Q5 of 26 Page 294

Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made:


















Temperature



Pressure thermometer A



Pressure


thermometer B



Triple-point of water



1.250 × 105 Pa



0.200 × 105 Pa



Normal melting point of sulphur



1.797 × 105 Pa



0.287 × 105 Pa



(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers A and B ?


(b) What do you think is the reason behind the slight difference in answers of thermometers A and B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?

(a) We know that the triple point of water, T0 = 273.16 K.


At this temperature, pressure in thermometer A,


PA = 1.250 × 105 Pa


Let T be the normal melting point of sulphur.


At this temperature, pressure in thermometer A,


P = 1.797 × 105 Pa


According to Charles’ law,


PA/T0 = P/T


∴ T = (PT0)/PA


⇒ T = (1.797×105 Pa × 273.16 K)/(1.250×105 Pa)


⇒ T = 392.69 K


Therefore, the absolute temperature corresponding to the normal melting point of sulphur according to the reading of thermometer A is 392.69 K.


At triple point T0 = 273.16 K, the pressure in thermometer B,


PB = 0.200×105 Pa


At temperature T, the pressure in thermometer B,


P’ = 0.287 × 105 Pa


According to Charles’ law,


PB/T0 = P’/T


⇒ (0.200 × 105 Pa)/(273.16 K)= (0.287 × 105 Pa)/T


∴ T = [(0.287 × 105 Pa)/(0.200 × 105 Pa)] × 273.16 K


⇒ T = 391.98 K


Therefore, the absolute temperature corresponding to the normal melting point of sulphur according to the reading of thermometer B is 391.98 K.


(b) The oxygen and hydrogen gases used in thermometers A and B respectively are not ideal gases. These gases have different physical behaviours. Hence, there is a slight difference between the readings of thermometers A and B. To reduce the discrepancy between the two readings, the experiment should be carried under low pressure conditions. At low pressure, these gases behave as ideal gases and will show same characteristics.


NOTE: Ideal gases are those gases which follow ideal gas equation exactly.


More from this chapter

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3

The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:

R = Ro [1 + α(T – To)]


The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?

 4

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?

 6

A steel tape 1m long is correctly calibrated for a temperature of 27.0°C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10–5 K–1.

 7

A large steel wheel is to be fitted on to a shaft of the same material. At 27°C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: αsteel = 1.20 × 10–5 K–1.