Question

The resistance of a thermometer is $100\Omega$ at the triple point of water $(273K)$ and is $300\Omega$ at the melting point of gold $(\sim 873K)$. The temperature at which the resistance of the thermometer is $200\Omega$ is

• A. 273 K
• B. 373 K
• C. 473 K
• D. 573 K

Answer 1

Answer: (D)

At $273K$ or $0^{\circ }C$, resistance, $R_0=100\Omega$
At $873K$ or $600^{\circ }C$, resistance $R_{600}=300\Omega$
Now, let at $\theta$ temperature resistance is given $R_0=200\Omega$
$\theta =?$
By the formula, $\theta =\frac{R_{\theta }-R_0}{R_{600}-R_0}\times 600$
$\theta =\frac{200-100}{300-100}\times 600$
$\theta =300^{\circ }C$
$\theta =300+273=573K$