Question

The resistance of the wire in the platinum resistance thermometer at ice point is $5\Omega$ and at steam point is $5.25\Omega$. When the thermometer is inserted in an unknown hot bath its resistance is found to be $5.5\Omega$. The temperature of the hot bath is?

• A. $100$ ${}^{o}C$
• B. $200$ ${}^{o}C$
• C. $300$ ${}^{o}C$
• D. $350$ ${}^{o}C$

Answer 1

The correct option is B $200$ ${}^{o}C$

Given,

Resistance at ice point,$R_0=5\Omega ,$

Resistance at steam point,$R_{100}=5.25\Omega ,$

Resistance when dip in unknow,$R_0=5\Omega ,R_{100}=5.25\Omega ,R_t=5.5\Omega$
$R_{100}=R_0(1+\alpha 100)$
$\alpha =\frac{R_{100}-R_0}{R_0\times 100}=\frac{5.25-5}{5\times 100}=5\times {10}^{-4}{}^o{C}^{-1}$

Let the temperature of hot bath = $t{}^{o}C$
$R_t=R_0(1+\alpha t)$
$t=\frac{R_t-R_0}{R_o\alpha }=\frac{5.5-5}{5\times (5\times {10}^{-4})}=200{}^{o}C$

Temperature of bath is $200{}^{o}C$