Read the following statements:

$A.$ When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.

$B.$ Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10^{\circ}\,C$ and $20^{\circ}\,C$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1: 1.15$

$C.$ A carnot Engine working between $100\,K$ and $400\,K$ has an efficiency of $75 \%$

$D.$ When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

A body takes $5$ minutes for cooling from ${50^o}C$ to ${40^o}C.$ Its temperature comes down to ${33.33^o}C$ in next $5$ minutes. Temperature of surroundings is ……. $^oC$ 

Equal masses of two liquids are filled in two similar calorimeters. The rate of cooling will

In an experment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference $(\Delta T )$ of the water and surroundings and time as shown in figure. The initial temperature of water is taken as $80^{\circ} \,C$. The value of $t _{2}$ as mentioned in the graph will be………..

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