Question

Two absolute scale A and B have triple points of water defined to be at 200 A an 350 B. The relation between $T_A$ and $T_B$ is

• A. $T_A=\frac{4}{7}{T}_B$
• B. $T_B=\frac{4}{7}{T}_A$
• C. $T_A=\frac{2}{\overline{7}}{T}_B$
• D. $T_B=\frac{2}{7}{T}_A$

Answer 1

The correct option is A $T_A=\frac{4}{7}{T}_B$

Triple point of water on absolute scale A $T_1=200A$

Triple point of water on absolute scale, B $T_2=350B$

Triple point of water on kelvin scale $T_k=273.15K$

The temperature $273.15K$ on Kelvin scale is equivalent to $200$A on absolute scale

$T_1=T_k$

$200A=273.15K$

$\therefore A=273.15/200$

The temperature $273.15k$ on Kelvin is equivalent to $350B$ on absolute scale.

$T_2=T_k$

$350B=273.15$

$\therefore B=273.15/350$

$T_A$ is triple point of water on scale $A$.

$T_B$ is triple point of water on scale $B$.

$\therefore \frac{273}{200}\times T_A=\frac{273.15}{350}\times T_B$

Therefore the ratio $T_A=T_B$ is given as $4:7$