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.