Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made : Temperature Pressure Pressure thermometer A thermometer B Triple-point of water 1.250 × 10⁵ Pa 0.200 × 10⁵ Pa Normal melting point 1.797 × 10⁵ Pa 0.287 × 10⁵ Pa of sulphur (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 ?
Given: At triple point of water, pressure in thermometer A is 1.250 × 10 5 Pa and pressure in thermometer B is 0.200 × 10 5 Pa . At normal melting point of sulphur, the pressure in thermometer A is 1.797 × 10 5 Pa and pressure in thermometer B is 0.287 × 10 5 Pa .
a)
The triple point of water is 273.16 K .
According to Charles’ law, the relation is given as,
P A T = P 1 T 1 T 1 = T × P 1 P A
Where, the temperature at triple point of water is T , at triple point of water the pressure in thermometer A is P A , the temperature at normal melting point of sulphur is T 1 and at normal melting point of sulphur pressure in thermometer A is P 1 .
By substituting the given values in the above relation, we get
T 1 = 273.16 × 1.797 × 10 5 1.250 × 10 5 = 392.69 K
Thus, the absolute temperature of the normal melting point of sulphur as reading by thermometer A is 392.69 K .
According to Charles’ law the relation is given as,
P B T = P 2 T 2 T 2 = T × P 2 P B
Where, the temperature at triple point of water is T , at triple point of water the pressure in thermometer B is P B , the temperature at normal melting point of sulphur is T 2 and at normal melting point of sulphur pressure in thermometer B is P 2 .
By substituting the given values in the above relation, we get
T 2 = 273.16 × 0.287 × 10 5 0.200 × 10 5 = 391.98 K
Thus, the absolute temperature of the normal melting point of sulphur as reading by thermometer B is 391.98 K .
b)
The slight difference between the readings of thermometer A and B is due to that the gases oxygen and hydrogen present in thermometer A and B respectively does not behave like an ideal gas.
Under the low pressure, conditions, real gases behave like an ideal gas. So, to reduce the discrepancy in two readings, the experiment should be carried under low pressure conditions.
Given: At triple point of water, pressure in thermometer A is
a)
The triple point of water is
According to Charles’ law, the relation is given as,
Where, the temperature at triple point of water is
By substituting the given values in the above relation, we get
Thus, the absolute temperature of the normal melting point of sulphur as reading by thermometer A is
According to Charles’ law the relation is given as,
Where, the temperature at triple point of water is
By substituting the given values in the above relation, we get
Thus, the absolute temperature of the normal melting point of sulphur as reading by thermometer B is
b)
The slight difference between the readings of thermometer A and B is due to that the gases oxygen and hydrogen present in thermometer A and B respectively does not behave like an ideal gas.
Under the low pressure, conditions, real gases behave like an ideal gas. So, to reduce the discrepancy in two readings, the experiment should be carried under low pressure conditions.
