- 2073 Bhadra · 6 marks
New temperature scale N conversion
Short answer
Freezing point 100°N (0°C), boiling point 400°N (100°C) gives a linear scale with slope 3°N per °C. Conversion: C = (N - 100) / 3. A 50°C temperature rise corresponds to an increase of 150°N.
On a new scale N of temperature the freezing point of ice and boiling point of water are 100°N and 400°N respectively. Derive an expression to convert a temperature reading on N scale to °C scale. Also determine the change in N scale when the temperature of a system increases by 50°C.
Given: ice point = 100 °N (0 °C), steam point = 400 °N (100 °C). Both scales are linear.
Conversion expression
N = a + b·C. At C = 0, N = 100 so a = 100. At C = 100, N = 400, so b = (400 − 100)/(100 − 0) = 3 °N per °C.
N = 100 + 3 C
C = (N − 100)/3
Equivalent form: (N − 100)/(400 − 100) = (C − 0)/(100 − 0).
Change in N when temperature rises by 50 °C
ΔN = 3 × ΔC = 3 × 50 = 150
Answer: C = (N − 100)/3; the N-scale reading increases by 150 °N.
✓ Answer checked by Claude Opus 5.5 (high effort)
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