$A$ liquid of mass $250 g$ is kept warm in a vessel using an electric heater. The liquid is maintained at $57^{\circ} C$ when the power supplied by the heater is $30 W$ and the surrounding temperature is $27^{\circ} C$. As the heater is switched off,it takes $10 s$ for the temperature of the liquid to fall from $47^{\circ} C$ to $46.9^{\circ} C$. The specific heat capacity of the liquid is:

Two circular discs $A$ and $B$ with equal radii and equal mass are blackened. They are heated to the same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

$A$ liquid in a beaker has temperature $\theta(t)$ at time $t$ and $\theta_0$ is the temperature of the surroundings. According to Newton's law of cooling,the correct graph between $\log_e(\theta - \theta_0)$ and $t$ is:

One day in the morning,Ramesh filled up $\frac{1}{3}$ of a bucket with hot water from a geyser to take a bath. The remaining $\frac{2}{3}$ was to be filled with cold water (at room temperature) to bring the mixture to a comfortable temperature. Suddenly,Ramesh had to attend to some work that would take $5-10 \text{ min}$ before he could take a bath. He had two options: $(1)$ fill the remaining bucket completely with cold water and then attend to the work,$(2)$ first attend to the work and then fill the remaining bucket just before taking a bath. Which option do you think would have kept the water warmer? Explain.

$A$ 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.

$A$ certain quantity of water cools from $70^\circ C$ to $60^\circ C$ in the first $5$ minutes and to $54^\circ C$ in the next $5$ minutes. The temperature of the surroundings is ..... $^\circ C$