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 $R_t=R_0\left(1+\alpha t\right)$
$\therefore R_{100}=R_0\left(1+\alpha 100\right)$
$\alpha =\frac{R_{100}-R_0}{R_0\times 100}\dots \left(i\right)$
Let the temperature of hot bath be $t{}^{\circ }C$
$R_t=R_0\left(1+\alpha t\right)$;
$\alpha =\frac{R_t-R_0}{R_0\times t}\dots \left(ii\right)$
Equating equations $\left(i\right)$ and $\left(ii\right)$, we get
$t=\frac{R_t-R_0}{R_{100}-R_0}\times 100$
$=\frac{5.5-5}{5.25-5}\times 100$
$=200{}^{\circ }C$