Two ideal gas thermometers A and B use ...

Thermal Properties of Matter

Question : 5 of 22

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

Temperature	Pressure
	thermometer A	thermometer B
Triple-point of water	$1.250 \times 10^5 \text{ Pa}$	$0.200 \times 10^5 \text{ Pa}$
Normal melting point of sulphur	$1.797 \times 10^5 \text{ Pa}$	$0.287 \times 10^5 \text{ Pa}$

(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 slightly 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?

Solution:

Let T be the melting point of sulphur.

The triple point of water,

T_{tr}=273.16 \text{ K}

For thermometer

A : P_{tr}=1.25 \times 10^{5} \text{ Pa}

P=1.797 \times 10^{5} \text{ Pa}

\therefore T_{A}= \frac{P}{P_{tr}} \times t_{r}

= \frac{1.797 \times 10^{5}}{1.250 \times 10^{5}} \times 273.16

=392.69 \text{ K}

For thermometer

B : P_{tr}=0.200 \times 10^{5} \text{ Pa}

P=0.287 \times 10^{5} \text{ Pa}

T_{B}= \frac{P}{P_{tr}} \times T_{tr}

= \frac{0.287 \times 10^{5}}{0.200 \times 10^{5}} \times 273.16

=391.98 \text{ K}

(b) The discrepancy arises because the gases are not perfectly ideal. To reduce the discrepancy, readings should be taken at lower pressure as in that case, the gases approach to the ideal gas behaviour.

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