Temperature of water at the surface of a lake is $ -20^{\circ}C$. Then,the temperature of water just below the lower surface of the ice layer is ...... $^{\circ}C$.

Maximum density of $H_2O$ is at the temperature

What is the difference between $^oC$ and $^oF$ thermometer values for freezing and boiling points of water?

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 electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:
$R = R_{0} [1 + \alpha (T - T_{0})]$
The resistance is $101.6 \; \Omega$ at the triple-point of water $(273.16 \; K)$,and $165.5 \; \Omega$ at the normal melting point of lead $(600.5 \; K)$. What is the temperature (in $K$) when the resistance is $123.4 \; \Omega$?

Explain the concept of heat and temperature based on everyday experience.