For a system with newtons law of cooling applicable the initial rate of cooling is $R^0\  C/sec$ find the time when temperature diff. $\Delta T_0 =$ initial temperature difference, is reduced to half.

Hot water cools from ${60^o}C$ to ${50^o}C$ in the first $10$ minutes and to ${42^o}C$ in the next $10$ minutes. The temperature of the surrounding is ……… $^oC$

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 …… $^oC$

A sphere of density $\rho $ , specific heat capacity $c$ and radius $r$ is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of sphere and is proportional to

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