#1

(a) The triple point of water is a standard fixed point in modem thermometer. Why ? What is wrong in taking melting point of ice and the boiling point of water as standard fixed points (as was originally done in Celsius scale) ?
(b) There were two fixed points in the original Celsius scale as mentioned above which were assigned the numbers 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 ?
© The absolute temperature (Kelvin scale) T is related to the temperature T 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 triple point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale ?

#2

This is due to the triple {joint of water is unique condition of temperature and pressure, i.e., it occurs only at one particular set* of values of pressure and temperature. Hence, it is easily reproducible. Hence it is used as a standard temperature in thermometry.
The melting point of ice and boiling point of water are pressure dependent it mean they change with change in the value of pressure. They are also very sensitive to the dissolved impurities. Therefore these have been discarded as a reference point triple of water has been taken as a fixed point.
(b) The 0 K or absolute zero itself is the other fixed point
on the absolute scale of temperature. It corresponds to the temperature when the volume and pressure of a gas will become zero.
© Triple point is 0.01°C and not 0°C. Thus to make
a celsius degree equal to Kelvin degree 273.15 is assigned instead of 273.16. Moreover ice point on Kelvin scale is 273.15 K and the corresponding is point on Celsius scale is 0°C which is clear from the relation, i.e.,\${{t}_{c}}\$ = T - 273.15 when we have 273.16 instead of 273.15 in the above relation, then the ice point on celsius scale will be 0 - 0.01°C which is not the case.
(d) The unit interval size of Fahrenheit scale is 212 - 32= 180 is given by
T = 273.16x180/100=491.69