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 container with $1 kg$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 Wm ^{-2}$ and it is absorbed by the water over an effective area of $0.05 m ^2$. Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${ }^{\circ} C$ ) in the temperature of water and the surroundings after a long time will be. . . . . . . . (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 s ^{-1}$, Heat capacity of water $\left.=4200 J kg ^{-1} K ^{-1}\right)$

A body cools in $7$ minutes from $60^{\circ}\,C$ to $40^{\circ}\,C$. The temperature of the surrounding is $10^{\circ}\,C$. The temperature of the body after the next $7$ minutes will be

Certain quantity of water cools from $70^o  C$ to $60^o C$ in the first $5$ minutes and to $54^o C$ in the next $5$ minutes. The temperature of the surroundings is ….. $^oC$