Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TA and TB?
Triple point of water on absolute scaleA, T1 = 200 A
Triple point of water on absolute scale B, T2 = 350 B
Triple point of water on Kelvin scale, TK = 273.15 K
The temperature 273.15 K on Kelvin scale is equivalent to 200 A on absolute scale A.
T1 = TK
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.
T2 = TK
350 B = 273.15
TA is triple point of water on scale A.
TB 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 TA : TB is given as 4 : 7.
As we know, triple point of water on absolute scale = 273.16 K, Size of one degree of kelvin scale on absolute scale A
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`