$A$ metal sphere cools at a rate of $1.5^{\circ} C / min$ when its temperature is $80^{\circ} C$. When the temperature of the sphere is $40^{\circ} C$,its rate of cooling is $0.3^{\circ} C / min$. The temperature of the surrounding $\left(\theta_0\right)$ is (in $^{\circ} C$)

$A$ sphere having temperature $600 \text{ K}$ is losing heat due to radiation. At this temperature its rate of cooling is $R$. The rate of cooling of this sphere at $400 \text{ K}$ is $\frac{x}{243}R$. The value of $x$ is (Temperature of surrounding is $300 \text{ K}$)

$A$ copper cube of side $a$ is heated and allowed to cool in a vacuum. It takes time $t$ to cool from temperature $\theta_1$ to $\theta_2$. Now,another copper cube of side $2a$ is allowed to cool in the same environment. How much time will it take to cool from $\theta_1$ to $\theta_2$?

$A$ liquid is filled in a container and placed in a room at a temperature of $20^{\circ}C$. When the temperature of the liquid is $80^{\circ}C$,it loses heat at a rate of $60 \, cal/sec$. Find the rate of heat loss when the temperature of the liquid is $40^{\circ}C$ in $cal/sec$.

The temperature of a body falls from $62^\circ C$ to $50^\circ C$ in $10$ minutes. If the temperature of the surroundings is $26^\circ C$,the temperature in the next $10$ minutes will become ...... $^\circ C$.

Two metallic spheres $S_1$ and $S_2$ are made of the same material and have identical surface finish. The mass of $S_1$ is three times that of $S_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of $S_1$ to that of $S_2$ is