How does the mean free path vary with the number density of a gas?

  • A
    Directly proportional
  • B
    Inversely proportional
  • C
    Independent of number density
  • D
    Proportional to the square of number density

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Two ideal gas thermometers $A$ and $B$ use oxygen and hydrogen respectively. The following observations are made:
Temperature Pressure thermometer $A$ Pressure thermometer $B$
Triple-point of water $1.250 \times 10^{5} \; Pa$ $0.200 \times 10^{5} \; Pa$
Normal melting point of sulphur $1.797 \times 10^{5} \; Pa$ $0.287 \times 10^{5} \; Pa$

$(a)$ What is the absolute temperature of the 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?

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