11.5 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

1.250×105Pa             
  

 0.200×105Pa

Normal melting point of
sulphur

1.797×105Pa                
 

0.28×105Pa

(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?

Let the normal melting point of sulphur = T1

At this temperature, pressure in thermometer A, P1 = 1.797 × 105 Pa

According to Charles’ law,

PAT=P1T1

 T1=P1TPA=1.797×105×273.161.250×105= 392.69 K

Therefore, the absolute temperature of the normal melting point of sulphur as read by thermometer A is 392.69 K.

At triple point 273.16 K, the pressure in thermometer B, PB = 0.200 × 105 Pa

At temperature T1, the pressure in thermometer B, P2 = 0.287 × 105 Pa

According to Charles’ law,

PBT=P1T10.200×105273.16=0.287×105T1 T1=0.287×1050.200×105×273.16=391.98K

 

Therefore, the absolute temperature of the normal melting point of sulphur as read by thermometer B is 391.98 K.

The oxygen and hydrogen gas present in thermometers A and B respectively are not perfect ideal gases. 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 perfect ideal gases.