$A$ 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 ...... $^\circ C$.

The temperature of a body on the Kelvin scale is $x \ K$. When the temperature of this body is measured with a Fahrenheit thermometer,it is found to be $x \ ^\circ F$. Then $x = $......

If the values of the temperature of a body in Fahrenheit and Celsius scales are in the ratio of $13:5$,then the temperature of the body is

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?

The absolute zero temperature on the Fahrenheit scale is ........ $^\circ F$.

$A$ 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 $x_0/2$?