Question
Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation betweenTA and TB?
Solution
Triple point of water on absolute scale A, T1 = 200 A
Triple point of water on absolute scale B, T2 = 350 B
Triple point of water on Kelvin scale, TK = 273.15 K
The temperature 273.15 K on Kelvin scale is equivalent to 200 A on absolute scale A.
T1 = TK
200 A = 273.15 K
∴ A = 273.15/200
The temperature 273.15 K on Kelvin scale is equivalent to 350 B on absolute scale B.
T2 = TK
350 B = 273.15
∴ B = 273.15/350
TA is triple point of water on scale A.
TB is triple point of water on scale B.
∴ 273.15/200 × TA = 273.15/350 × TB
Therefore, the ratio TA : TB is given as 4 : 7
Triple point of water on absolute scale B, T2 = 350 B
Triple point of water on Kelvin scale, TK = 273.15 K
The temperature 273.15 K on Kelvin scale is equivalent to 200 A on absolute scale A.
T1 = TK
200 A = 273.15 K
∴ A = 273.15/200
The temperature 273.15 K on Kelvin scale is equivalent to 350 B on absolute scale B.
T2 = TK
350 B = 273.15
∴ B = 273.15/350
TA is triple point of water on scale A.
TB is triple point of water on scale B.
∴ 273.15/200 × TA = 273.15/350 × TB
Therefore, the ratio TA : TB is given as 4 : 7
