Ncert Exercises & Solutions

The graph between two temperature scales A and B is shown in the figure. Between upper fixed and lower fixed points, there are 150 equal divisions on scale A and 100 on scale B. The relationship for conversion between the two scales is given by

1. $\frac{t_{A} - 180}{100} = \frac{t_{B}}{150}$

2. $\frac{t_{A} - 30}{150} = \frac{t_{B}}{100}$

3. $\frac{t_{B} - 180}{150} = \frac{t_{A}}{100}$

4. $\frac{t_{B} - 40}{100} = \frac{t_{A}}{180}$

(2) Hint: Use the concept of conversion of scales.

Step 1: Find the lowest and highest points of the scales.

It is clear from the graph that the lowest point for scale A is 30° and the lowest point for scale B 0°. The highest point for scale A is 180° and for scale, B is 100°.

Step 2: Use the conversion formula.

Hence, the correct relation is:

$\frac{t_{A} - {(L F P)}_{A}}{{(U F P)}_{A} - {(L F P)}_{A}} = \frac{t_{B} - {(L F P)}_{B}}{{(U F P)}_{B} - {(L F P)}_{B}}$

$\Rightarrow \frac{t_{A} - 30}{180 - 30} = \frac{t_{B} - 0}{100 - 0}$

$\Rightarrow \frac{t_{A} - 30}{150} = \frac{t_{B}}{100}$

where LFP

$\overset{}{\to}$ Lower fixed point

UFP

$\overset{}{\to}$ Upper fixed point

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