Question

A faulty thermometer has its fixed points marked as ${10}^o$ and ${90}^o$. The temperature of a body as measured by the faulty thermometer si ${61}^o$. Find the correct temperature of the body on celsius scale.

Answer 1

Let ${\theta }_0$ be the lower fixed point of the faulty thermometer and 'n' be the number of divisions between its lower and the upper fixed points. If a temperature C on celsius scale corresponds to temperature $\theta$ on the scale of faulty thermometer, then
$\frac{C}{100}=\frac{\theta -{\theta }_0}{n}$

Here, ${\theta }_0={10}^o,n=90-10=80$ and $\theta ={61}^o$
Therefore, the equation becomes
$\frac{C}{100}=\frac{61-10}{90-10}$

$C=\frac{56}{80}\times 100$

$C={63.75}^{o}C$