A cubic metal block of mass $5 \,kg$ and edge length $0.1 \,m$ and at an initial temperature of $100^{\circ} C$ is placed on a thermally insulating flat surface and exposed to air at $0^{\circ} C$. The time in seconds required to cool the block to a temperature of $37^{\circ} C$ is closest to

(Note: Specific heat of the metal $=500 \,J / kg /{ }^{\circ} C$; Heat transfer coefficient from block to air $=50 \,W / m ^2 /{ }^{\circ} C$ )

On what does the proportionality constant depends given in Newton's law of cooling.

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

Liquid cools from $50^oC$  to  $45^oC$  in  $5\  minutes$ and from $45^oC$ to $41.5^oC$ in the next $5\   minutes$.The temperature of the surrounding is ......... $^oC$

A sphere at temperature $600\,K$ is placed in an environment of temperature is $200\,K$ . Its cooling rate is $H$ . If its temperature reduced to $400\,K$ then cooling rate in same environment will become

Cooling rate of a sphere of $600\,K$ at external environment $(200\,K)$ is $R$ . When the temperature of sphere is reduced to $400\,K$ then cooling rate of the sphere becomes