The graph between two temperature scales A and B is shown in...

The graph between two temperature scales $A$ and $B$ is shown in Fig. 10.16 between upper fixed point and lower fixed point there are 150 equal division on scale $A$ and 100 on scale $B$. The relationship for conversion between the two scales is given by (FIGURE CAN'T COPY) Fig. 10.16 (A) $\frac{t_A-180}{100}=\frac{t_B}{150}$ (B) $\frac{t_A-30}{150}=\frac{t_B}{100}$ (C) $\frac{t_B-180}{150}=\frac{t_A}{100}$ (D) $\frac{t_B-40}{100}=\frac{t_A}{180}$

The graph between two temperature scales $A$ and $B$ is shown in Fig. 10.16 between upper fixed point and lower fixed point there are 150 equal division on scale $A$ and 100 on scale $B$. The relationship for conversion between the two scales is given by
(FIGURE CAN'T COPY)
Fig. 10.16
(A) $\frac{t_A-180}{100}=\frac{t_B}{150}$
(B) $\frac{t_A-30}{150}=\frac{t_B}{100}$
(C) $\frac{t_B-180}{150}=\frac{t_A}{100}$
(D) $\frac{t_B-40}{100}=\frac{t_A}{180}$

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Key Concepts

Temperature Scales

Temperature scales are systems for measuring thermal energy where particular reference points (often called fixed points) such as the melting or boiling point of a substance are defined. These scales enable consistent and quantitative comparisons of temperature between different systems or experiments.

Linear Relationships in Scale Conversion

Converting between two temperature scales typically involves a linear (affine) relationship, which accounts for differences in the zero point and the scale interval size. This linear transformation ensures that equal increments in one scale correspond to equal increments in the other.

Fixed Points and Calibration

Fixed points serve as the calibration marks for temperature scales. By assigning specific numerical values to these universal reference temperatures, a scale can be standardized, allowing for accurate conversion and reproducibility across different measurement systems.

Equal Division of Intervals

The division of the interval between fixed points into equal parts is fundamental to creating a uniform scale. This equal spacing underpins the linear relationship between scales, as it allows different temperature measuring systems to be directly related by comparing their division counts over the same temperature range.

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