Question

The resistance of the platinum wire of a platinum resistance thermometer at the ice point is $ 5\,\Omega $ and at steam point is $ 5.23\,\Omega $ . When the thermometer is inserted in a hot bath, the resistance of the platinum wire will be $ 5.795\,\Omega $ . Calculate the temperature of the bath.

• A. $ 3.456\,{}^{\circ}C $
• B. $ 34.565\,{}^{\circ}C $
• C. $ 345.65\,{}^{\circ}C $
• D. $ 45.65\,{}^{\circ}C $

Answer 1

Answer: (C)

$R_{0}=5\,\Omega , R_{100}=5.23\, \Omega, R_{t}=5.795\,\Omega $
$\alpha=\frac{R_{100}-R_{0}}{R_{0}\times100}=\frac{R_{t}-R_{0}}{R_{0}\times t}$
$Therefore, t=\frac{R_{t}-R_{0}}{R_{100}-R_{0}}\times100$
$=\left(\frac{5.795-5}{5.23-5}\right)\times100$
$=345.65\,{}^{\circ} C$