Question

In a new scale of temperature the lower fixed point is marked as $0$ corresponding to the melting point of substance which is equal to ${25}^{0}C$ and the upper fixed point is marked corresponding to the boiling point of a substance which is equal to ${175}^{0}C$. The total length of scale between the UFP and LFP is divided into $200$ equal parts. Determine the temperature in the new scale when the temperature of substance measured by celsius scale thermometer is ${50}^{0}C$.

Answer 1

Step 1: Given data

In the new scale of temperature,

The lower fixed point (LFP) = Melting Point of substance = $0$ units = ${25}^{0}C$

The upper fixed point (UFP) = Boiling point of a substance = ${175}^{0}C$

The total length of the new scale= $200units$

Step 2: Finding the temperature in the new scale

We know that, $\frac{F-32}{180}=\frac{C-0}{100}$

Here in the new scale of temperature ($N$), $\frac{N-0}{200}=\frac{C-25}{(175-25)}\Rightarrow \frac{N-0}{200}=\frac{C-25}{150}$

$$\begin{gathered} \Rightarrow \frac{N-0}{4}=\frac{C-25}{3} \\ \Rightarrow N=\frac{4C-100}{3} \end{gathered}$$

To determine the temperature in the new scale when the temperature of substance measured by Celsius scale thermometer is ${50}^{0}C$.

$C={50}^{0}C$

Thus, $\Rightarrow N=\frac{4\times 50-100}{3}=\frac{100}{3}=33.{33}^0$

Hence, $33.{33}^0$ is the temperature in the new scale when the temperature of substance measured by Celsius scale thermometer is ${50}^{0}C$.