$A$ thermometer graduated according to a linear scale reads a value $x_0$ when in contact with boiling water,and $x_0/3$ when in contact with ice. What is the temperature of an object in ${}^oC$,if this thermometer in contact with the object reads $x_0/2$?

An ideal thermometer should have

The triple point of water is

What is the slope of the line $AB$ in the given graph?

$Assertion :$ 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.

$A$ new temperature scale uses $X$ as a unit of temperature,where the numerical value of the temperature $t_x$ in this scale is related to the absolute temperature $T$ by $t_x = 3T + 100$. If the specific heat of a material using this unit is $1400 \, J \, kg^{-1} X^{-1}$,its specific heat in the $SI$ system of units is: