Question

The temperature t on a thermometric scale is defined in terms of a property K by the relation

t = a ln K + b 

Where a and b are constants.

The values of K are found to be 1.83 and 6.78 at the ice point and the steam point, the temperatures of which are assigned the numbers 0 and 100 respectively. 

Determine the temperature corresponding to a reading of K equal to 2.42 on the thermometer.

Answer 1

t = a ln x + b

0 = a ln 1.83 + b    … (i)

100 = a ln 6.78 + b   … (ii)

Equation {(ii) – (i)} gives