$A$ black body calorimeter filled with hot water cools from $60^{\circ}C$ to $50^{\circ}C$ in $4 \text{ min}$ and from $40^{\circ}C$ to $30^{\circ}C$ in $8 \text{ min}$. The approximate temperature of the surrounding is ........ $^{\circ}C$.

Are the rate of heat emission and the rate of cooling the same? Explain this.

Four spheres $A, B, C$ and $D$ are of the same radius but made of different metals. Their densities are in the ratio $6 : 3 : 4 : 5$ and specific heats are in the ratio $2 : 5 : 4 : 6$. These are initially kept at the same temperature and placed in the same surroundings. The sphere which has the slowest rate of cooling is

For a system where Newton's law of cooling is applicable,the initial rate of cooling is $R \ ^\circ C/sec$. Find the time when the temperature difference $\Delta T_0$ (initial temperature difference) is reduced to half.

If a metallic sphere cools from $62^{\circ}C$ to $50^{\circ}C$ in $10 \; \text{minutes}$ and in the next $10 \; \text{minutes}$ cools to $42^{\circ}C$,then the temperature of the surroundings is ......... $^{\circ}C$.

According to Newton's law of cooling,the rate of cooling of a body is proportional to $(\Delta \theta )^n$,where $\Delta \theta$ is the difference of the temperature of the body and the surroundings,and $n$ is equal to