$A$ 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 $cal/sec$.

$A$ system $S$ receives heat continuously from an electrical heater of power $10 \ W$. The temperature of $S$ becomes constant at $50^{\circ}C$ when the surrounding temperature is $20^{\circ}C$. After the heater is switched off, $S$ cools from $35.1^{\circ}C$ to $34.9^{\circ}C$ in $1 \ minute$. The heat capacity of $S$ is........ $J/^{\circ}C$.

$A$ 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?

$A$ body cools in a surrounding which is at a constant temperature of $\theta_0$. Assume that it obeys Newton's law of cooling. Its temperature $\theta$ is plotted against time $t$. Tangents are drawn to the curve at the points $P(\theta = \theta_2)$ and $Q(\theta = \theta_1)$. These tangents meet the time axis at angles of $\varphi_2$ and $\varphi_1$,as shown in the figure.

The rate of cooling at $600 \ K$ is $R$,given the surrounding temperature is $300 \ K$. What is the rate of cooling at $900 \ K$?

$A$ solid copper cube of edges $1\;cm$ is suspended in an evacuated enclosure. Its temperature is found to fall from $100^{\circ}C$ to $99^{\circ}C$ in $100\;s$. Another solid copper cube of edges $2\;cm$,with similar surface nature,is suspended in a similar manner. The time required for this cube to cool from $100^{\circ}C$ to $99^{\circ}C$ will be approximately ...... $s$.