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 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?

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Solution

(a) The triple point of water has a unique value of 273.16 K. At particular values of volume and pressure, the triple point of water is always 273.16 K. The melting point of ice and boiling point of water do not have particular values because these points depend on pressure and temperature.

(b) The absolute zero or 0 K is the other fixed point on the Kelvin absolute scale.

(c) The temperature 273.16 K is the triple point of water. It is not the melting point of ice. The temperature 0°C on Celsius scale is the melting point of ice. Its corresponding value on Kelvin scale is 273.15 K.

Hence, absolute temperature (Kelvin scale) T, is related to temperature t_c, on Celsius scale as:

t_c = T – 273.15

(d) Let T_F be the temperature on Fahrenheit scale and T_K be the temperature on absolute scale. Both the temperatures can be related as:

Let T_F1 be the temperature on Fahrenheit scale and T_K1 be the temperature on absolute scale. Both the temperatures can be related as:

It is given that:

T_K1 – T_K = 1 K

Subtracting equation (i) from equation (ii), we get:

Triple point of water = 273.16 K

∴Triple point of water on absolute scale = = 491.69

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Similar questions

Q. Why is it 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)?

Q. 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?

Q. Two absolute scales

A

and

B

have triple points of water defined to be

200 A

and

300 B

. A temperature is measured on these scales as

T_{A}

and

T_{B}

What is the relation between

T_{A}

and

T_{B}

? Given, that triple point of water as

273.16 K

Given that P, V and T stand for vapour pressure, volume and temperature, an ideal gas obeys the law -PV α T. If the volume is kept constant, P α T. With decreasing temperature the vapour pressure drops, until P = 0 at some temperature T₀. Since P cannot be less than zero, or negative, T₀naturally becomes the lowest temperature that we can reach, and can be used as a "natural” lower fixed point while constructing a temperature scale. This is the "absolute zero”, which in the Celsius scale is - 273.15⁰C.

To construct an absolute temperature scale , where the absolute zero is naturally 0. Let us choose the triple point of mercury (-38.8⁰C, at 0.2 mPa) as our upper fixed point, and give assign it a value 100. What will be the boiling point of water on this scale?

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