Oxygen boils at $-183^{\circ} C$. This temperature is approximately (in $^{\circ} F$)

At a common temperature,a block of wood and a block of metal feel equally cold or hot. The temperatures of the block of wood and the block of metal are:

On a temperature scale $Y$, water freezes at $-160^{\circ} Y$ and boils at $-50^{\circ} Y$. On this $Y$ scale, a temperature of $340 \ K$ is (in $^{\circ} Y$)

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?

$A$ thermometer bulb has a volume of $10^{-6} \,m^3$ and the cross-section of the stem is $0.002 \,cm^2$. The bulb is filled with mercury at $0^{\circ} C$. If the thermometer reads a temperature of $100^{\circ} C$, what is the length of the mercury column? (Coefficient of cubical expansion of mercury $\gamma = 18 \times 10^{-5} /{ }^{\circ} C$)

The temperature of a body is measured both in ${ }^{\circ} C$ and ${ }^{\circ} F$. $A$ graph is plotted with ${ }^{\circ} F$ on the $X$-axis and ${ }^{\circ} C$ on the $Y$-axis. Then,the cosine of the angle between the graph and the $X$-axis is