Question 2 of 20intermediate🔧 ApplyNumerical2 marks

Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TAT_A and TBT_B?

Correct Answer

The relation between TAT_A and TBT_B is: TA=200350TBT_A = \frac{200}{350} T_B or equivalently TA=47TBT_A = \frac{4}{7} T_B.

For any absolute temperature scale, the triple point of water represents the same physical temperature. On scale A, this is defined as 200 A, and on scale B, it is defined as 350 B.

Since both values represent the same physical temperature, the ratio of temperatures on the two scales remains constant. Therefore, for any temperature measured on both scales:

TATB=200350=47\frac{T_A}{T_B} = \frac{200}{350} = \frac{4}{7}

This gives us the relation: TA=47TBT_A = \frac{4}{7} T_B or TB=74TAT_B = \frac{7}{4} T_A

Exercise: EXERCISES | Q: 10.2 | (Page 22)
For More Understanding

Explanation

This question tests understanding of absolute temperature scales. The triple point of water is a unique fixed point in thermometry. When two different absolute scales define this same physical point with different numerical values (200 A and 350 B), the ratio between the scales is established. Since the triple point is the same physical temperature on both scales, any temperature measured will maintain this ratio. The derivation uses the principle that for the same physical temperature, the ratio of numerical values on two scales equals the ratio of their triple point definitions.

Solution Steps

  1. Step 1: Identify that triple point of water is the same physical temperature on both scales A and B.

  2. Step 2: Set up the ratio: On scale A, triple point = 200 A; On scale B, triple point = 350 B.

  3. Step 3: Since both represent the same physical temperature, the ratio TATB=200350=47\frac{T_A}{T_B} = \frac{200}{350} = \frac{4}{7}.

  4. Step 4: Express the relation as TA=47TBT_A = \frac{4}{7} T_B or TB=74TAT_B = \frac{7}{4} T_A.

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