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

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 $123.4 \; \Omega$?

Check whether the following statements are True or False:
$(a)$ The equation to convert Celsius temperature to Fahrenheit is $t^{\circ}F = \frac{5}{9}t^{\circ}C + 32$.
$(b)$ For an ideal gas,absolute zero temperature is $273.15^{\circ}C$.
$(c)$ The volume of water is maximum at $4^{\circ}C$.
$(d)$ The temperature gradient is negative if a cube block is heated at the cold end and heat transfers to the hot end.

The temperature of a body shown by a faulty Celsius thermometer is $49^{\circ} C$ and by a correct Fahrenheit thermometer is $122^{\circ} F$. The correction to be applied to the faulty thermometer is

What is the value of absolute zero temperature on the Fahrenheit scale?

Explain the study of thermal properties of matter by giving definitions of temperature and heat.