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 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 is unique ( 273.16 K ) because it occurs only at a certain set of values of temperature and pressure. Therefore, it is a standard fixed point in thermometry.

The melting point of ice and boiling point of water change with the change in pressure and it is also change if some impurities are dissolved in water.

Thus, melting point of ice and boiling point of water are not fixed.

b)

Different book says that there are basically two fixed points on the Kelvin scale as one fixed point is 273.16 K and other is 373.16 K. But there is only one fixed point exist on the Kelvin scale as triple point of the water.

c)

The temperature 0 °C on Celsius scale represents the melting point of ice. It is not the triple point of water. The corresponding melting point of ice on Kelvin scale is 273.15 K.

Thus, the absolute temperature Ton Kelvin scale is related to Celsius scale as 273.15 K.

d)

The triple point of water is 273.16 K.

The Fahrenheit scale is related to Kelvin scale is given as,

T F −32 180 = T K −273.15 100 (1)

Where, the temperature on Fahrenheit scale is T F and the temperature on absolute scale is T K .

For another set of the readings the Fahrenheit scale is related to Kelvin scale is given as,

T ′ F −32 180 = T ′ K −273.15 100 (2)

Where, the temperature on Fahrenheit scale is T ′ F and the temperature on absolute scale is T ′ K .

By subtracting equation (1) and (2), we get

T ′ F − T F 180 = T ′ K − T K 100 T ′ F − T F = 18 10 ( T ′ K − T K )

By substituting the given value in the above relation, we get

T ′ F − T F = 18 10 ×1 = 9 5

Now, the temperature of the triple point on the new scale is given as

T ′ =273.16× 9 5 =491.69 K

Thus, the temperature of the triple point on the new scale is 491.69 K.

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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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