Question

A faulty thermometer who's LFP is $-5^{0}C$ and UFP is ${105}^{0}C$ measures a temperature as ${80}^{0}C$. What is the correct temperature?

Answer 1

Step 1: Given data:

$$\begin{gathered} LFP=-5^{0}C \\ UFP={105}^{0}C \end{gathered}$$

Temperature measured is ${80}^{0}C$.

Step 2: Finding the correct temperature:

We know that,

,${\left(\frac{S-LFP}{UFP-LFP}\right)}_{faultyscale}={\left(\frac{S-LFP}{UFP-LFP}\right)}_{correctscale}$

Where, $S$ is the reading on the faulty thermometer.

$LFP$ is the lower fixed point of the thermometer.

$UFP$ is the upper fixed point of the thermometer.

Substituting the know values,

$\Rightarrow \left(\frac{80-(-5)}{105-(-5)}\right)=\left(\frac{S-0}{100-0}\right)$

$\Rightarrow \frac{S}{100}=\frac{85}{110}$

$\Rightarrow S=\frac{85}{110}\times 100$

$\Rightarrow S=77.{27}^{0}C$

Thus, the correct temperature is $77.{27}^{0}C$.