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Q.
Two absolute scale $A$ and $B$ have triple points of water defined to be at $200 \,A$ and $350\, B$. The relation between $T_A$ and $T_B$ is
Thermal Properties of Matter
Solution:
Here, triple point of water on scale $A = 200A$
Triple point of water on scale $B = 350B$
$200A = 350B - 273.16 \,K$ (given)
or $A=\frac{273.16}{200}K$ and $B=\frac{273.16}{350}K$
If $T_{A}$ and $T_{B}$ represent the triple point of water on scales $A$ and $B$, then
$\frac{273.16}{200}T_{A}=\frac{273.16}{350}T_{B}$ or $\frac{T_{A}}{T_{B}}=\frac{200}{350}$
or $T_{A}=\frac{4}{7}T_{B}$