Two ideal gas thermometer `A` and `B` use oxygen and hydrogen respectively . The following observations are made:
Temperature, Pressure therometer A, Pressure therometer B
Triple point of water, `1.250xx10^(5)Pa`, `0.200xx10^(5)Pa`
Normal melting point of sulphur, ` 1.797xx10^(5)Pa`, `0.287xx10^(5)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 for the slightly different answers from `A` and `B` ? (The thermometers are not faulty). what further procedure is needed in the experiment to reduce the discrepancy between the two readings.

Explanation

(a) Let `T_A` be the normal melting point of sulphur as measured from thermometer A.
Triple point of water = `T_(Tr) = 273.16 K`
We know that for constant volume thermometer
`(P_1)/(T_1) = P_2/T_2`
For thermometer A
` T_A = T_(Tr) xx (P_A)/(P_(Tr) ) `
`T_A = 273.16 xx (1.797 xx 10^5 Pa)/(1.250 xx 10^5 Pa)`
= 392.69 K
Similarly for thermometer B, let the normal melting point of sulphur be `T_B`
`(P_(Tr) )/(T_(Tr) ) = (P_B)/(T_B)`
` T_B = T_(Tr) xx (P_B)/(P_(Tr ) ) `
` T_B = 273.16 xx (0.287 xx 10^5 Pa)/(0.200 xx 10^5 Pa) = 391.98K`
(b) The discrepancy arises because the gases oxygen and hydrogen are not perfectly ideal at the given temperature and pressure conditions. To reduce the discrepancy, readings should be taken for lower pressures as the gases approach ideal gas behaviour at low pressures.