- 2072 Magh · 6 marks
Scale N: reading at 150°C, equal reading
Short answer
Linear relation N = 100 + 3C. At 150°C, N = 550°N. Setting N = C gives C = -50; both scales read the same at -50°.
A new scale N of temperature is devised in such a way that the freezing point of ice is 100°N and boiling point is 400°N. What is the temperature reading on this new scale when the temperature is 150°C? At what temperature, both the celsius and new temperature scale reading would be the same?
Given: ice point 100 °N (0 °C) and steam point 400 °N (100 °C), linear scale.
Relation: (N − 100)/(400 − 100) = C/100
N = 100 + 3C
(a) Reading at 150 °C
N = 100 + 3(150) = 100 + 450 = 550 °N
(b) Temperature where both readings are equal
Put N = C:
C = 100 + 3C
−2C = 100
C = −50
Answer: 150 °C = 550 °N; both scales read the same at −50° (−50 °C = −50 °N).
Check: N = 100 + 3(−50) = −50. Correct.
✓ Answer checked by Claude Opus 5.5 (high effort)
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