$A$ 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........ $J/^{\circ}C$.

If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$,the graph between the temperature $T$ of the metal and time $t$ will be closest to:

$A$ liquid is filled in a vessel which is kept in a room with a temperature of $20^{\circ}C$. When the temperature of the liquid is $80^{\circ}C$,it loses heat at the rate of $60 \; cal/sec$. What will be the rate of loss of heat when the temperature of the liquid is $40^{\circ}C$ in $cal/sec$?

In Newton's experiment of cooling,the water equivalent of two similar calorimeters is $10 \ g$ each. They are filled with $350 \ g$ of water and $300 \ g$ of a liquid (equal volumes) separately. The time taken by water and liquid to cool from $70^{\circ}C$ to $60^{\circ}C$ is $3 \ min$ and $95 \ s$ respectively. The specific heat of the liquid will be ...... $Cal/g^{\circ}C$.

$A$ bucket full of hot water is kept in a room. If it cools from $75^{\circ} C$ to $70^{\circ} C$ in $t_1$ minutes,from $70^{\circ} C$ to $65^{\circ} C$ in $t_2$ minutes and $65^{\circ} C$ to $60^{\circ} C$ in $t_3$ minutes,then

$A$ 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 $300 \text{ K}$)