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?

(N/A) For thermometer $A$:
At triple point of water,$T = 273.16 \; K$,$P_A = 1.250 \times 10^{5} \; Pa$.
At melting point of sulphur,$P_1 = 1.797 \times 10^{5} \; Pa$.
Using Charles' Law,$T_1 = (P_1 / P_A) \times 273.16 = (1.797 / 1.250) \times 273.16 = 392.69 \; K$.
For thermometer $B$:
At triple point of water,$T = 273.16 \; K$,$P_B = 0.200 \times 10^{5} \; Pa$.
At melting point of sulphur,$P_2 = 0.287 \times 10^{5} \; Pa$.
Using Charles' Law,$T_1 = (P_2 / P_B) \times 273.16 = (0.287 / 0.200) \times 273.16 = 391.98 \; K$.
$(b)$ The gases oxygen and hydrogen are not perfectly ideal. The discrepancy arises because real gases deviate from ideal gas behavior. To reduce the discrepancy,the experiment should be performed at lower pressures,where gases behave more like ideal gases.