---
title: "New temperature scale N conversion"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 1
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:new-scale-n-temperature-conversion"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/new-scale-n-temperature-conversion
site: BCT Engineering
---

# New temperature scale N conversion

Fundamental of Thermodynamics & Heat Transfer · Chapter 1: Introduction

- Asked in: 2073 Bhadra, 6 marks
- Video: [Temperature Scales  | Basic Thermodynamics | Physics](https://www.youtube.com/watch?v=XtYH6tnCIbk) — Engineering Xplained
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/new-scale-n-temperature-conversion
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-1

## Question

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.

## 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.

## Answer

**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.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Ice point is 100 °N and steam point is 400 °N. What is the slope b in N = a + bC?
   A. 3 °N per °C
   B. 4 °N per °C
   C. 0.33 °N per °C
   D. 300 °N per °C
   Answer: A. b = (400 - 100)/(100 - 0) = 3 °N per °C. (Key point: Linear scale relation)

2. Which expression converts N to Celsius?
   A. C = 3(N - 100)
   B. C = (N + 100)/3
   C. C = N - 100
   D. C = (N - 100)/3
   Answer: D. From N = 100 + 3C, solving for C gives C = (N - 100)/3. (Key point: Conversion expression)

3. A system's temperature increases by 50 °C. What is the increase on the N scale?
   A. 50 °N
   B. 150 °N
   C. 250 °N
   D. 16.7 °N
   Answer: B. A change uses only the slope: dN = 3 x 50 = 150 °N, with no offset of 100. (Key point: Temperature change)

4. Why is a = 100 in N = a + bC?
   A. Because the slope is 100
   B. Because the steam point is 100 °C
   C. Because at C = 0 the reading N is 100
   D. Because both scales read the same at 100
   Answer: C. At the ice point C = 0 and N = 100, so a = 100. (Key point: Constant a)

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