Question

The resistance of a platinum wire of a platinum resistance thermometer at the ice point is $5\Omega$ and at steam point is $5.4\Omega$. When the thermometer is inserted in a hot bath, the resistance of the platinum wire is $6.2\Omega$. Find the temperature of the hot bath.

• A. ${300}^{\circ }C$
• B. ${30}^{\circ }C$
• C. ${3000}^{\circ }C$
• D. $300K$

Answer 1

Answer: (A)

${300}^{\circ }C$

Given,

Resistance of platinum wire at ice point, $R_0=5\Omega$

Resistance of platinum wire at hot bath $R_H=6.2\Omega$

Temperature at hot bath $T_H=?$

We have,

$R_T=R_0[1+\alpha (T-T_0\left)\right]$

$⟹R_{100}=R_0[1+\alpha (T_{100}-T_0\left)\right]$

$⟹5.4=5[1+\alpha (100-0\left)\right]$

$⟹\frac{5.4}{5}-1=100\alpha$

$⟹\alpha =\frac{1}{1250}{}^0{C}^{-1}$

Also,

$R_H=R_0[1+\alpha (T_H-T_0\left)\right]$

That is,

$6.2=5[1+\frac{1}{1250}(T_H-0\left)\right]$

$\frac{6.2}{5}-1=\frac{1}{1250}\times T_H$

$⟹T_H={300}^{0}C$