Question

A new scale for temperature is introduced. One degree temperature difference on the new scale is found to be equal to $\frac{5}{8}{}^{0}C$. Determine the temperature in Celsius scale when the new scale and the Celsius scale shows the same reading. The lower fixed point on the new scale is ${33}^0$degree.

Answer 1

Step 1: Given data

One degree temperature difference on the new scale, $\frac{5}{8}{}^{0}C$

The lower fixed point (LFP) on the new scale is ${33}^0$.

Step 2: Finding the temperature in Celsius scale

$1$ division of the new scale, $\frac{5}{8}{}^{0}C$

Let $T^{0}C$ shows in the new scale, $T$

$0^{0}C={33}^0$

$$\begin{gathered} T=\frac{5}{8}\times \left(T^{0}C\right)+33 \\ T-\frac{5}{8}T=33 \\ \frac{3}{8}T=33 \\ T=\frac{33\times 8}{3}={88}^{0}C \end{gathered}$$

Thus, the temperature in Celsius scale when the new scale and the Celsius scale shows the same reading is ${88}^{0}C$.