$A$ new temperature scale uses $X$ as a unit of temperature,where the numerical value of the temperature $t_x$ in this scale is related to the absolute temperature $T$ by $t_x = 3T + 100$. If the specific heat of a material using this unit is $1400 \, J \, kg^{-1} X^{-1}$,its specific heat in the $SI$ system of units is:

On the Celsius scale,the temperature of a body increases by $40^{\circ} C$. The increase in temperature on the Fahrenheit scale is: (in $^{\circ} F$)

At $NTP$,water boils at $100^{\circ}C$. Deep down in a mine,water will boil at a temperature:

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?

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

What is the value of the fixed point on the standard (Kelvin) scale?