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 × 105 Pa | 0.200 × 105 Pa |
Normal melting point of sulphur | 1.797 × 105 Pa | 0.287 × 105 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 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?
(a) We know that the triple point of water, T0 = 273.16 K.
At this temperature, pressure in thermometer A,
PA = 1.250 × 105 Pa
Let T be the normal melting point of sulphur.
At this temperature, pressure in thermometer A,
P = 1.797 × 105 Pa
According to Charles’ law,
PA/T0 = P/T
∴ T = (PT0)/PA
⇒ T = (1.797×105 Pa × 273.16 K)/(1.250×105 Pa)
⇒ T = 392.69 K
Therefore, the absolute temperature corresponding to the normal melting point of sulphur according to the reading of thermometer A is 392.69 K.
At triple point T0 = 273.16 K, the pressure in thermometer B,
PB = 0.200×105 Pa
At temperature T, the pressure in thermometer B,
P’ = 0.287 × 105 Pa
According to Charles’ law,
PB/T0 = P’/T
⇒ (0.200 × 105 Pa)/(273.16 K)= (0.287 × 105 Pa)/T
∴ T = [(0.287 × 105 Pa)/(0.200 × 105 Pa)] × 273.16 K
⇒ T = 391.98 K
Therefore, the absolute temperature corresponding to the normal melting point of sulphur according to the reading of thermometer B is 391.98 K.
(b) The oxygen and hydrogen gases used in thermometers A and B respectively are not ideal gases. These gases have different physical behaviours. 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 ideal gases and will show same characteristics.
NOTE: Ideal gases are those gases which follow ideal gas equation exactly.