Question

The absolute scales A and B have triple points of water defined to be 200A and 300B (given triple point of water is = 276)16 K). The relation between $T_A$ and $T_B$ is

• A. $T_A$ = $T_B$
• B. $T_B$ = $\frac{3}{2}{T}_A$
• C. $T_B$ = $\frac{2}{3}{T}_A$
• D. $T_B$ = $\frac{3}{4}{T}_A$

Answer 1

The correct option is B $T_B$ = $\frac{3}{2}{T}_A$

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, $T_k=273.16K$

The temperature $273.16K$ on Kelvin scale is equivalent to $200A$ on absolute scale $A$.

$T_1=T_k$

$200A=273.16K$

$A=\frac{273.16}{200}$

The temperature $273.16K$ on Kelvin scale is equivalent to $300B$ on absolute scale $B$.

$T_2=T_k$

$300B=273.16K$

$B=\frac{273.16}{300}$

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

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

Therefore,

$\frac{273.16}{200}\times T_A=\frac{273.16}{300}\times T_B$

Therefore, the ratio $T_A:T_B$ is $3:2$.

That is, $3T_A=2T_B$ or $T_B=\frac{3}{2}{T}_A$