$ in $5$ minutes. Calculate the time it takes to cool from $60^{\circ} C$ to $30^{\circ} C$. The temperature of the surroundings is $20^{\circ} C$. (in $min.$)

$A$ 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

$A$ calorimeter contains $10 \ g$ of water at $20^{\circ}C$. The temperature falls to $15^{\circ}C$ in $10 \ min$. When the calorimeter contains $20 \ g$ of water at $20^{\circ}C$,it takes $15 \ min$ for the temperature to become $15^{\circ}C$. The water equivalent of the calorimeter is: (in $g$)

Two bodies $A$ and $B$ of equal masses,surface area,and emissivity are cooling under Newton's law of cooling from the same initial temperature. Their cooling curves are represented by the graph. If $\theta$ is the instantaneous temperature of the body and $\theta_0$ is the temperature of the surroundings,then the relationship between their specific heats $S_A$ and $S_B$ is:

An object is cooled from $75^{\circ} C$ to $65^{\circ} C$ in $2 \text{ min}$. The time it takes to cool from $55^{\circ} C$ to $45^{\circ} C$ is [The temperature of the surrounding is $30^{\circ} C$] (in $\text{ min}$)