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 $${{0}^{{}^\circ }}C$$ 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 $$273.16K$$. What is the other fixed point on this (kelvin) scale?$$c.$$ The absolute temperature (kelvin scale) $$T$$ is relate to the temperature $${{t}_{\begin{smallmatrix} c \\ \end{smallmatrix}}}$$ on the celsius scale by$${{t}_{\begin{smallmatrix} c \\ \end{smallmatrix}}}=T-273.15$$. 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?

Question

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 $${{0}^{{}^\circ }}C$$ 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 $$273.16K$$. What is the other fixed point on this (kelvin) scale?$$c.$$ The absolute temperature (kelvin  scale) $$T$$ is relate to the temperature $${{t}_{\begin{smallmatrix}  c \\   \end{smallmatrix}}}$$ on the celsius scale by$${{t}_{\begin{smallmatrix}  c \\   \end{smallmatrix}}}=T-273.15$$. 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?

Vedantu Content Team · Accepted Answer

Hint:  $$a.$$ While talking about it we should be aware that it should remain constant at all  times. It should not vary with any parameters such as pressure. $$b.$$ The name absolute scale itself indicates the point fixed on the scale$$c.$$ This anomaly arises due to the fixed triple point of water.$$d.$$ We can convert the triple point on kelvin scale to Fahrenheit scale by standard conversion formula from kelvin to degree Fahrenheit.     Formula used:  Only used in sub-question (d)                                     $${{T}_{fahrenheit}}={{T}_{kelvin}}\times \dfrac{9}{5}$$ Complete solution:$$a.$$ As I mentioned in the hint, the triple point must not vary  with any variable parameters. That is the reason why it is fixed in modern calorimetry. We can’t use the melting point or boiling point of water as a standard fixed point because they can be varied by change in pressure. Triple point is a temperature which doesn’t vary with pressure.$$b.$$ As mentioned in the question there are only 2 fixed points in absolute scale. Triple point and absolute zero. i.e, $$0K$$.$$c.$$ The relation between temperature measures on absolute scale and Celsius scale is given as   $${{t}_{\begin{smallmatrix}  c \\   \end{smallmatrix}}}=T-273.15$$. We use $$273.15$$  instead of $$273.16$$, because we reduce the triple point of water ($$0.01{}^\circ C$$) from $$273.16$$(absolute zero). That is $$273.16-0.01=273.15$$.$$d.$$ We can use the formula to measure triple point of water on absolute scale if unit interval is as of Fahrenheit scale as,               $${{T}_{fahrenheit}}={{T}_{kelvin}}\times \dfrac{9}{5}$$   Triple point on absolute scale is, $${{T}_{kelvin}}=273.15K$$    $$\Rightarrow {{T}_{fahrenheit}}=273.15\times \dfrac{9}{5}=491.69$$Note: While going through this problem we must be aware of conversion of one scale to another. The relation between Absolute temperature and triple point, i.e., $${{T}_{absolute}}=273.16-T.P.$$. Also, we must keep in mind the dependence of temperature and other parameters like pressure on triple because triple point is a single combination of pressure and temperature where all the 3 states of water can coexist. It must not be varied with change in pressure.