Question

The resistance of a thermometer is $100\, \Omega$ at the triple point of water $(273\, K )$ and is $300\, \Omega$ at the melting point of gold $(\sim 873\, K )$. 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 $273\, K$ or $0^{\circ} C$, resistance, $R_{0}=100\, \Omega$
At $873\, K$ 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, $\theta=\frac{R_{\theta}-R_{0}}{R_{600}-R_{0}} \times 600$
$\theta =\frac{200-100}{300-100} \times 600$
$\theta =300^{\circ} C$
$\theta =300+273=573\, K$