$Assertion :$ In a pressure cooker,water is brought to a boil. The cooker is then removed from the stove. Now,upon removing the lid of the pressure cooker,the water starts boiling again.
$Reason :$ The impurities in water bring down its boiling point.

On a linear temperature scale $Y$,water freezes at $-160^{\circ}Y$ and boils at $-50^{\circ}Y$. On this $Y$ scale,a temperature of $340\,K$ would be read as........ $^{\circ}Y$ (water freezes at $273\,K$ and boils at $373\,K$).

If $H_C, H_K$ and $H_F$ are the heat required to raise the temperature of one gram of water by one degree Celsius,Kelvin,and Fahrenheit temperature scales respectively,then:

Answer the following:
$(a)$ The triple-point of water is a standard fixed point in modern thermometry. Why? What is wrong with taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)?
$(b)$ There were two fixed points in the original Celsius scale as mentioned above,which were assigned the numbers $0^{\circ}C$ and $100^{\circ}C$ respectively. On the absolute scale,one of the fixed points is the triple-point of water,which on the Kelvin absolute scale is assigned the number $273.16\; K$. What is the other fixed point on this (Kelvin) scale?
$(c)$ The absolute temperature (Kelvin scale) $T$ is related to the temperature $t_c$ on the Celsius scale by $t_c = T - 273.15$. Why do we have $273.15$ in this relation,and not $273.16$?
$(d)$ What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?

On the Celsius scale,the temperature of a body increases by $40^{\circ} C$. The increase in temperature on the Fahrenheit scale is: (in $^{\circ} F$)

$A$ Centigrade and a Fahrenheit thermometer are dipped in boiling water. The water is then cooled until the Fahrenheit thermometer reads $140 ^\circ F$. The corresponding drop in temperature as recorded by the Centigrade thermometer is ...... $^\circ C$.