$A$ container is filled with a liquid that cools from $100^{\circ}C$ to $70^{\circ}C$ in $5 \text{ min}$, when kept at a room temperature of $30^{\circ}C$. The time that it must have taken to cool down to $80^{\circ}C$ from its initial temperature is approximately: (in $\text{ min}$)

$A$ liquid of mass $250 g$ is kept warm in a vessel using an electric heater. The liquid is maintained at $57^{\circ} C$ when the power supplied by the heater is $30 W$ and the surrounding temperature is $27^{\circ} C$. As the heater is switched off,it takes $10 s$ for the temperature of the liquid to fall from $47^{\circ} C$ to $46.9^{\circ} C$. The specific heat capacity of the liquid is:

Two solid spheres $A$ and $B$ made of the same material have radii $r_A$ and $r_B$ respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of $A$ and $B$ is :

$A$ sphere,a cube,and a disc,all of the same material,quality,and volume,are heated to $600\,^{\circ}C$ and left in air. Which of these will have the lowest rate of cooling?

State Newton's law of cooling and derive its mathematical equation.

Two identical beakers $A$ and $B$ contain equal volumes of two different liquids at $60\,^oC$ each and are left to cool down. The liquid in $A$ has a density of $8 \times 10^2\, kg/m^3$ and a specific heat of $2000\, Jkg^{-1}K^{-1}$,while the liquid in $B$ has a density of $10^3\, kg/m^3$ and a specific heat of $4000\, Jkg^{-1}K^{-1}$. Which of the following best describes their temperature versus time graph schematically? (Assume the emissivity of both the beakers to be the same.)