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. $100\,{}^{\circ}C$
• B. $200\,{}^{\circ}C$
• C. $300\,{}^{\circ}C$
• D. $350\,{}^{\circ}C$

Answer 1

Answer: (B)

Here, $R_{0}=5\,\Omega$, $R_{100}=5.25\,\Omega$, $R_{t}=5.5\,\Omega$
As $R_{t}=R_{0}\left(1+\alpha t\right)$
$\therefore R_{100}=R_{0}\left(1+\alpha 100\right)$
$\alpha=\frac{R_{100}-R_{0}}{R_{0} \times 100}\quad\ldots\left(i\right)$
Let the temperature of hot bath be $t\,{}^{\circ}C$
$R_{t}=R_{0}\left(1+\alpha t\right)$;
$\alpha=\frac{R_{t}-R_{0}}{R_{0} \times t}\quad\ldots\left(ii\right)$
Equating equations $\left(i\right)$ and $\left(ii\right)$, we get
$t=\frac{R_{t}-R_{0}}{R_{100}-R_{0}} \times 100$
$=\frac{5.5-5}{5.25-5}\times 100$
$=200\,{}^{\circ}C$