The temperature of a body on the Kelvin scale is found to be $X \; K$. When it is measured by a Fahrenheit thermometer,it is found to be $X \; ^\circ F$. Then $X$ is:

Write the equation that gives the relation between $t_F$ and $t_C$.

$A$ scientist proposes a new temperature scale in which the ice point is $25 X$ ($X$ is the new unit of temperature) and the steam point is $305 X$. The specific heat capacity of water in this new scale is (in $J kg^{-1} X^{-1}$):

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?

Water has maximum density at

If a graph is plotted with Fahrenheit temperature on the $Y$-axis and Celsius temperature on the $X$-axis,the resulting straight line is one that .....