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 contains hot water at ${100^o}C$. If in time ${T_1}$ temperature falls to ${80^o}C$ and in time ${T_2}$ temperature falls to ${60^o}C$ from ${80^o}C$, then

For a system with newtons law of cooling applicable the initial rate of cooling is $R^0\  C/sec$ find the time when temperature diff. $\Delta T_0 =$ initial temperature difference, is reduced to half.

$Assertion :$ A tube light emits white light.
$Reason :$ Emission of light in a tube takes place at a very high temperature.

A body takes $10$ minutes to cool down from $62^o C$ to $50^o C$. If the temperature of surrounding is $26^o C$ then in the next $10$ minutes temperature of the body will be ......... $^oC$

Hot water kept in a beaker placed in a room cools from ${70^o}C$ to $60°C$ in $4$ minutes. The time taken by it to cool from ${69^o}C$ to ${59^o}c$ will be