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} and *T*_{B}?

#### Solution 1

Triple point of water on absolute scaleA, *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 = 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= 273.15/350`

*T*_{A} is triple point of water on scale A.

*T*_{B} is triple point of water on scale B.

`:. (273.15)/200 xx T_A = (273.15)/350 xx T_B`

`T_A = 200/350 T_B`

Therefore, the ratio *T*_{A} : *T*_{B }is given as 4 : 7.

#### Solution 2

As we know, triple point of water on absolute scale = 273.16 K, Size of one degree of kelvin scale on absolute scale A

`= 273.16/200`

Value of temperature `T_A` on absolute scale A

`= 273.16/200 T_A`

Value of temperature `T_B` on absolute scale B

`= 273.16/350 T_B`

Since `T_A " and " T_B` represent the same temperature

`:. 273.16/200T_A = 273.16/350T_B`

or ` T_A = 200/350T_B = 4/7 T_B`