Two thermometers are used to record the temperature of a room. If the bulb of one is wrapped in a wet hanky,which of the following statements is correct?

The temperature on a Fahrenheit temperature scale that is twice the temperature on a Celsius temperature scale is: (in $^{\circ} F$)

$A$ hypothetical thermometer reads $5^{\circ} C$ in melting ice and $99^{\circ} C$ at the steam point. What is the correct temperature in $^{\circ} F$ when this faulty thermometer reads $52^{\circ} C$?

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?

Write the relation between Celsius and Fahrenheit scales with a graph.

The surface of the lake is at $2^{\circ}C$. Find the temperature of the bottom of the lake in $^{\circ}C$.