Question: Figure 18-24 shows three linear temperature scales, with the freezing and boiling points of water indicated. Rank the three scales according to the size of one degree on them, greatest first.

From the Figure 18-24, on a linear temperature scale

• i)The freezing point$FB=-50°C$.
• ii)The boiling point$BP=150°C$ .

On linear temperature scale Y

• i)The freezing point$FP=-140°C$.
• ii)The boiling point$BP=120°C$.

In linear temperature scale Z

• i)The freezing point$FB=20°C$ .
• ii) The boiling point $BP=60°C$.

Temperature is a unit used to represent hotness or coolness using any of a number of scales, including Fahrenheit and Celsius. By finding the total number of degrees on the given linear temperature scale and the size of the corresponding linear temperature scale, we can find the ranking of the given three scales according to the size of one degree on them.

Formula:

The total number of degrees on the linear temperature scale, $T=BP-FB$ …(i)
where, BP is the boiling point and FP is the freezing point on the corresponding linear temperature scale.

Using the given values in equation (i), the total number of degrees on the linear temperature scale X is given by:

$$\begin{gathered} T=150-(-50) \\ =200°C \end{gathered}$$

Now, the size of the scale onlinear temperature scale X is given as:
$$\begin{gathered} scaleX=\frac{1°C}{200°C} \\ =5.0\times {10}^{-3} \end{gathered}$$

Similarly, using the given values in equation (i), the total number of degrees on the linear temperature scale Y is given by:

role="math" localid="1663149806918" $$\begin{gathered} T=120-(-140) \\ =260°C \end{gathered}$$

Now, the size of the scale onlinear temperature scale Y is given as:
role="math" localid="1663149625961" $$\begin{gathered} scaleY=\frac{1°C}{260°C} \\ =3.8\times {10}^{-3} \end{gathered}$$

Similarly, using the given values in equation (i), the total number of degrees on the linear temperature scale Z is given by:

$$\begin{gathered} T=60-\left(20\right) \\ =40°C \end{gathered}$$

Now, the size of the scale onlinear temperature scale Y is given as:

$$\begin{gathered} scaleZ=\frac{1°C}{40°C} \\ =25.0\times {10}^{-3} \end{gathered}$$

Therefore, the ranking according to the size of one degree on linear temperature scales X, Y and Z is scale Z > scale X > scale Y .