Question

Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between \(T_A \space and \space T_B\) ?

Answer 1

Triple point of water on absolute scale A, \(T_1\) = 200 A 
Triple point of water on absolute scale B, \(T_2\) = 350 B 
Triple point of water on Kelvin scale, \(T_K\) = 273.15 K 
The temperature 273.15 K on Kelvin scale is equivalent to 200 A on absolute scale A.
\(T_1 = T_K\)
200 A = 273.15 K
∴ A = \(\frac{273.15}{200}\)

The temperature 273.15 K on Kelvin scale is equivalent to 350 B on absolute scale B.
\(T_2 = T_K\)
350 B = 273.15
∴ B = \(\frac{273.15}{350}\)

\(T_A\) is triple point of water on scale A.
\(T_B\) is triple point of water on scale B.

∴ \(\frac{273.15}{200}\) x \(T_A\) = \(\frac{273.15}{350}\) x \(T_B\)

\(T_A = \frac{200}{350} T_B\)

Therefore, the ratio \(T_A : T_B\) is given as 4 : 7.