Question

A temperature scale of certain thermometer is given by the relation 

t = a ln p + b 

where a and b are constants and p is the thermometric property of the fluid in the thermometer. If at the ice point and steam point the thermometric properties are found to be 1.5 and 7.5 respectively what will be the temperature corresponding to the thermometric property of 3.5 on Celsius scale.

Answer 1

t = a ln p + b ...(Given)

On Celsius scale :

Ice point = 0°C, and

Steam point = 100°C

\(\therefore\) From given conditions, we have

0 = a ln 1.5 + b ...(i)

and 100 = a ln 7.5 + b ...(ii)

i.e., 0 = a × 0.4054 + b ...(iii)

and 100 = a × 2.015 + b ...(iv)

Subtracting (iii) from (iv), we get

100 = 1.61a 

or a = 62.112

Substituting this value in eqn. (iii), we get

b = – 0.4054 × 62.112= – 25.18 

∴ When p = 3.5 the value of temperature is given b

t = 62.112 ln (3.5) – 25.18= 52.63°C.