Answer the following:
(a) The triple-point of water is a standard fixed point in modern thermometry.
Why? What is wrong in 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 number 0°C and 100°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 tc on the Celsius scale by
tc = 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) The melting point of ice and boiling point of water are temperature and pressure dependent but the triple point of water is not. Hence, the triple-point of water is a standard fixed point in modern thermometry.
(b) The absolute zero temperature or 0K is the other fixed point on the Kelvin scale.
(c) The temperature 273.16 K is the triple point of water. The temperature 273.15 K which is the melting point of ice in Kelvin scale corresponds to 0°C in Celsius scale. Hence, the relation has 273.15 in it and not 273.16.
(d) Let TF be the temperature on Fahrenheit scale and TK be the temperature on absolute scale.
The relation between both the temperatures is as follows:
(TF - 32)/180 = (TK - 273.15)/100 …………(1)
Let TF’ be the temperature on Fahrenheit scale and TK’ be the temperature on absolute scale.
The relation between both the temperatures is as follows:
(TF’ - 32)/180 = (TK’ - 273.15)/100 …………(2)
It is given that TK’ – TK = 1 K
Subtracting equation (1) from equation (2), we get
(TF’ – TF)/180 = (TK’ - TK)/100 = 1/100
⇒ TF’ – TF = (1×180)/100
⇒ TF’ = 9/5
Triple point of water = 273.16 K
∴ Triple point of water on absolute scale, T = 273.16×(9/5)
⇒ T = 491.69
NOTE: The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.