Question

Two absolute scales A and B have triple points of water defined to be 200 A and 300 B (given triple point of water is = 276.16 K). The relation between TA and TB is

Answer 1

Given :-

Triple point of water on absolute scale B = 300 B

Triple point of water on absolute scale A = 200 A

Triple point of water on Kelvin scale = 273.15 K

To Find :-

The relation between TA and TB

Solution :-

We know that,

• $\sf T_1 =$ Triple point of water on absolute scale A
• $\sf T_2=$ Triple point of water on absolute scale B
• $\sf T_K=$ Triple point of water on Kelvin scale

According to the question,

276.16 K on the Kelvin scale is equivalent to 200 A on absolute scale A$\implies \sf T_1=T_K$

Substituting their values,

$\sf 200 \ A = 276.16 \ K$

Thus,

$\sf A=\dfrac{276.16}{200}$

276.16 K on the Kelvin scale is equivalent to 300 B on absolute scale B

$\sf \implies \sf T_2=T_K$

Substituting their values,

$\sf 300\ B = 276.16 \ K$

Thus,

$\sf B=\dfrac{276.16}{300}$

Let, $\sf T_A$ and $\sf T_B$ be the triple point of water on scale A and B respectively.

Thus, we have,

$\sf \dfrac{276.16}{200} \times T_A=\dfrac{276.16}{300} \times T_B$

Therefore,

$\sf \bf{T_A : T_B = 2 : 3}$

Answer 2

We know that,

\sf T_1 =T

1

= Triple point of water on absolute scale A

\sf T_2=T

2

= Triple point of water on absolute scale B

\sf T_K=T

K

= Triple point of water on Kelvin scale

According to the question,

276.16 K on the Kelvin scale is equivalent to 200 A on absolute scale A\implies \sf T_1=T_K⟹T

1

=T

K

Substituting their values,

\sf 200 \ A = 276.16 \ K200 A=276.16 K

Thus,

\sf A=\dfrac{276.16}{200}A=

200

276.16

276.16 K on the Kelvin scale is equivalent to 300 B on absolute scale B

\sf \implies \sf T_2=T_K⟹T

2

=T

K

Substituting their values,

\sf 300\ B = 276.16 \ K300 B=276.16 K

Thus,

\sf B=\dfrac{276.16}{300}B=

300

276.16

Let, \sf T_AT

A

and \sf T_BT

B

be the triple point of water on scale A and B respectively.

Thus, we have,

\sf \dfrac{276.16}{200} \times T_A=\dfrac{276.16}{300} \times T_B

200

276.16

×T

A

=

300

276.16

×T

B

Therefore,

\sf \bf{T_A : T_B = 2 : 3}T

A

:T

B

=2:3