The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 10 Ω and at steam point is 10.46 Ω. When the thermometer is inserted in a hot bath, the resistance of the platinum wire is 11.6 Ω. Calculate the temperature of the bath.

348° C

The correct answer is Option (2) → 348° C

The resistance $R_T$ of a platinum based resistance thermometer is -

$R_T=R_0(1+αT)$

When, $R_T=10.46Ω,R_0=10Ω$ at steam point

$10.46=10(1+α×100)$

$⇒α=\frac{0.046}{100}=0.00046$ per C°

$R_T=11.6Ω$

$11.6=10(1+0.00046×T)$

$0.00046T=0.16$

$T=348° C$